Numeric.Signal:interpolate from hsignal-0.2.7.1

Percentage Accurate: 79.6% → 93.2%

Time: 10.5s

Alternatives: 25

Speedup: 0.4×

Specification

Math

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

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: 79.6% accurate, 1.0× speedup

Math

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

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: 93.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-11}:\\ \;\;\;\;-1 \cdot \frac{t \cdot \left(z - y\right)}{a - z} + x \cdot \left(\left(1 + \frac{z}{a - z}\right) - \frac{y}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (* (- x t) (/ (- z y) (- a z))))))
  (if (<= t -4.2e+96)
    t_1
    (if (<= t 7.5e-11)
      (+
       (* -1.0 (/ (* t (- z y)) (- a z)))
       (* x (- (+ 1.0 (/ z (- a z))) (/ y (- a z)))))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((x - t) * ((z - y) / (a - z)));
	double tmp;
	if (t <= -4.2e+96) {
		tmp = t_1;
	} else if (t <= 7.5e-11) {
		tmp = (-1.0 * ((t * (z - y)) / (a - z))) + (x * ((1.0 + (z / (a - z))) - (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 + ((x - t) * ((z - y) / (a - z)))
    if (t <= (-4.2d+96)) then
        tmp = t_1
    else if (t <= 7.5d-11) then
        tmp = ((-1.0d0) * ((t * (z - y)) / (a - z))) + (x * ((1.0d0 + (z / (a - z))) - (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 + ((x - t) * ((z - y) / (a - z)));
	double tmp;
	if (t <= -4.2e+96) {
		tmp = t_1;
	} else if (t <= 7.5e-11) {
		tmp = (-1.0 * ((t * (z - y)) / (a - z))) + (x * ((1.0 + (z / (a - z))) - (y / (a - z))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((x - t) * ((z - y) / (a - z)))
	tmp = 0
	if t <= -4.2e+96:
		tmp = t_1
	elif t <= 7.5e-11:
		tmp = (-1.0 * ((t * (z - y)) / (a - z))) + (x * ((1.0 + (z / (a - z))) - (y / (a - z))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / Float64(a - z))))
	tmp = 0.0
	if (t <= -4.2e+96)
		tmp = t_1;
	elseif (t <= 7.5e-11)
		tmp = Float64(Float64(-1.0 * Float64(Float64(t * Float64(z - y)) / Float64(a - z))) + Float64(x * Float64(Float64(1.0 + Float64(z / Float64(a - z))) - Float64(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 + ((x - t) * ((z - y) / (a - z)));
	tmp = 0.0;
	if (t <= -4.2e+96)
		tmp = t_1;
	elseif (t <= 7.5e-11)
		tmp = (-1.0 * ((t * (z - y)) / (a - z))) + (x * ((1.0 + (z / (a - z))) - (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[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.2e+96], t$95$1, If[LessEqual[t, 7.5e-11], N[(N[(-1.0 * N[(N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(1.0 + N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.2000000000000002e96 or 7.5e-11 < t

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. associate-*l/ N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. frac-2neg-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 84.1%

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

   3. Applied rewrites 84.1%

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

   if -4.2000000000000002e96 < t < 7.5e-11

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. associate-*l/ N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. frac-2neg-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 84.1%

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

   3. Applied rewrites 84.1%

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

   4. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-+.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower--.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 78.8%

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

   6. Applied rewrites 78.8%

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

Alternative 2: 90.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t + -1 \cdot \frac{y \cdot \left(t - x\right) - a \cdot \left(t - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (* (- x t) (/ (- z y) (- a z)))))
       (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
  (if (<= t_2 -4e-303)
    t_1
    (if (<= t_2 0.0)
      (+ t (* -1.0 (/ (- (* y (- t x)) (* a (- t x))) z)))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((x - t) * ((z - y) / (a - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -4e-303) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (-1.0 * (((y * (t - x)) - (a * (t - x))) / 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) :: t_2
    real(8) :: tmp
    t_1 = x + ((x - t) * ((z - y) / (a - z)))
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-4d-303)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = t + ((-1.0d0) * (((y * (t - x)) - (a * (t - x))) / 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 + ((x - t) * ((z - y) / (a - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -4e-303) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t + (-1.0 * (((y * (t - x)) - (a * (t - x))) / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((x - t) * ((z - y) / (a - z)))
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -4e-303:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t + (-1.0 * (((y * (t - x)) - (a * (t - x))) / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -4e-303)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t + Float64(-1.0 * Float64(Float64(Float64(y * Float64(t - x)) - Float64(a * Float64(t - x))) / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((x - t) * ((z - y) / (a - z)));
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -4e-303)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t + (-1.0 * (((y * (t - x)) - (a * (t - x))) / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $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]}, If[LessEqual[t$95$2, -4e-303], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t + N[(-1.0 * N[(N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -3.9999999999999997e-303 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. associate-*l/ N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. frac-2neg-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 84.1%

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

   3. Applied rewrites 84.1%

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

   if -3.9999999999999997e-303 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 79.6%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 19.7%

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

   4. Applied rewrites 19.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto x + -1 \cdot \color{blue}{x} \]
   6. Step-by-step derivation

      1. lower-*.f64 2.8%

         \[\leadsto x + -1 \cdot x \]

   7. Applied rewrites 2.8%

      \[\leadsto x + -1 \cdot \color{blue}{x} \]

   8. Taylor expanded in z around -inf

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower--.f64 46.9%

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

   10. Applied rewrites 46.9%

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

Alternative 3: 88.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (* (- x t) (/ (- z y) (- a z)))))
       (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
  (if (<= t_2 -4e-303)
    t_1
    (if (<= t_2 0.0) (* t (- 1.0 (/ y z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((x - t) * ((z - y) / (a - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -4e-303) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t * (1.0 - (y / 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) :: t_2
    real(8) :: tmp
    t_1 = x + ((x - t) * ((z - y) / (a - z)))
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-4d-303)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = t * (1.0d0 - (y / 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 + ((x - t) * ((z - y) / (a - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -4e-303) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((x - t) * ((z - y) / (a - z)))
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -4e-303:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -4e-303)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((x - t) * ((z - y) / (a - z)));
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -4e-303)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t * (1.0 - (y / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $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]}, If[LessEqual[t$95$2, -4e-303], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -3.9999999999999997e-303 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. associate-*l/ N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. frac-2neg-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 84.1%

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

   3. Applied rewrites 84.1%

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

   if -3.9999999999999997e-303 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

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

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

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

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

      17. lower-*.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lower--.f64 68.2%

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

   3. Applied rewrites 68.2%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.7%

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

   6. Applied rewrites 51.7%

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

   7. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 36.6%

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

   9. Applied rewrites 36.6%

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

Alternative 4: 87.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := x + \left(x - t\right) \cdot \frac{z - y}{a - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-303}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t \cdot \left(\frac{y}{a - z} - \frac{z}{a - z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (* (- x t) (/ (- z y) (- a z)))))
       (t_2 (+ x (* (- y z) (/ (- t x) (- a z))))))
  (if (<= t_2 -4e-303)
    t_1
    (if (<= t_2 0.0) (* t (- (/ y (- a z)) (/ z (- a z)))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((x - t) * ((z - y) / (a - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -4e-303) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t * ((y / (a - z)) - (z / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((x - t) * ((z - y) / (a - z)))
    t_2 = x + ((y - z) * ((t - x) / (a - z)))
    if (t_2 <= (-4d-303)) then
        tmp = t_1
    else if (t_2 <= 0.0d0) then
        tmp = t * ((y / (a - z)) - (z / (a - z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((x - t) * ((z - y) / (a - z)));
	double t_2 = x + ((y - z) * ((t - x) / (a - z)));
	double tmp;
	if (t_2 <= -4e-303) {
		tmp = t_1;
	} else if (t_2 <= 0.0) {
		tmp = t * ((y / (a - z)) - (z / (a - z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((x - t) * ((z - y) / (a - z)))
	t_2 = x + ((y - z) * ((t - x) / (a - z)))
	tmp = 0
	if t_2 <= -4e-303:
		tmp = t_1
	elif t_2 <= 0.0:
		tmp = t * ((y / (a - z)) - (z / (a - z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / Float64(a - z))))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(Float64(t - x) / Float64(a - z))))
	tmp = 0.0
	if (t_2 <= -4e-303)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = Float64(t * Float64(Float64(y / Float64(a - z)) - Float64(z / Float64(a - z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((x - t) * ((z - y) / (a - z)));
	t_2 = x + ((y - z) * ((t - x) / (a - z)));
	tmp = 0.0;
	if (t_2 <= -4e-303)
		tmp = t_1;
	elseif (t_2 <= 0.0)
		tmp = t * ((y / (a - z)) - (z / (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[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $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]}, If[LessEqual[t$95$2, -4e-303], t$95$1, If[LessEqual[t$95$2, 0.0], N[(t * N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -3.9999999999999997e-303 or 0.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. associate-*l/ N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. frac-2neg-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 84.1%

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

   3. Applied rewrites 84.1%

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

   if -3.9999999999999997e-303 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 0.0

   1. Initial program 79.6%

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

   2. Taylor expanded in z around inf

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

      1. lower--.f64 19.7%

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

   4. Applied rewrites 19.7%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.7%

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

   7. Applied rewrites 51.7%

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

Alternative 5: 73.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t - x}{a - z}\\ t_2 := x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{-303}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-246}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - t\right) \cdot y}{z - a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (* (- y z) (/ (- t x) (- a z)))))
       (t_2 (+ x (* (- y z) (/ t (- a z))))))
  (if (<= t_1 (- INFINITY))
    (+ x (/ (* y (- t x)) (- a z)))
    (if (<= t_1 -4e-303)
      t_2
      (if (<= t_1 1e-246)
        (* t (/ z (- z a)))
        (if (<= t_1 5e+305) t_2 (/ (* (- x t) y) (- z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * ((t - x) / (a - z)));
	double t_2 = x + ((y - z) * (t / (a - z)));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else if (t_1 <= -4e-303) {
		tmp = t_2;
	} else if (t_1 <= 1e-246) {
		tmp = t * (z / (z - a));
	} else if (t_1 <= 5e+305) {
		tmp = t_2;
	} else {
		tmp = ((x - t) * y) / (z - a);
	}
	return tmp;
}

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 t_2 = x + ((y - z) * (t / (a - z)));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else if (t_1 <= -4e-303) {
		tmp = t_2;
	} else if (t_1 <= 1e-246) {
		tmp = t * (z / (z - a));
	} else if (t_1 <= 5e+305) {
		tmp = t_2;
	} else {
		tmp = ((x - t) * y) / (z - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * ((t - x) / (a - z)))
	t_2 = x + ((y - z) * (t / (a - z)))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + ((y * (t - x)) / (a - z))
	elif t_1 <= -4e-303:
		tmp = t_2
	elif t_1 <= 1e-246:
		tmp = t * (z / (z - a))
	elif t_1 <= 5e+305:
		tmp = t_2
	else:
		tmp = ((x - t) * y) / (z - a)
	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))))
	t_2 = Float64(x + Float64(Float64(y - z) * Float64(t / Float64(a - z))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / Float64(a - z)));
	elseif (t_1 <= -4e-303)
		tmp = t_2;
	elseif (t_1 <= 1e-246)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	elseif (t_1 <= 5e+305)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(x - t) * y) / Float64(z - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * ((t - x) / (a - z)));
	t_2 = x + ((y - z) * (t / (a - z)));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + ((y * (t - x)) / (a - z));
	elseif (t_1 <= -4e-303)
		tmp = t_2;
	elseif (t_1 <= 1e-246)
		tmp = t * (z / (z - a));
	elseif (t_1 <= 5e+305)
		tmp = t_2;
	else
		tmp = ((x - t) * y) / (z - a);
	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]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -4e-303], t$95$2, If[LessEqual[t$95$1, 1e-246], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+305], t$95$2, N[(N[(N[(x - t), $MachinePrecision] * y), $MachinePrecision] / N[(z - a), $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 79.6%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 54.8%

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

   4. Applied rewrites 54.8%

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

   if -inf.0 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < -3.9999999999999997e-303 or 9.9999999999999996e-247 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 5.0000000000000001e305

   1. Initial program 79.6%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 63.8%

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

   if -3.9999999999999997e-303 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))) < 9.9999999999999996e-247

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

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

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

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

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

      17. lower-*.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lower--.f64 68.2%

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

   3. Applied rewrites 68.2%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.7%

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

   6. Applied rewrites 51.7%

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

   7. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 29.9%

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

   9. Applied rewrites 29.9%

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

   if 5.0000000000000001e305 < (+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

   1. Initial program 79.6%

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

   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. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 41.5%

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

   4. Applied rewrites 41.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. sub-div N/A

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

      7. frac-2neg N/A

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

      8. sub-negate-rev N/A

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

      9. lift--.f64 N/A

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

      10. associate-*l/ N/A

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

      11. lower-/.f64 N/A

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

      12. lower-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. lower--.f64 37.4%

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

   6. Applied rewrites 37.4%

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

Alternative 6: 68.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+93}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-113}:\\ \;\;\;\;x + \left(x - t\right) \cdot \frac{z - y}{a}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (/ (* t (- y z)) (- a z)))))
  (if (<= z -2.1e+93)
    (* t (- 1.0 (/ y z)))
    (if (<= z -3.6e-29)
      t_1
      (if (<= z 4.4e-113)
        (+ x (* (- x t) (/ (- z y) a)))
        (if (<= z 5.4e+81) t_1 (* t (/ z (- z a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t * (y - z)) / (a - z));
	double tmp;
	if (z <= -2.1e+93) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= -3.6e-29) {
		tmp = t_1;
	} else if (z <= 4.4e-113) {
		tmp = x + ((x - t) * ((z - y) / a));
	} else if (z <= 5.4e+81) {
		tmp = t_1;
	} else {
		tmp = t * (z / (z - a));
	}
	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 - z))
    if (z <= (-2.1d+93)) then
        tmp = t * (1.0d0 - (y / z))
    else if (z <= (-3.6d-29)) then
        tmp = t_1
    else if (z <= 4.4d-113) then
        tmp = x + ((x - t) * ((z - y) / a))
    else if (z <= 5.4d+81) then
        tmp = t_1
    else
        tmp = t * (z / (z - a))
    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 - z));
	double tmp;
	if (z <= -2.1e+93) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= -3.6e-29) {
		tmp = t_1;
	} else if (z <= 4.4e-113) {
		tmp = x + ((x - t) * ((z - y) / a));
	} else if (z <= 5.4e+81) {
		tmp = t_1;
	} else {
		tmp = t * (z / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t * (y - z)) / (a - z))
	tmp = 0
	if z <= -2.1e+93:
		tmp = t * (1.0 - (y / z))
	elif z <= -3.6e-29:
		tmp = t_1
	elif z <= 4.4e-113:
		tmp = x + ((x - t) * ((z - y) / a))
	elif z <= 5.4e+81:
		tmp = t_1
	else:
		tmp = t * (z / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t * Float64(y - z)) / Float64(a - z)))
	tmp = 0.0
	if (z <= -2.1e+93)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (z <= -3.6e-29)
		tmp = t_1;
	elseif (z <= 4.4e-113)
		tmp = Float64(x + Float64(Float64(x - t) * Float64(Float64(z - y) / a)));
	elseif (z <= 5.4e+81)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(z / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t * (y - z)) / (a - z));
	tmp = 0.0;
	if (z <= -2.1e+93)
		tmp = t * (1.0 - (y / z));
	elseif (z <= -3.6e-29)
		tmp = t_1;
	elseif (z <= 4.4e-113)
		tmp = x + ((x - t) * ((z - y) / a));
	elseif (z <= 5.4e+81)
		tmp = t_1;
	else
		tmp = t * (z / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+93], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e-29], t$95$1, If[LessEqual[z, 4.4e-113], N[(x + N[(N[(x - t), $MachinePrecision] * N[(N[(z - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e+81], t$95$1, N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.0999999999999998e93

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

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

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

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

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

      17. lower-*.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lower--.f64 68.2%

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

   3. Applied rewrites 68.2%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.7%

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

   6. Applied rewrites 51.7%

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

   7. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 36.6%

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

   9. Applied rewrites 36.6%

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

   if -2.0999999999999998e93 < z < -3.5999999999999997e-29 or 4.4000000000000001e-113 < z < 5.3999999999999999e81

   1. Initial program 79.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 56.1%

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

   4. Applied rewrites 56.1%

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

   if -3.5999999999999997e-29 < z < 4.4000000000000001e-113

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. frac-2neg N/A

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

      5. associate-*l/ N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. lower--.f64 N/A

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

      11. lift--.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. frac-2neg-rev N/A

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

      14. lower-/.f64 N/A

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

      15. lower--.f64 84.1%

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

   3. Applied rewrites 84.1%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 52.6%

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

   if 5.3999999999999999e81 < z

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

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

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

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

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

      17. lower-*.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lower--.f64 68.2%

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

   3. Applied rewrites 68.2%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.7%

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

   6. Applied rewrites 51.7%

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

   7. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 29.9%

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

   9. Applied rewrites 29.9%

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

Alternative 7: 67.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+93}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-117}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+81}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= z -2.1e+93)
  (* t (- 1.0 (/ y z)))
  (if (<= z -7.2e-117)
    (+ x (/ (* t (- y z)) (- a z)))
    (if (<= z 4.6e+81)
      (+ x (/ (* y (- t x)) (- a z)))
      (* t (/ z (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e+93) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= -7.2e-117) {
		tmp = x + ((t * (y - z)) / (a - z));
	} else if (z <= 4.6e+81) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else {
		tmp = t * (z / (z - a));
	}
	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 <= (-2.1d+93)) then
        tmp = t * (1.0d0 - (y / z))
    else if (z <= (-7.2d-117)) then
        tmp = x + ((t * (y - z)) / (a - z))
    else if (z <= 4.6d+81) then
        tmp = x + ((y * (t - x)) / (a - z))
    else
        tmp = t * (z / (z - a))
    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 <= -2.1e+93) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= -7.2e-117) {
		tmp = x + ((t * (y - z)) / (a - z));
	} else if (z <= 4.6e+81) {
		tmp = x + ((y * (t - x)) / (a - z));
	} else {
		tmp = t * (z / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.1e+93:
		tmp = t * (1.0 - (y / z))
	elif z <= -7.2e-117:
		tmp = x + ((t * (y - z)) / (a - z))
	elif z <= 4.6e+81:
		tmp = x + ((y * (t - x)) / (a - z))
	else:
		tmp = t * (z / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.1e+93)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (z <= -7.2e-117)
		tmp = Float64(x + Float64(Float64(t * Float64(y - z)) / Float64(a - z)));
	elseif (z <= 4.6e+81)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / Float64(a - z)));
	else
		tmp = Float64(t * Float64(z / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.1e+93)
		tmp = t * (1.0 - (y / z));
	elseif (z <= -7.2e-117)
		tmp = x + ((t * (y - z)) / (a - z));
	elseif (z <= 4.6e+81)
		tmp = x + ((y * (t - x)) / (a - z));
	else
		tmp = t * (z / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.1e+93], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.2e-117], N[(x + N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+81], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.0999999999999998e93

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

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

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

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

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

      17. lower-*.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lower--.f64 68.2%

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

   3. Applied rewrites 68.2%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.7%

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

   6. Applied rewrites 51.7%

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

   7. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 36.6%

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

   9. Applied rewrites 36.6%

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

   if -2.0999999999999998e93 < z < -7.2000000000000001e-117

   1. Initial program 79.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 56.1%

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

   4. Applied rewrites 56.1%

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

   if -7.2000000000000001e-117 < z < 4.5999999999999998e81

   1. Initial program 79.6%

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

   2. Taylor expanded in y around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 54.8%

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

   4. Applied rewrites 54.8%

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

   if 4.5999999999999998e81 < z

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

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

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

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

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

      17. lower-*.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lower--.f64 68.2%

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

   3. Applied rewrites 68.2%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.7%

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

   6. Applied rewrites 51.7%

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

   7. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 29.9%

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

   9. Applied rewrites 29.9%

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

Alternative 8: 63.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{-139}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{t \cdot \left(y - z\right)}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* (- t x) (/ y (- a z)))))
  (if (<= y -3.1e-61)
    t_1
    (if (<= y -1.52e-139)
      (* t (/ z (- z a)))
      (if (<= y 2.8e+23) (+ x (/ (* t (- y z)) (- a z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -3.1e-61) {
		tmp = t_1;
	} else if (y <= -1.52e-139) {
		tmp = t * (z / (z - a));
	} else if (y <= 2.8e+23) {
		tmp = x + ((t * (y - z)) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - x) * (y / (a - z))
    if (y <= (-3.1d-61)) then
        tmp = t_1
    else if (y <= (-1.52d-139)) then
        tmp = t * (z / (z - a))
    else if (y <= 2.8d+23) then
        tmp = x + ((t * (y - z)) / (a - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -3.1e-61) {
		tmp = t_1;
	} else if (y <= -1.52e-139) {
		tmp = t * (z / (z - a));
	} else if (y <= 2.8e+23) {
		tmp = x + ((t * (y - z)) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	tmp = 0
	if y <= -3.1e-61:
		tmp = t_1
	elif y <= -1.52e-139:
		tmp = t * (z / (z - a))
	elif y <= 2.8e+23:
		tmp = x + ((t * (y - z)) / (a - z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -3.1e-61)
		tmp = t_1;
	elseif (y <= -1.52e-139)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	elseif (y <= 2.8e+23)
		tmp = Float64(x + Float64(Float64(t * Float64(y - z)) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	tmp = 0.0;
	if (y <= -3.1e-61)
		tmp = t_1;
	elseif (y <= -1.52e-139)
		tmp = t * (z / (z - a));
	elseif (y <= 2.8e+23)
		tmp = x + ((t * (y - z)) / (a - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e-61], t$95$1, If[LessEqual[y, -1.52e-139], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+23], N[(x + N[(N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.0999999999999999e-61 or 2.8000000000000002e23 < y

   1. Initial program 79.6%

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

   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. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 41.5%

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

   4. Applied rewrites 41.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 41.5%

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. sub-div N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 41.8%

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

   6. Applied rewrites 41.8%

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

      1. associate-*r/ 41.8%

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

      2. sub-negate-rev 41.8%

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

      3. distribute-rgt-neg-out 41.8%

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

      4. distribute-lft-neg-out 41.8%

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

      5. sub-negate-rev 41.8%

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

      6. frac-2neg-rev 41.8%

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

      7. mul-1-neg 41.8%

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

      8. sub-negate-rev 41.8%

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

      9. lift--.f64 N/A

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

      10. associate-*l/ N/A

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

      11. lift--.f64 41.8%

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

      12. lift-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift-/.f64 N/A

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

      16. associate-*l/ N/A

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

      17. associate-/l* N/A

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

      18. lower-*.f64 N/A

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

   8. Applied rewrites 43.3%

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

   if -3.0999999999999999e-61 < y < -1.52e-139

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

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

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

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

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

      17. lower-*.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lower--.f64 68.2%

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

   3. Applied rewrites 68.2%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.7%

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

   6. Applied rewrites 51.7%

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

   7. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 29.9%

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

   9. Applied rewrites 29.9%

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

   if -1.52e-139 < y < 2.8000000000000002e23

   1. Initial program 79.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 56.1%

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

   4. Applied rewrites 56.1%

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

Alternative 9: 60.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := x + \left(y - z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -9.2 \cdot 10^{+198}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1 \cdot 10^{-81}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;a \leq 16000000000:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (* (- y z) (/ t a)))))
  (if (<= a -9.2e+198)
    t_1
    (if (<= a -1e-81)
      (+ x (/ (* y (- t x)) a))
      (if (<= a 16000000000.0) (* t (- 1.0 (/ y z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y - z) * (t / a));
	double tmp;
	if (a <= -9.2e+198) {
		tmp = t_1;
	} else if (a <= -1e-81) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 16000000000.0) {
		tmp = t * (1.0 - (y / 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 + ((y - z) * (t / a))
    if (a <= (-9.2d+198)) then
        tmp = t_1
    else if (a <= (-1d-81)) then
        tmp = x + ((y * (t - x)) / a)
    else if (a <= 16000000000.0d0) then
        tmp = t * (1.0d0 - (y / 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 + ((y - z) * (t / a));
	double tmp;
	if (a <= -9.2e+198) {
		tmp = t_1;
	} else if (a <= -1e-81) {
		tmp = x + ((y * (t - x)) / a);
	} else if (a <= 16000000000.0) {
		tmp = t * (1.0 - (y / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y - z) * (t / a))
	tmp = 0
	if a <= -9.2e+198:
		tmp = t_1
	elif a <= -1e-81:
		tmp = x + ((y * (t - x)) / a)
	elif a <= 16000000000.0:
		tmp = t * (1.0 - (y / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y - z) * Float64(t / a)))
	tmp = 0.0
	if (a <= -9.2e+198)
		tmp = t_1;
	elseif (a <= -1e-81)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	elseif (a <= 16000000000.0)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y - z) * (t / a));
	tmp = 0.0;
	if (a <= -9.2e+198)
		tmp = t_1;
	elseif (a <= -1e-81)
		tmp = x + ((y * (t - x)) / a);
	elseif (a <= 16000000000.0)
		tmp = t * (1.0 - (y / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y - z), $MachinePrecision] * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9.2e+198], t$95$1, If[LessEqual[a, -1e-81], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 16000000000.0], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.2000000000000002e198 or 1.6e10 < a

   1. Initial program 79.6%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 63.8%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 44.0%

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

   if -9.2000000000000002e198 < a < -9.9999999999999996e-82

   1. Initial program 79.6%

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

   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. lower-*.f64 N/A

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

      3. lower--.f64 43.9%

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

   4. Applied rewrites 43.9%

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

   if -9.9999999999999996e-82 < a < 1.6e10

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

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

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

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

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

      17. lower-*.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lower--.f64 68.2%

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

   3. Applied rewrites 68.2%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.7%

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

   6. Applied rewrites 51.7%

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

   7. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 36.6%

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

   9. Applied rewrites 36.6%

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

Alternative 10: 59.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-14}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-110}:\\ \;\;\;\;x + \frac{y \cdot \left(t - x\right)}{a}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+102}:\\ \;\;\;\;\left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= z -6.5e-14)
  (* t (- 1.0 (/ y z)))
  (if (<= z 1.05e-110)
    (+ x (/ (* y (- t x)) a))
    (if (<= z 2.2e+102)
      (* (- t x) (/ y (- a z)))
      (* t (/ z (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e-14) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 1.05e-110) {
		tmp = x + ((y * (t - x)) / a);
	} else if (z <= 2.2e+102) {
		tmp = (t - x) * (y / (a - z));
	} else {
		tmp = t * (z / (z - a));
	}
	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 <= (-6.5d-14)) then
        tmp = t * (1.0d0 - (y / z))
    else if (z <= 1.05d-110) then
        tmp = x + ((y * (t - x)) / a)
    else if (z <= 2.2d+102) then
        tmp = (t - x) * (y / (a - z))
    else
        tmp = t * (z / (z - a))
    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 <= -6.5e-14) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 1.05e-110) {
		tmp = x + ((y * (t - x)) / a);
	} else if (z <= 2.2e+102) {
		tmp = (t - x) * (y / (a - z));
	} else {
		tmp = t * (z / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e-14:
		tmp = t * (1.0 - (y / z))
	elif z <= 1.05e-110:
		tmp = x + ((y * (t - x)) / a)
	elif z <= 2.2e+102:
		tmp = (t - x) * (y / (a - z))
	else:
		tmp = t * (z / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e-14)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (z <= 1.05e-110)
		tmp = Float64(x + Float64(Float64(y * Float64(t - x)) / a));
	elseif (z <= 2.2e+102)
		tmp = Float64(Float64(t - x) * Float64(y / Float64(a - z)));
	else
		tmp = Float64(t * Float64(z / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e-14)
		tmp = t * (1.0 - (y / z));
	elseif (z <= 1.05e-110)
		tmp = x + ((y * (t - x)) / a);
	elseif (z <= 2.2e+102)
		tmp = (t - x) * (y / (a - z));
	else
		tmp = t * (z / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e-14], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-110], N[(x + N[(N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+102], N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.5000000000000001e-14

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

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

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

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

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

      17. lower-*.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lower--.f64 68.2%

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

   3. Applied rewrites 68.2%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.7%

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

   6. Applied rewrites 51.7%

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

   7. Taylor expanded in a around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 36.6%

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

   9. Applied rewrites 36.6%

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

   if -6.5000000000000001e-14 < z < 1.05e-110

   1. Initial program 79.6%

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

   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. lower-*.f64 N/A

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

      3. lower--.f64 43.9%

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

   4. Applied rewrites 43.9%

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

   if 1.05e-110 < z < 2.2000000000000001e102

   1. Initial program 79.6%

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

   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. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 41.5%

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

   4. Applied rewrites 41.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 41.5%

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. sub-div N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 41.8%

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

   6. Applied rewrites 41.8%

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

      1. associate-*r/ 41.8%

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

      2. sub-negate-rev 41.8%

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

      3. distribute-rgt-neg-out 41.8%

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

      4. distribute-lft-neg-out 41.8%

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

      5. sub-negate-rev 41.8%

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

      6. frac-2neg-rev 41.8%

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

      7. mul-1-neg 41.8%

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

      8. sub-negate-rev 41.8%

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

      9. lift--.f64 N/A

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

      10. associate-*l/ N/A

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

      11. lift--.f64 41.8%

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

      12. lift-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift-/.f64 N/A

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

      16. associate-*l/ N/A

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

      17. associate-/l* N/A

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

      18. lower-*.f64 N/A

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

   8. Applied rewrites 43.3%

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

   if 2.2000000000000001e102 < z

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

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

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

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

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

      17. lower-*.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lower--.f64 68.2%

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

   3. Applied rewrites 68.2%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.7%

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

   6. Applied rewrites 51.7%

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

   7. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 29.9%

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

   9. Applied rewrites 29.9%

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

Alternative 11: 55.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \left(t - x\right) \cdot \frac{y}{a - z}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{-61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* (- t x) (/ y (- a z)))))
  (if (<= y -3.1e-61)
    t_1
    (if (<= y 4.8e+18) (* t (/ z (- z a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - x) * (y / (a - z));
	double tmp;
	if (y <= -3.1e-61) {
		tmp = t_1;
	} else if (y <= 4.8e+18) {
		tmp = t * (z / (z - a));
	} 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 = (t - x) * (y / (a - z))
    if (y <= (-3.1d-61)) then
        tmp = t_1
    else if (y <= 4.8d+18) then
        tmp = t * (z / (z - a))
    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 - x) * (y / (a - z));
	double tmp;
	if (y <= -3.1e-61) {
		tmp = t_1;
	} else if (y <= 4.8e+18) {
		tmp = t * (z / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t - x) * (y / (a - z))
	tmp = 0
	if y <= -3.1e-61:
		tmp = t_1
	elif y <= 4.8e+18:
		tmp = t * (z / (z - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - x) * Float64(y / Float64(a - z)))
	tmp = 0.0
	if (y <= -3.1e-61)
		tmp = t_1;
	elseif (y <= 4.8e+18)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t - x) * (y / (a - z));
	tmp = 0.0;
	if (y <= -3.1e-61)
		tmp = t_1;
	elseif (y <= 4.8e+18)
		tmp = t * (z / (z - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e-61], t$95$1, If[LessEqual[y, 4.8e+18], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0999999999999999e-61 or 4.8e18 < y

   1. Initial program 79.6%

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

   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. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 41.5%

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

   4. Applied rewrites 41.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 41.5%

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. sub-div N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 41.8%

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

   6. Applied rewrites 41.8%

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

      1. associate-*r/ 41.8%

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

      2. sub-negate-rev 41.8%

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

      3. distribute-rgt-neg-out 41.8%

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

      4. distribute-lft-neg-out 41.8%

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

      5. sub-negate-rev 41.8%

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

      6. frac-2neg-rev 41.8%

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

      7. mul-1-neg 41.8%

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

      8. sub-negate-rev 41.8%

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

      9. lift--.f64 N/A

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

      10. associate-*l/ N/A

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

      11. lift--.f64 41.8%

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

      12. lift-*.f64 N/A

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

      13. lift--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift-/.f64 N/A

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

      16. associate-*l/ N/A

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

      17. associate-/l* N/A

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

      18. lower-*.f64 N/A

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

   8. Applied rewrites 43.3%

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

   if -3.0999999999999999e-61 < y < 4.8e18

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

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

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

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

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

      17. lower-*.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lower--.f64 68.2%

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

   3. Applied rewrites 68.2%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.7%

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

   6. Applied rewrites 51.7%

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

   7. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 29.9%

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

   9. Applied rewrites 29.9%

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

Alternative 12: 55.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \frac{t - x}{a - z} \cdot y\\ \mathbf{if}\;y \leq -4 \cdot 10^{-54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* (/ (- t x) (- a z)) y)))
  (if (<= y -4e-54) t_1 (if (<= y 4.8e+18) (* t (/ z (- z a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((t - x) / (a - z)) * y;
	double tmp;
	if (y <= -4e-54) {
		tmp = t_1;
	} else if (y <= 4.8e+18) {
		tmp = t * (z / (z - a));
	} 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 = ((t - x) / (a - z)) * y
    if (y <= (-4d-54)) then
        tmp = t_1
    else if (y <= 4.8d+18) then
        tmp = t * (z / (z - a))
    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 - x) / (a - z)) * y;
	double tmp;
	if (y <= -4e-54) {
		tmp = t_1;
	} else if (y <= 4.8e+18) {
		tmp = t * (z / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((t - x) / (a - z)) * y
	tmp = 0
	if y <= -4e-54:
		tmp = t_1
	elif y <= 4.8e+18:
		tmp = t * (z / (z - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(t - x) / Float64(a - z)) * y)
	tmp = 0.0
	if (y <= -4e-54)
		tmp = t_1;
	elseif (y <= 4.8e+18)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((t - x) / (a - z)) * y;
	tmp = 0.0;
	if (y <= -4e-54)
		tmp = t_1;
	elseif (y <= 4.8e+18)
		tmp = t * (z / (z - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - x), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4e-54], t$95$1, If[LessEqual[y, 4.8e+18], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.0000000000000001e-54 or 4.8e18 < y

   1. Initial program 79.6%

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

   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. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 41.5%

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

   4. Applied rewrites 41.5%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 41.5%

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. sub-div N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 41.8%

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

   6. Applied rewrites 41.8%

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

   if -4.0000000000000001e-54 < y < 4.8e18

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. frac-2neg N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower--.f64 N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

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

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

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

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

      17. lower-*.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lower--.f64 68.2%

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

   3. Applied rewrites 68.2%

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

   4. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 51.7%

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

   6. Applied rewrites 51.7%

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

   7. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 29.9%

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

   9. Applied rewrites 29.9%

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

Alternative 13: 49.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{-14}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-110}:\\ \;\;\;\;\left(\frac{-y}{a} - -1\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= z -6.5e-14)
  (* t (- 1.0 (/ y z)))
  (if (<= z 1.05e-110)
    (* (- (/ (- y) a) -1.0) x)
    (* t (/ z (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e-14) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 1.05e-110) {
		tmp = ((-y / a) - -1.0) * x;
	} else {
		tmp = t * (z / (z - a));
	}
	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 <= (-6.5d-14)) then
        tmp = t * (1.0d0 - (y / z))
    else if (z <= 1.05d-110) then
        tmp = ((-y / a) - (-1.0d0)) * x
    else
        tmp = t * (z / (z - a))
    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 <= -6.5e-14) {
		tmp = t * (1.0 - (y / z));
	} else if (z <= 1.05e-110) {
		tmp = ((-y / a) - -1.0) * x;
	} else {
		tmp = t * (z / (z - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e-14:
		tmp = t * (1.0 - (y / z))
	elif z <= 1.05e-110:
		tmp = ((-y / a) - -1.0) * x
	else:
		tmp = t * (z / (z - a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e-14)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (z <= 1.05e-110)
		tmp = Float64(Float64(Float64(Float64(-y) / a) - -1.0) * x);
	else
		tmp = Float64(t * Float64(z / Float64(z - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.5e-14)
		tmp = t * (1.0 - (y / z));
	elseif (z <= 1.05e-110)
		tmp = ((-y / a) - -1.0) * x;
	else
		tmp = t * (z / (z - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e-14], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-110], N[(N[(N[((-y) / a), $MachinePrecision] - -1.0), $MachinePrecision] * x), $MachinePrecision], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5000000000000001e-14

   1. Initial program 79.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. mult-flip N/A

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(\left(t - x\right) \cdot \frac{1}{a - z}\right)} \]

      4. associate-*r* N/A

         \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \left(t - x\right)\right) \cdot \frac{1}{a - z}} \]

      5. *-commutative N/A

         \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

      7. frac-2neg N/A

         \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto x + \frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - z\right)\right)} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      9. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{-1}{\mathsf{neg}\left(\left(a - z\right)\right)}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      10. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      11. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{\color{blue}{z - a}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      12. lower--.f64 N/A

          \[\leadsto x + \frac{-1}{\color{blue}{z - a}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(y - z\right)} \cdot \left(t - x\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(\mathsf{neg}\left(\left(z - y\right)\right)\right)} \cdot \left(t - x\right)\right) \]

      15. distribute-lft-neg-out N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - y\right) \cdot \left(t - x\right)\right)\right)} \]

      16. distribute-rgt-neg-out N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)} \]

      17. lower-*.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)} \]

      18. lower--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(z - y\right)} \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      19. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t - x\right)}\right)\right)\right) \]

      20. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \color{blue}{\left(x - t\right)}\right) \]

      21. lower--.f64 68.2%

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \color{blue}{\left(x - t\right)}\right) \]

   3. Applied rewrites 68.2%

      \[\leadsto x + \color{blue}{\frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \left(x - t\right)\right)} \]

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \color{blue}{\frac{y}{z - a}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{\color{blue}{y}}{z - a}\right) \]

      4. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{\color{blue}{z - a}}\right) \]

      6. lower--.f64 51.7%

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - \color{blue}{a}}\right) \]

   6. Applied rewrites 51.7%

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

   7. Taylor expanded in a around 0

      \[\leadsto t \cdot \left(1 - \color{blue}{\frac{y}{z}}\right) \]
   8. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto t \cdot \left(1 - \frac{y}{\color{blue}{z}}\right) \]

      2. lower-/.f64 36.6%

         \[\leadsto t \cdot \left(1 - \frac{y}{z}\right) \]

   9. Applied rewrites 36.6%

      \[\leadsto t \cdot \left(1 - \color{blue}{\frac{y}{z}}\right) \]

   if -6.5000000000000001e-14 < z < 1.05e-110

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   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. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{y - z}{a - z}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{y - z}{a - z}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{\color{blue}{a - z}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{\color{blue}{a} - z}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{y}{a}}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{\color{blue}{a}}\right) \]

      2. lower-/.f64 36.0%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{a}\right) \]

   7. Applied rewrites 36.0%

      \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{y}{a}}\right) \]
   8. Step-by-step derivation

      1. associate-*r/ 36.0%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{a}\right) \]

      2. sub-negate-rev 36.0%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{a}\right) \]

      3. distribute-rgt-neg-out 36.0%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{a}\right) \]

      4. distribute-lft-neg-out 36.0%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{a}\right) \]

      5. sub-negate-rev 36.0%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{a}\right) \]

      6. frac-2neg-rev 36.0%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{a}\right) \]

      7. mul-1-neg 36.0%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{a}\right) \]

      8. sub-negate-rev 36.0%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{a}\right) \]

      9. lift--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{a}\right) \]

      10. associate-*l/ N/A

          \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{a}\right) \]

      11. lift--.f64 36.0%

          \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{a}\right) \]

      12. lift-*.f64 N/A

          \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{y}{a}\right)} \]

      13. *-commutative N/A

          \[\leadsto \left(1 + -1 \cdot \frac{y}{a}\right) \cdot \color{blue}{x} \]

      14. lower-*.f64 36.0%

          \[\leadsto \left(1 + -1 \cdot \frac{y}{a}\right) \cdot \color{blue}{x} \]

   9. Applied rewrites 36.0%

      \[\leadsto \color{blue}{\left(\frac{-y}{a} - -1\right) \cdot x} \]

   if 1.05e-110 < z

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{t - x}{a - z}} \]

      3. mult-flip N/A

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(\left(t - x\right) \cdot \frac{1}{a - z}\right)} \]

      4. associate-*r* N/A

         \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \left(t - x\right)\right) \cdot \frac{1}{a - z}} \]

      5. *-commutative N/A

         \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

      7. frac-2neg N/A

         \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto x + \frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - z\right)\right)} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      9. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{-1}{\mathsf{neg}\left(\left(a - z\right)\right)}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      10. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      11. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{\color{blue}{z - a}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      12. lower--.f64 N/A

          \[\leadsto x + \frac{-1}{\color{blue}{z - a}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(y - z\right)} \cdot \left(t - x\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(\mathsf{neg}\left(\left(z - y\right)\right)\right)} \cdot \left(t - x\right)\right) \]

      15. distribute-lft-neg-out N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - y\right) \cdot \left(t - x\right)\right)\right)} \]

      16. distribute-rgt-neg-out N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)} \]

      17. lower-*.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)} \]

      18. lower--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(z - y\right)} \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      19. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t - x\right)}\right)\right)\right) \]

      20. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \color{blue}{\left(x - t\right)}\right) \]

      21. lower--.f64 68.2%

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \color{blue}{\left(x - t\right)}\right) \]

   3. Applied rewrites 68.2%

      \[\leadsto x + \color{blue}{\frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \left(x - t\right)\right)} \]

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \color{blue}{\frac{y}{z - a}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{\color{blue}{y}}{z - a}\right) \]

      4. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{\color{blue}{z - a}}\right) \]

      6. lower--.f64 51.7%

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - \color{blue}{a}}\right) \]

   6. Applied rewrites 51.7%

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

   7. Taylor expanded in y around 0

      \[\leadsto t \cdot \frac{z}{\color{blue}{z - a}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto t \cdot \frac{z}{z - \color{blue}{a}} \]

      2. lower--.f64 29.9%

         \[\leadsto t \cdot \frac{z}{z - a} \]

   9. Applied rewrites 29.9%

      \[\leadsto t \cdot \frac{z}{\color{blue}{z - a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 45.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \frac{t - x}{a} \cdot y\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+225}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-61}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \frac{z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* (/ (- t x) a) y)))
  (if (<= y -8.5e+225)
    t_1
    (if (<= y -1.8e-61)
      (* t (- 1.0 (/ y z)))
      (if (<= y 4e+31) (* t (/ z (- z a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((t - x) / a) * y;
	double tmp;
	if (y <= -8.5e+225) {
		tmp = t_1;
	} else if (y <= -1.8e-61) {
		tmp = t * (1.0 - (y / z));
	} else if (y <= 4e+31) {
		tmp = t * (z / (z - a));
	} 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 = ((t - x) / a) * y
    if (y <= (-8.5d+225)) then
        tmp = t_1
    else if (y <= (-1.8d-61)) then
        tmp = t * (1.0d0 - (y / z))
    else if (y <= 4d+31) then
        tmp = t * (z / (z - a))
    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 - x) / a) * y;
	double tmp;
	if (y <= -8.5e+225) {
		tmp = t_1;
	} else if (y <= -1.8e-61) {
		tmp = t * (1.0 - (y / z));
	} else if (y <= 4e+31) {
		tmp = t * (z / (z - a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((t - x) / a) * y
	tmp = 0
	if y <= -8.5e+225:
		tmp = t_1
	elif y <= -1.8e-61:
		tmp = t * (1.0 - (y / z))
	elif y <= 4e+31:
		tmp = t * (z / (z - a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(t - x) / a) * y)
	tmp = 0.0
	if (y <= -8.5e+225)
		tmp = t_1;
	elseif (y <= -1.8e-61)
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	elseif (y <= 4e+31)
		tmp = Float64(t * Float64(z / Float64(z - a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((t - x) / a) * y;
	tmp = 0.0;
	if (y <= -8.5e+225)
		tmp = t_1;
	elseif (y <= -1.8e-61)
		tmp = t * (1.0 - (y / z));
	elseif (y <= 4e+31)
		tmp = t * (z / (z - a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -8.5e+225], t$95$1, If[LessEqual[y, -1.8e-61], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+31], N[(t * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.4999999999999995e225 or 3.9999999999999999e31 < y

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   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. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.5%

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      3. lower-*.f64 41.5%

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      4. lift--.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      5. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      6. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      7. sub-div N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      8. lower-/.f64 N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      9. lift--.f64 41.8%

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

   6. Applied rewrites 41.8%

      \[\leadsto \frac{t - x}{a - z} \cdot \color{blue}{y} \]

   7. Taylor expanded in z around 0

      \[\leadsto \frac{t - x}{a} \cdot y \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t - x}{a} \cdot y \]

      2. lower--.f64 24.9%

         \[\leadsto \frac{t - x}{a} \cdot y \]

   9. Applied rewrites 24.9%

      \[\leadsto \frac{t - x}{a} \cdot y \]

   if -8.4999999999999995e225 < y < -1.8000000000000001e-61

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{t - x}{a - z}} \]

      3. mult-flip N/A

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(\left(t - x\right) \cdot \frac{1}{a - z}\right)} \]

      4. associate-*r* N/A

         \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \left(t - x\right)\right) \cdot \frac{1}{a - z}} \]

      5. *-commutative N/A

         \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

      7. frac-2neg N/A

         \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto x + \frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - z\right)\right)} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      9. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{-1}{\mathsf{neg}\left(\left(a - z\right)\right)}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      10. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      11. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{\color{blue}{z - a}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      12. lower--.f64 N/A

          \[\leadsto x + \frac{-1}{\color{blue}{z - a}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(y - z\right)} \cdot \left(t - x\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(\mathsf{neg}\left(\left(z - y\right)\right)\right)} \cdot \left(t - x\right)\right) \]

      15. distribute-lft-neg-out N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - y\right) \cdot \left(t - x\right)\right)\right)} \]

      16. distribute-rgt-neg-out N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)} \]

      17. lower-*.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)} \]

      18. lower--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(z - y\right)} \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      19. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t - x\right)}\right)\right)\right) \]

      20. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \color{blue}{\left(x - t\right)}\right) \]

      21. lower--.f64 68.2%

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \color{blue}{\left(x - t\right)}\right) \]

   3. Applied rewrites 68.2%

      \[\leadsto x + \color{blue}{\frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \left(x - t\right)\right)} \]

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \color{blue}{\frac{y}{z - a}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{\color{blue}{y}}{z - a}\right) \]

      4. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{\color{blue}{z - a}}\right) \]

      6. lower--.f64 51.7%

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - \color{blue}{a}}\right) \]

   6. Applied rewrites 51.7%

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

   7. Taylor expanded in a around 0

      \[\leadsto t \cdot \left(1 - \color{blue}{\frac{y}{z}}\right) \]
   8. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto t \cdot \left(1 - \frac{y}{\color{blue}{z}}\right) \]

      2. lower-/.f64 36.6%

         \[\leadsto t \cdot \left(1 - \frac{y}{z}\right) \]

   9. Applied rewrites 36.6%

      \[\leadsto t \cdot \left(1 - \color{blue}{\frac{y}{z}}\right) \]

   if -1.8000000000000001e-61 < y < 3.9999999999999999e31

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{t - x}{a - z}} \]

      3. mult-flip N/A

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(\left(t - x\right) \cdot \frac{1}{a - z}\right)} \]

      4. associate-*r* N/A

         \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \left(t - x\right)\right) \cdot \frac{1}{a - z}} \]

      5. *-commutative N/A

         \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

      7. frac-2neg N/A

         \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto x + \frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - z\right)\right)} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      9. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{-1}{\mathsf{neg}\left(\left(a - z\right)\right)}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      10. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      11. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{\color{blue}{z - a}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      12. lower--.f64 N/A

          \[\leadsto x + \frac{-1}{\color{blue}{z - a}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(y - z\right)} \cdot \left(t - x\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(\mathsf{neg}\left(\left(z - y\right)\right)\right)} \cdot \left(t - x\right)\right) \]

      15. distribute-lft-neg-out N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - y\right) \cdot \left(t - x\right)\right)\right)} \]

      16. distribute-rgt-neg-out N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)} \]

      17. lower-*.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)} \]

      18. lower--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(z - y\right)} \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      19. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t - x\right)}\right)\right)\right) \]

      20. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \color{blue}{\left(x - t\right)}\right) \]

      21. lower--.f64 68.2%

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \color{blue}{\left(x - t\right)}\right) \]

   3. Applied rewrites 68.2%

      \[\leadsto x + \color{blue}{\frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \left(x - t\right)\right)} \]

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \color{blue}{\frac{y}{z - a}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{\color{blue}{y}}{z - a}\right) \]

      4. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{\color{blue}{z - a}}\right) \]

      6. lower--.f64 51.7%

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - \color{blue}{a}}\right) \]

   6. Applied rewrites 51.7%

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

   7. Taylor expanded in y around 0

      \[\leadsto t \cdot \frac{z}{\color{blue}{z - a}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto t \cdot \frac{z}{z - \color{blue}{a}} \]

      2. lower--.f64 29.9%

         \[\leadsto t \cdot \frac{z}{z - a} \]

   9. Applied rewrites 29.9%

      \[\leadsto t \cdot \frac{z}{\color{blue}{z - a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 15: 41.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-144}:\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* t (- 1.0 (/ y z)))))
  (if (<= z -3.2e-28)
    t_1
    (if (<= z 5.5e-144) (* (/ (- t x) a) y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (1.0 - (y / z));
	double tmp;
	if (z <= -3.2e-28) {
		tmp = t_1;
	} else if (z <= 5.5e-144) {
		tmp = ((t - x) / a) * y;
	} 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 = t * (1.0d0 - (y / z))
    if (z <= (-3.2d-28)) then
        tmp = t_1
    else if (z <= 5.5d-144) then
        tmp = ((t - x) / a) * y
    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 * (1.0 - (y / z));
	double tmp;
	if (z <= -3.2e-28) {
		tmp = t_1;
	} else if (z <= 5.5e-144) {
		tmp = ((t - x) / a) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (1.0 - (y / z))
	tmp = 0
	if z <= -3.2e-28:
		tmp = t_1
	elif z <= 5.5e-144:
		tmp = ((t - x) / a) * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(1.0 - Float64(y / z)))
	tmp = 0.0
	if (z <= -3.2e-28)
		tmp = t_1;
	elseif (z <= 5.5e-144)
		tmp = Float64(Float64(Float64(t - x) / a) * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (1.0 - (y / z));
	tmp = 0.0;
	if (z <= -3.2e-28)
		tmp = t_1;
	elseif (z <= 5.5e-144)
		tmp = ((t - x) / a) * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e-28], t$95$1, If[LessEqual[z, 5.5e-144], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1999999999999998e-28 or 5.4999999999999997e-144 < z

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{t - x}{a - z}} \]

      3. mult-flip N/A

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(\left(t - x\right) \cdot \frac{1}{a - z}\right)} \]

      4. associate-*r* N/A

         \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \left(t - x\right)\right) \cdot \frac{1}{a - z}} \]

      5. *-commutative N/A

         \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

      7. frac-2neg N/A

         \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto x + \frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - z\right)\right)} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      9. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{-1}{\mathsf{neg}\left(\left(a - z\right)\right)}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      10. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      11. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{\color{blue}{z - a}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      12. lower--.f64 N/A

          \[\leadsto x + \frac{-1}{\color{blue}{z - a}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(y - z\right)} \cdot \left(t - x\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(\mathsf{neg}\left(\left(z - y\right)\right)\right)} \cdot \left(t - x\right)\right) \]

      15. distribute-lft-neg-out N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - y\right) \cdot \left(t - x\right)\right)\right)} \]

      16. distribute-rgt-neg-out N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)} \]

      17. lower-*.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)} \]

      18. lower--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(z - y\right)} \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      19. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t - x\right)}\right)\right)\right) \]

      20. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \color{blue}{\left(x - t\right)}\right) \]

      21. lower--.f64 68.2%

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \color{blue}{\left(x - t\right)}\right) \]

   3. Applied rewrites 68.2%

      \[\leadsto x + \color{blue}{\frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \left(x - t\right)\right)} \]

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \color{blue}{\frac{y}{z - a}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{\color{blue}{y}}{z - a}\right) \]

      4. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{\color{blue}{z - a}}\right) \]

      6. lower--.f64 51.7%

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - \color{blue}{a}}\right) \]

   6. Applied rewrites 51.7%

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

   7. Taylor expanded in a around 0

      \[\leadsto t \cdot \left(1 - \color{blue}{\frac{y}{z}}\right) \]
   8. Step-by-step derivation

      1. lower--.f64 N/A

         \[\leadsto t \cdot \left(1 - \frac{y}{\color{blue}{z}}\right) \]

      2. lower-/.f64 36.6%

         \[\leadsto t \cdot \left(1 - \frac{y}{z}\right) \]

   9. Applied rewrites 36.6%

      \[\leadsto t \cdot \left(1 - \color{blue}{\frac{y}{z}}\right) \]

   if -3.1999999999999998e-28 < z < 5.4999999999999997e-144

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   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. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.5%

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      3. lower-*.f64 41.5%

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      4. lift--.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      5. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      6. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      7. sub-div N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      8. lower-/.f64 N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      9. lift--.f64 41.8%

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

   6. Applied rewrites 41.8%

      \[\leadsto \frac{t - x}{a - z} \cdot \color{blue}{y} \]

   7. Taylor expanded in z around 0

      \[\leadsto \frac{t - x}{a} \cdot y \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t - x}{a} \cdot y \]

      2. lower--.f64 24.9%

         \[\leadsto \frac{t - x}{a} \cdot y \]

   9. Applied rewrites 24.9%

      \[\leadsto \frac{t - x}{a} \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 36.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \frac{t - x}{a} \cdot y\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-182}:\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+31}:\\ \;\;\;\;\frac{t \cdot z}{z - a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* (/ (- t x) a) y)))
  (if (<= y -2.5e-53)
    t_1
    (if (<= y -2e-182)
      (+ x (- t x))
      (if (<= y 4e+31) (/ (* t z) (- z a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((t - x) / a) * y;
	double tmp;
	if (y <= -2.5e-53) {
		tmp = t_1;
	} else if (y <= -2e-182) {
		tmp = x + (t - x);
	} else if (y <= 4e+31) {
		tmp = (t * z) / (z - a);
	} 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 = ((t - x) / a) * y
    if (y <= (-2.5d-53)) then
        tmp = t_1
    else if (y <= (-2d-182)) then
        tmp = x + (t - x)
    else if (y <= 4d+31) then
        tmp = (t * z) / (z - a)
    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 - x) / a) * y;
	double tmp;
	if (y <= -2.5e-53) {
		tmp = t_1;
	} else if (y <= -2e-182) {
		tmp = x + (t - x);
	} else if (y <= 4e+31) {
		tmp = (t * z) / (z - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((t - x) / a) * y
	tmp = 0
	if y <= -2.5e-53:
		tmp = t_1
	elif y <= -2e-182:
		tmp = x + (t - x)
	elif y <= 4e+31:
		tmp = (t * z) / (z - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(t - x) / a) * y)
	tmp = 0.0
	if (y <= -2.5e-53)
		tmp = t_1;
	elseif (y <= -2e-182)
		tmp = Float64(x + Float64(t - x));
	elseif (y <= 4e+31)
		tmp = Float64(Float64(t * z) / Float64(z - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((t - x) / a) * y;
	tmp = 0.0;
	if (y <= -2.5e-53)
		tmp = t_1;
	elseif (y <= -2e-182)
		tmp = x + (t - x);
	elseif (y <= 4e+31)
		tmp = (t * z) / (z - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -2.5e-53], t$95$1, If[LessEqual[y, -2e-182], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+31], N[(N[(t * z), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5e-53 or 3.9999999999999999e31 < y

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   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. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.5%

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      3. lower-*.f64 41.5%

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      4. lift--.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      5. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      6. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      7. sub-div N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      8. lower-/.f64 N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      9. lift--.f64 41.8%

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

   6. Applied rewrites 41.8%

      \[\leadsto \frac{t - x}{a - z} \cdot \color{blue}{y} \]

   7. Taylor expanded in z around 0

      \[\leadsto \frac{t - x}{a} \cdot y \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t - x}{a} \cdot y \]

      2. lower--.f64 24.9%

         \[\leadsto \frac{t - x}{a} \cdot y \]

   9. Applied rewrites 24.9%

      \[\leadsto \frac{t - x}{a} \cdot y \]

   if -2.5e-53 < y < -2.0000000000000001e-182

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 19.7%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 19.7%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   if -2.0000000000000001e-182 < y < 3.9999999999999999e31

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{t - x}{a - z}} \]

      3. mult-flip N/A

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(\left(t - x\right) \cdot \frac{1}{a - z}\right)} \]

      4. associate-*r* N/A

         \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \left(t - x\right)\right) \cdot \frac{1}{a - z}} \]

      5. *-commutative N/A

         \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

      7. frac-2neg N/A

         \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto x + \frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - z\right)\right)} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      9. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{-1}{\mathsf{neg}\left(\left(a - z\right)\right)}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      10. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      11. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{\color{blue}{z - a}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      12. lower--.f64 N/A

          \[\leadsto x + \frac{-1}{\color{blue}{z - a}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(y - z\right)} \cdot \left(t - x\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(\mathsf{neg}\left(\left(z - y\right)\right)\right)} \cdot \left(t - x\right)\right) \]

      15. distribute-lft-neg-out N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - y\right) \cdot \left(t - x\right)\right)\right)} \]

      16. distribute-rgt-neg-out N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)} \]

      17. lower-*.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)} \]

      18. lower--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(z - y\right)} \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      19. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t - x\right)}\right)\right)\right) \]

      20. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \color{blue}{\left(x - t\right)}\right) \]

      21. lower--.f64 68.2%

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \color{blue}{\left(x - t\right)}\right) \]

   3. Applied rewrites 68.2%

      \[\leadsto x + \color{blue}{\frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \left(x - t\right)\right)} \]

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \color{blue}{\frac{y}{z - a}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{\color{blue}{y}}{z - a}\right) \]

      4. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{\color{blue}{z - a}}\right) \]

      6. lower--.f64 51.7%

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - \color{blue}{a}}\right) \]

   6. Applied rewrites 51.7%

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

   7. Taylor expanded in y around 0

      \[\leadsto \frac{t \cdot z}{\color{blue}{z - a}} \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t \cdot z}{z - \color{blue}{a}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{t \cdot z}{z - a} \]

      3. lower--.f64 21.8%

         \[\leadsto \frac{t \cdot z}{z - a} \]

   9. Applied rewrites 21.8%

      \[\leadsto \frac{t \cdot z}{\color{blue}{z - a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 17: 35.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := x + \left(t - x\right)\\ \mathbf{if}\;z \leq -3500000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 110000000:\\ \;\;\;\;\frac{t - x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (- t x))))
  (if (<= z -3500000000000.0)
    t_1
    (if (<= z 110000000.0) (* (/ (- t x) a) y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t - x);
	double tmp;
	if (z <= -3500000000000.0) {
		tmp = t_1;
	} else if (z <= 110000000.0) {
		tmp = ((t - x) / a) * y;
	} 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 - x)
    if (z <= (-3500000000000.0d0)) then
        tmp = t_1
    else if (z <= 110000000.0d0) then
        tmp = ((t - x) / a) * y
    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 - x);
	double tmp;
	if (z <= -3500000000000.0) {
		tmp = t_1;
	} else if (z <= 110000000.0) {
		tmp = ((t - x) / a) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t - x)
	tmp = 0
	if z <= -3500000000000.0:
		tmp = t_1
	elif z <= 110000000.0:
		tmp = ((t - x) / a) * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t - x))
	tmp = 0.0
	if (z <= -3500000000000.0)
		tmp = t_1;
	elseif (z <= 110000000.0)
		tmp = Float64(Float64(Float64(t - x) / a) * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t - x);
	tmp = 0.0;
	if (z <= -3500000000000.0)
		tmp = t_1;
	elseif (z <= 110000000.0)
		tmp = ((t - x) / a) * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3500000000000.0], t$95$1, If[LessEqual[z, 110000000.0], N[(N[(N[(t - x), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5e12 or 1.1e8 < z

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 19.7%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 19.7%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   if -3.5e12 < z < 1.1e8

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   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. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.5%

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      3. lower-*.f64 41.5%

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      4. lift--.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      5. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      6. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      7. sub-div N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      8. lower-/.f64 N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      9. lift--.f64 41.8%

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

   6. Applied rewrites 41.8%

      \[\leadsto \frac{t - x}{a - z} \cdot \color{blue}{y} \]

   7. Taylor expanded in z around 0

      \[\leadsto \frac{t - x}{a} \cdot y \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t - x}{a} \cdot y \]

      2. lower--.f64 24.9%

         \[\leadsto \frac{t - x}{a} \cdot y \]

   9. Applied rewrites 24.9%

      \[\leadsto \frac{t - x}{a} \cdot y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 32.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \frac{t}{a - z} \cdot y\\ \mathbf{if}\;y \leq -1.62 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \frac{y - a}{z}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+50}:\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* (/ t (- a z)) y)))
  (if (<= y -1.62e+131)
    t_1
    (if (<= y -5.2e-11)
      (* x (/ (- y a) z))
      (if (<= y 1.45e+50) (+ x (- t x)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / (a - z)) * y;
	double tmp;
	if (y <= -1.62e+131) {
		tmp = t_1;
	} else if (y <= -5.2e-11) {
		tmp = x * ((y - a) / z);
	} else if (y <= 1.45e+50) {
		tmp = x + (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t / (a - z)) * y
    if (y <= (-1.62d+131)) then
        tmp = t_1
    else if (y <= (-5.2d-11)) then
        tmp = x * ((y - a) / z)
    else if (y <= 1.45d+50) then
        tmp = x + (t - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / (a - z)) * y;
	double tmp;
	if (y <= -1.62e+131) {
		tmp = t_1;
	} else if (y <= -5.2e-11) {
		tmp = x * ((y - a) / z);
	} else if (y <= 1.45e+50) {
		tmp = x + (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t / (a - z)) * y
	tmp = 0
	if y <= -1.62e+131:
		tmp = t_1
	elif y <= -5.2e-11:
		tmp = x * ((y - a) / z)
	elif y <= 1.45e+50:
		tmp = x + (t - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t / Float64(a - z)) * y)
	tmp = 0.0
	if (y <= -1.62e+131)
		tmp = t_1;
	elseif (y <= -5.2e-11)
		tmp = Float64(x * Float64(Float64(y - a) / z));
	elseif (y <= 1.45e+50)
		tmp = Float64(x + Float64(t - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t / (a - z)) * y;
	tmp = 0.0;
	if (y <= -1.62e+131)
		tmp = t_1;
	elseif (y <= -5.2e-11)
		tmp = x * ((y - a) / z);
	elseif (y <= 1.45e+50)
		tmp = x + (t - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -1.62e+131], t$95$1, If[LessEqual[y, -5.2e-11], N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+50], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6199999999999999e131 or 1.45e50 < y

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   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. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.5%

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      3. lower-*.f64 41.5%

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot \color{blue}{y} \]

      4. lift--.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      5. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      6. lift-/.f64 N/A

         \[\leadsto \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \cdot y \]

      7. sub-div N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      8. lower-/.f64 N/A

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

      9. lift--.f64 41.8%

         \[\leadsto \frac{t - x}{a - z} \cdot y \]

   6. Applied rewrites 41.8%

      \[\leadsto \frac{t - x}{a - z} \cdot \color{blue}{y} \]

   7. Taylor expanded in x around 0

      \[\leadsto \frac{t}{a - z} \cdot y \]
   8. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t}{a - z} \cdot y \]

      2. lower--.f64 23.1%

         \[\leadsto \frac{t}{a - z} \cdot y \]

   9. Applied rewrites 23.1%

      \[\leadsto \frac{t}{a - z} \cdot y \]

   if -1.6199999999999999e131 < y < -5.2000000000000001e-11

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   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. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{y - z}{a - z}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{y - z}{a - z}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{\color{blue}{a - z}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{\color{blue}{a} - z}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{y}{a}}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{\color{blue}{a}}\right) \]

      2. lower-/.f64 36.0%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{a}\right) \]

   7. Applied rewrites 36.0%

      \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{y}{a}}\right) \]

   8. Taylor expanded in z around -inf

      \[\leadsto x \cdot \frac{y - a}{\color{blue}{z}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x \cdot \frac{y - a}{z} \]

      2. lower--.f64 23.6%

         \[\leadsto x \cdot \frac{y - a}{z} \]

   10. Applied rewrites 23.6%

       \[\leadsto x \cdot \frac{y - a}{\color{blue}{z}} \]

   if -5.2000000000000001e-11 < y < 1.45e50

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 19.7%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 19.7%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 19: 30.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \frac{x \cdot \left(y - a\right)}{z}\\ t_2 := x + \left(t - x\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{-15}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-142}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (* x (- y a)) z)) (t_2 (+ x (- t x))))
  (if (<= z -6.8e-15)
    t_2
    (if (<= z -6e-169)
      t_1
      (if (<= z 5e-142) (/ (* t y) a) (if (<= z 1.85e+81) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * (y - a)) / z;
	double t_2 = x + (t - x);
	double tmp;
	if (z <= -6.8e-15) {
		tmp = t_2;
	} else if (z <= -6e-169) {
		tmp = t_1;
	} else if (z <= 5e-142) {
		tmp = (t * y) / a;
	} else if (z <= 1.85e+81) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = (x * (y - a)) / z
    t_2 = x + (t - x)
    if (z <= (-6.8d-15)) then
        tmp = t_2
    else if (z <= (-6d-169)) then
        tmp = t_1
    else if (z <= 5d-142) then
        tmp = (t * y) / a
    else if (z <= 1.85d+81) then
        tmp = t_1
    else
        tmp = t_2
    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 - a)) / z;
	double t_2 = x + (t - x);
	double tmp;
	if (z <= -6.8e-15) {
		tmp = t_2;
	} else if (z <= -6e-169) {
		tmp = t_1;
	} else if (z <= 5e-142) {
		tmp = (t * y) / a;
	} else if (z <= 1.85e+81) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * (y - a)) / z
	t_2 = x + (t - x)
	tmp = 0
	if z <= -6.8e-15:
		tmp = t_2
	elif z <= -6e-169:
		tmp = t_1
	elif z <= 5e-142:
		tmp = (t * y) / a
	elif z <= 1.85e+81:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * Float64(y - a)) / z)
	t_2 = Float64(x + Float64(t - x))
	tmp = 0.0
	if (z <= -6.8e-15)
		tmp = t_2;
	elseif (z <= -6e-169)
		tmp = t_1;
	elseif (z <= 5e-142)
		tmp = Float64(Float64(t * y) / a);
	elseif (z <= 1.85e+81)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * (y - a)) / z;
	t_2 = x + (t - x);
	tmp = 0.0;
	if (z <= -6.8e-15)
		tmp = t_2;
	elseif (z <= -6e-169)
		tmp = t_1;
	elseif (z <= 5e-142)
		tmp = (t * y) / a;
	elseif (z <= 1.85e+81)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e-15], t$95$2, If[LessEqual[z, -6e-169], t$95$1, If[LessEqual[z, 5e-142], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 1.85e+81], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8000000000000001e-15 or 1.85e81 < z

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 19.7%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 19.7%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   if -6.8000000000000001e-15 < z < -5.9999999999999998e-169 or 5.0000000000000002e-142 < z < 1.85e81

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   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. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{y - z}{a - z}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{y - z}{a - z}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{\color{blue}{a - z}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{\color{blue}{a} - z}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]

   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. lower--.f64 20.0%

         \[\leadsto \frac{x \cdot \left(y - a\right)}{z} \]

   7. Applied rewrites 20.0%

      \[\leadsto \frac{x \cdot \left(y - a\right)}{\color{blue}{z}} \]

   if -5.9999999999999998e-169 < z < 5.0000000000000002e-142

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{t - x}{a - z}} \]

      3. mult-flip N/A

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(\left(t - x\right) \cdot \frac{1}{a - z}\right)} \]

      4. associate-*r* N/A

         \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \left(t - x\right)\right) \cdot \frac{1}{a - z}} \]

      5. *-commutative N/A

         \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

      7. frac-2neg N/A

         \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto x + \frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - z\right)\right)} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      9. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{-1}{\mathsf{neg}\left(\left(a - z\right)\right)}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      10. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      11. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{\color{blue}{z - a}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      12. lower--.f64 N/A

          \[\leadsto x + \frac{-1}{\color{blue}{z - a}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(y - z\right)} \cdot \left(t - x\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(\mathsf{neg}\left(\left(z - y\right)\right)\right)} \cdot \left(t - x\right)\right) \]

      15. distribute-lft-neg-out N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - y\right) \cdot \left(t - x\right)\right)\right)} \]

      16. distribute-rgt-neg-out N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)} \]

      17. lower-*.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)} \]

      18. lower--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(z - y\right)} \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      19. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t - x\right)}\right)\right)\right) \]

      20. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \color{blue}{\left(x - t\right)}\right) \]

      21. lower--.f64 68.2%

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \color{blue}{\left(x - t\right)}\right) \]

   3. Applied rewrites 68.2%

      \[\leadsto x + \color{blue}{\frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \left(x - t\right)\right)} \]

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \color{blue}{\frac{y}{z - a}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{\color{blue}{y}}{z - a}\right) \]

      4. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{\color{blue}{z - a}}\right) \]

      6. lower--.f64 51.7%

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - \color{blue}{a}}\right) \]

   6. Applied rewrites 51.7%

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

   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 16.5%

         \[\leadsto \frac{t \cdot y}{a} \]

   9. Applied rewrites 16.5%

      \[\leadsto \frac{t \cdot y}{\color{blue}{a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 30.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := x + \left(t - x\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-169}:\\ \;\;\;\;\frac{x \cdot \left(y - a\right)}{z}\\ \mathbf{elif}\;z \leq 0.0024:\\ \;\;\;\;\frac{t \cdot y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (- t x))))
  (if (<= z -6.8e-15)
    t_1
    (if (<= z -6e-169)
      (/ (* x (- y a)) z)
      (if (<= z 0.0024) (/ (* t y) (- a z)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t - x);
	double tmp;
	if (z <= -6.8e-15) {
		tmp = t_1;
	} else if (z <= -6e-169) {
		tmp = (x * (y - a)) / z;
	} else if (z <= 0.0024) {
		tmp = (t * 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 - x)
    if (z <= (-6.8d-15)) then
        tmp = t_1
    else if (z <= (-6d-169)) then
        tmp = (x * (y - a)) / z
    else if (z <= 0.0024d0) then
        tmp = (t * 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 - x);
	double tmp;
	if (z <= -6.8e-15) {
		tmp = t_1;
	} else if (z <= -6e-169) {
		tmp = (x * (y - a)) / z;
	} else if (z <= 0.0024) {
		tmp = (t * y) / (a - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t - x)
	tmp = 0
	if z <= -6.8e-15:
		tmp = t_1
	elif z <= -6e-169:
		tmp = (x * (y - a)) / z
	elif z <= 0.0024:
		tmp = (t * y) / (a - z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t - x))
	tmp = 0.0
	if (z <= -6.8e-15)
		tmp = t_1;
	elseif (z <= -6e-169)
		tmp = Float64(Float64(x * Float64(y - a)) / z);
	elseif (z <= 0.0024)
		tmp = Float64(Float64(t * 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 - x);
	tmp = 0.0;
	if (z <= -6.8e-15)
		tmp = t_1;
	elseif (z <= -6e-169)
		tmp = (x * (y - a)) / z;
	elseif (z <= 0.0024)
		tmp = (t * 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 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e-15], t$95$1, If[LessEqual[z, -6e-169], N[(N[(x * N[(y - a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 0.0024], N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8000000000000001e-15 or 0.0023999999999999998 < z

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 19.7%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 19.7%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   if -6.8000000000000001e-15 < z < -5.9999999999999998e-169

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   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. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{y - z}{a - z}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{y - z}{a - z}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{\color{blue}{a - z}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{\color{blue}{a} - z}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]

   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. lower--.f64 20.0%

         \[\leadsto \frac{x \cdot \left(y - a\right)}{z} \]

   7. Applied rewrites 20.0%

      \[\leadsto \frac{x \cdot \left(y - a\right)}{\color{blue}{z}} \]

   if -5.9999999999999998e-169 < z < 0.0023999999999999998

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   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. lower-*.f64 N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \color{blue}{\frac{x}{a - z}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{\color{blue}{x}}{a - z}\right) \]

      4. lower--.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{\color{blue}{a - z}}\right) \]

      6. lower--.f64 41.5%

         \[\leadsto y \cdot \left(\frac{t}{a - z} - \frac{x}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 41.5%

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a - z} - \frac{x}{a - z}\right)} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{t \cdot y}{\color{blue}{a - z}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{t \cdot y}{a - \color{blue}{z}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{t \cdot y}{a - z} \]

      3. lower--.f64 21.3%

         \[\leadsto \frac{t \cdot y}{a - z} \]

   7. Applied rewrites 21.3%

      \[\leadsto \frac{t \cdot y}{\color{blue}{a - z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 29.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := x \cdot \frac{y - a}{z}\\ \mathbf{if}\;x \leq -6 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+30}:\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* x (/ (- y a) z))))
  (if (<= x -6e+20) t_1 (if (<= x 2.8e+30) (+ x (- t x)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (x <= -6e+20) {
		tmp = t_1;
	} else if (x <= 2.8e+30) {
		tmp = x + (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y - a) / z)
    if (x <= (-6d+20)) then
        tmp = t_1
    else if (x <= 2.8d+30) then
        tmp = x + (t - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * ((y - a) / z);
	double tmp;
	if (x <= -6e+20) {
		tmp = t_1;
	} else if (x <= 2.8e+30) {
		tmp = x + (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * ((y - a) / z)
	tmp = 0
	if x <= -6e+20:
		tmp = t_1
	elif x <= 2.8e+30:
		tmp = x + (t - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(Float64(y - a) / z))
	tmp = 0.0
	if (x <= -6e+20)
		tmp = t_1;
	elseif (x <= 2.8e+30)
		tmp = Float64(x + Float64(t - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * ((y - a) / z);
	tmp = 0.0;
	if (x <= -6e+20)
		tmp = t_1;
	elseif (x <= 2.8e+30)
		tmp = x + (t - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(N[(y - a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+20], t$95$1, If[LessEqual[x, 2.8e+30], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -6e20 or 2.7999999999999998e30 < x

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   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. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{y - z}{a - z}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{y - z}{a - z}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{\color{blue}{a - z}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{\color{blue}{a} - z}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{y}{a}}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{\color{blue}{a}}\right) \]

      2. lower-/.f64 36.0%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{a}\right) \]

   7. Applied rewrites 36.0%

      \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{y}{a}}\right) \]

   8. Taylor expanded in z around -inf

      \[\leadsto x \cdot \frac{y - a}{\color{blue}{z}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x \cdot \frac{y - a}{z} \]

      2. lower--.f64 23.6%

         \[\leadsto x \cdot \frac{y - a}{z} \]

   10. Applied rewrites 23.6%

       \[\leadsto x \cdot \frac{y - a}{\color{blue}{z}} \]

   if -6e20 < x < 2.7999999999999998e30

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 19.7%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 19.7%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 22: 28.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := x + \left(t - x\right)\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-170}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \leq 0.0024:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (- t x))))
  (if (<= z -6.8e-15)
    t_1
    (if (<= z -9e-170)
      (/ (* x y) z)
      (if (<= z 0.0024) (/ (* t y) a) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t - x);
	double tmp;
	if (z <= -6.8e-15) {
		tmp = t_1;
	} else if (z <= -9e-170) {
		tmp = (x * y) / z;
	} else if (z <= 0.0024) {
		tmp = (t * y) / a;
	} 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 - x)
    if (z <= (-6.8d-15)) then
        tmp = t_1
    else if (z <= (-9d-170)) then
        tmp = (x * y) / z
    else if (z <= 0.0024d0) then
        tmp = (t * y) / a
    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 - x);
	double tmp;
	if (z <= -6.8e-15) {
		tmp = t_1;
	} else if (z <= -9e-170) {
		tmp = (x * y) / z;
	} else if (z <= 0.0024) {
		tmp = (t * y) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t - x)
	tmp = 0
	if z <= -6.8e-15:
		tmp = t_1
	elif z <= -9e-170:
		tmp = (x * y) / z
	elif z <= 0.0024:
		tmp = (t * y) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t - x))
	tmp = 0.0
	if (z <= -6.8e-15)
		tmp = t_1;
	elseif (z <= -9e-170)
		tmp = Float64(Float64(x * y) / z);
	elseif (z <= 0.0024)
		tmp = Float64(Float64(t * y) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t - x);
	tmp = 0.0;
	if (z <= -6.8e-15)
		tmp = t_1;
	elseif (z <= -9e-170)
		tmp = (x * y) / z;
	elseif (z <= 0.0024)
		tmp = (t * y) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.8e-15], t$95$1, If[LessEqual[z, -9e-170], N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 0.0024], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.8000000000000001e-15 or 0.0023999999999999998 < z

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 19.7%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 19.7%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]

   if -6.8000000000000001e-15 < z < -9e-170

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   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. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{y - z}{a - z}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{y - z}{a - z}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{\color{blue}{a - z}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{\color{blue}{a} - z}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{y}{a}}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{\color{blue}{a}}\right) \]

      2. lower-/.f64 36.0%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{a}\right) \]

   7. Applied rewrites 36.0%

      \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{y}{a}}\right) \]

   8. Taylor expanded in a around 0

      \[\leadsto \frac{x \cdot y}{\color{blue}{z}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot y}{z} \]

      2. lower-*.f64 16.7%

         \[\leadsto \frac{x \cdot y}{z} \]

   10. Applied rewrites 16.7%

       \[\leadsto \frac{x \cdot y}{\color{blue}{z}} \]

   if -9e-170 < z < 0.0023999999999999998

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]
   2. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto x + \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\frac{t - x}{a - z}} \]

      3. mult-flip N/A

         \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(\left(t - x\right) \cdot \frac{1}{a - z}\right)} \]

      4. associate-*r* N/A

         \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \left(t - x\right)\right) \cdot \frac{1}{a - z}} \]

      5. *-commutative N/A

         \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

      6. lower-*.f64 N/A

         \[\leadsto x + \color{blue}{\frac{1}{a - z} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right)} \]

      7. frac-2neg N/A

         \[\leadsto x + \color{blue}{\frac{\mathsf{neg}\left(1\right)}{\mathsf{neg}\left(\left(a - z\right)\right)}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto x + \frac{\color{blue}{-1}}{\mathsf{neg}\left(\left(a - z\right)\right)} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      9. lower-/.f64 N/A

         \[\leadsto x + \color{blue}{\frac{-1}{\mathsf{neg}\left(\left(a - z\right)\right)}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      10. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{\mathsf{neg}\left(\color{blue}{\left(a - z\right)}\right)} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      11. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{\color{blue}{z - a}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      12. lower--.f64 N/A

          \[\leadsto x + \frac{-1}{\color{blue}{z - a}} \cdot \left(\left(y - z\right) \cdot \left(t - x\right)\right) \]

      13. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(y - z\right)} \cdot \left(t - x\right)\right) \]

      14. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(\mathsf{neg}\left(\left(z - y\right)\right)\right)} \cdot \left(t - x\right)\right) \]

      15. distribute-lft-neg-out N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z - y\right) \cdot \left(t - x\right)\right)\right)} \]

      16. distribute-rgt-neg-out N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)} \]

      17. lower-*.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \color{blue}{\left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right)} \]

      18. lower--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\color{blue}{\left(z - y\right)} \cdot \left(\mathsf{neg}\left(\left(t - x\right)\right)\right)\right) \]

      19. lift--.f64 N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \left(\mathsf{neg}\left(\color{blue}{\left(t - x\right)}\right)\right)\right) \]

      20. sub-negate-rev N/A

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \color{blue}{\left(x - t\right)}\right) \]

      21. lower--.f64 68.2%

          \[\leadsto x + \frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \color{blue}{\left(x - t\right)}\right) \]

   3. Applied rewrites 68.2%

      \[\leadsto x + \color{blue}{\frac{-1}{z - a} \cdot \left(\left(z - y\right) \cdot \left(x - t\right)\right)} \]

   4. Taylor expanded in t around inf

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]
   5. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto t \cdot \color{blue}{\left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

      2. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \color{blue}{\frac{y}{z - a}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{\color{blue}{y}}{z - a}\right) \]

      4. lower--.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right) \]

      5. lower-/.f64 N/A

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{\color{blue}{z - a}}\right) \]

      6. lower--.f64 51.7%

         \[\leadsto t \cdot \left(\frac{z}{z - a} - \frac{y}{z - \color{blue}{a}}\right) \]

   6. Applied rewrites 51.7%

      \[\leadsto \color{blue}{t \cdot \left(\frac{z}{z - a} - \frac{y}{z - a}\right)} \]

   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 16.5%

         \[\leadsto \frac{t \cdot y}{a} \]

   9. Applied rewrites 16.5%

      \[\leadsto \frac{t \cdot y}{\color{blue}{a}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 23: 26.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \frac{x \cdot y}{z}\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+30}:\\ \;\;\;\;x + \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (* x y) z)))
  (if (<= x -1.05e+83) t_1 (if (<= x 2.8e+30) (+ x (- t x)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / z;
	double tmp;
	if (x <= -1.05e+83) {
		tmp = t_1;
	} else if (x <= 2.8e+30) {
		tmp = x + (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) / z
    if (x <= (-1.05d+83)) then
        tmp = t_1
    else if (x <= 2.8d+30) then
        tmp = x + (t - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) / z;
	double tmp;
	if (x <= -1.05e+83) {
		tmp = t_1;
	} else if (x <= 2.8e+30) {
		tmp = x + (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x * y) / z
	tmp = 0
	if x <= -1.05e+83:
		tmp = t_1
	elif x <= 2.8e+30:
		tmp = x + (t - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) / z)
	tmp = 0.0
	if (x <= -1.05e+83)
		tmp = t_1;
	elseif (x <= 2.8e+30)
		tmp = Float64(x + Float64(t - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) / z;
	tmp = 0.0;
	if (x <= -1.05e+83)
		tmp = t_1;
	elseif (x <= 2.8e+30)
		tmp = x + (t - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[x, -1.05e+83], t$95$1, If[LessEqual[x, 2.8e+30], N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05e83 or 2.7999999999999998e30 < x

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   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. lower-*.f64 N/A

         \[\leadsto x \cdot \color{blue}{\left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]

      2. lower-+.f64 N/A

         \[\leadsto x \cdot \left(1 + \color{blue}{-1 \cdot \frac{y - z}{a - z}}\right) \]

      3. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{y - z}{a - z}}\right) \]

      4. lower-/.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{\color{blue}{a - z}}\right) \]

      5. lower--.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{\color{blue}{a} - z}\right) \]

      6. lower--.f64 43.2%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y - z}{a - \color{blue}{z}}\right) \]

   4. Applied rewrites 43.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \frac{y - z}{a - z}\right)} \]

   5. Taylor expanded in z around 0

      \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{y}{a}}\right) \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{\color{blue}{a}}\right) \]

      2. lower-/.f64 36.0%

         \[\leadsto x \cdot \left(1 + -1 \cdot \frac{y}{a}\right) \]

   7. Applied rewrites 36.0%

      \[\leadsto x \cdot \left(1 + -1 \cdot \color{blue}{\frac{y}{a}}\right) \]

   8. Taylor expanded in a around 0

      \[\leadsto \frac{x \cdot y}{\color{blue}{z}} \]
   9. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \frac{x \cdot y}{z} \]

      2. lower-*.f64 16.7%

         \[\leadsto \frac{x \cdot y}{z} \]

   10. Applied rewrites 16.7%

       \[\leadsto \frac{x \cdot y}{\color{blue}{z}} \]

   if -1.05e83 < x < 2.7999999999999998e30

   1. Initial program 79.6%

      \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

   2. Taylor expanded in z around inf

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
   3. Step-by-step derivation

      1. lower--.f64 19.7%

         \[\leadsto x + \left(t - \color{blue}{x}\right) \]

   4. Applied rewrites 19.7%

      \[\leadsto x + \color{blue}{\left(t - x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 24: 19.7% accurate, 4.1× speedup

Math

\[x + \left(t - x\right) \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (+ x (- t x)))

C

double code(double x, double y, double z, double t, double a) {
	return x + (t - x);
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (t - x)
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (t - x);
}

Python

def code(x, y, z, t, a):
	return x + (t - x)

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(t - x))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (t - x);
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(t - x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.6%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

2. Taylor expanded in z around inf

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]
3. Step-by-step derivation

   1. lower--.f64 19.7%

      \[\leadsto x + \left(t - \color{blue}{x}\right) \]

4. Applied rewrites 19.7%

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]
5. Add Preprocessing

Alternative 25: 2.8% accurate, 4.8× speedup

Math

\[\left(-x\right) + x \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (+ (- x) x))

C

double code(double x, double y, double z, double t, double a) {
	return -x + x;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = -x + x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return -x + x;
}

Python

def code(x, y, z, t, a):
	return -x + x

Julia

function code(x, y, z, t, a)
	return Float64(Float64(-x) + x)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = -x + x;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[((-x) + x), $MachinePrecision]

Derivation

1. Initial program 79.6%

   \[x + \left(y - z\right) \cdot \frac{t - x}{a - z} \]

2. Taylor expanded in z around inf

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]
3. Step-by-step derivation

   1. lower--.f64 19.7%

      \[\leadsto x + \left(t - \color{blue}{x}\right) \]

4. Applied rewrites 19.7%

   \[\leadsto x + \color{blue}{\left(t - x\right)} \]

5. Taylor expanded in x around inf

   \[\leadsto x + -1 \cdot \color{blue}{x} \]
6. Step-by-step derivation

   1. lower-*.f64 2.8%

      \[\leadsto x + -1 \cdot x \]

7. Applied rewrites 2.8%

   \[\leadsto x + -1 \cdot \color{blue}{x} \]
8. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{x + -1 \cdot x} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{-1 \cdot x + x} \]

   3. lower-+.f64 2.8%

      \[\leadsto \color{blue}{-1 \cdot x + x} \]

   4. lift-*.f64 N/A

      \[\leadsto -1 \cdot x + x \]

   5. mul-1-neg N/A

      \[\leadsto \left(\mathsf{neg}\left(x\right)\right) + x \]

   6. lower-neg.f64 2.8%

      \[\leadsto \left(-x\right) + x \]

9. Applied rewrites 2.8%

   \[\leadsto \color{blue}{\left(-x\right) + x} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2025258 
(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)))))