Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Percentage Accurate: 96.8% → 96.8%

Time: 4.9s

Alternatives: 13

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing

Alternative 2: 94.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -200:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;-\mathsf{fma}\left(t, \frac{x}{y}, -t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -200.0)
     (* x (/ t (- z y)))
     (if (<= t_1 5e-10)
       (* (/ (- x y) z) t)
       (if (<= t_1 2.0) (- (fma t (/ x y) (- t))) (* (/ x (- z y)) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -200.0) {
		tmp = x * (t / (z - y));
	} else if (t_1 <= 5e-10) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = -fma(t, (x / y), -t);
	} else {
		tmp = (x / (z - y)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -200.0)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (t_1 <= 5e-10)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (t_1 <= 2.0)
		tmp = Float64(-fma(t, Float64(x / y), Float64(-t)));
	else
		tmp = Float64(Float64(x / Float64(z - y)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -200.0], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-10], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2.0], (-N[(t * N[(x / y), $MachinePrecision] + (-t)), $MachinePrecision]), N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -200

   1. Initial program 94.3%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 90.2

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

   3. Applied rewrites 90.2%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 89.4%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 90.1

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

   8. Applied rewrites 90.1%

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

   if -200 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5.00000000000000031e-10

   1. Initial program 95.7%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 94.4%

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

   if 5.00000000000000031e-10 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 72.0

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

   4. Applied rewrites 72.0%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 96.5

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

   7. Applied rewrites 96.5%

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

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.4%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 93.6%

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

Alternative 3: 94.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -200:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -200.0)
     (* x (/ t (- z y)))
     (if (<= t_1 5e-10)
       (* (/ (- x y) z) t)
       (if (<= t_1 2.0) (* (- 1.0 (/ x y)) t) (* (/ x (- z y)) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -200.0) {
		tmp = x * (t / (z - y));
	} else if (t_1 <= 5e-10) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = (x / (z - y)) * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= (-200.0d0)) then
        tmp = x * (t / (z - y))
    else if (t_1 <= 5d-10) then
        tmp = ((x - y) / z) * t
    else if (t_1 <= 2.0d0) then
        tmp = (1.0d0 - (x / y)) * t
    else
        tmp = (x / (z - y)) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -200.0) {
		tmp = x * (t / (z - y));
	} else if (t_1 <= 5e-10) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 2.0) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = (x / (z - y)) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -200.0:
		tmp = x * (t / (z - y))
	elif t_1 <= 5e-10:
		tmp = ((x - y) / z) * t
	elif t_1 <= 2.0:
		tmp = (1.0 - (x / y)) * t
	else:
		tmp = (x / (z - y)) * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -200.0)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (t_1 <= 5e-10)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (t_1 <= 2.0)
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	else
		tmp = Float64(Float64(x / Float64(z - y)) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -200.0)
		tmp = x * (t / (z - y));
	elseif (t_1 <= 5e-10)
		tmp = ((x - y) / z) * t;
	elseif (t_1 <= 2.0)
		tmp = (1.0 - (x / y)) * t;
	else
		tmp = (x / (z - y)) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -200.0], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-10], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -200

   1. Initial program 94.3%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 90.2

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

   3. Applied rewrites 90.2%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 89.4%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 90.1

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

   8. Applied rewrites 90.1%

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

   if -200 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5.00000000000000031e-10

   1. Initial program 95.7%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 94.4%

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

   if 5.00000000000000031e-10 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 72.0

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

   4. Applied rewrites 72.0%

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

   5. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 96.4

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

   7. Applied rewrites 96.4%

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

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.4%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 93.6%

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

Alternative 4: 93.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;-\mathsf{fma}\left(t, \frac{x}{y}, -t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 5e-10)
     (* (- x y) (/ t (- z y)))
     (if (<= t_1 2.0) (- (fma t (/ x y) (- t))) (* (/ x (- z y)) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e-10) {
		tmp = (x - y) * (t / (z - y));
	} else if (t_1 <= 2.0) {
		tmp = -fma(t, (x / y), -t);
	} else {
		tmp = (x / (z - y)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 5e-10)
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	elseif (t_1 <= 2.0)
		tmp = Float64(-fma(t, Float64(x / y), Float64(-t)));
	else
		tmp = Float64(Float64(x / Float64(z - y)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-10], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], (-N[(t * N[(x / y), $MachinePrecision] + (-t)), $MachinePrecision]), N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 5.00000000000000031e-10

   1. Initial program 95.2%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 89.5

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

   3. Applied rewrites 89.5%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 90.5

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

   5. Applied rewrites 90.5%

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

   if 5.00000000000000031e-10 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 72.0

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

   4. Applied rewrites 72.0%

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

   5. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 96.5

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

   7. Applied rewrites 96.5%

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

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.4%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 93.6%

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

Alternative 5: 91.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -200:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-15}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 -200.0)
     (* x (/ t (- z y)))
     (if (<= t_1 2e-15)
       (/ (* (- x y) t) z)
       (if (<= t_1 2.0) (* (- 1.0 (/ x y)) t) (* (/ x (- z y)) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -200.0) {
		tmp = x * (t / (z - y));
	} else if (t_1 <= 2e-15) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2.0) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = (x / (z - y)) * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= (-200.0d0)) then
        tmp = x * (t / (z - y))
    else if (t_1 <= 2d-15) then
        tmp = ((x - y) * t) / z
    else if (t_1 <= 2.0d0) then
        tmp = (1.0d0 - (x / y)) * t
    else
        tmp = (x / (z - y)) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -200.0) {
		tmp = x * (t / (z - y));
	} else if (t_1 <= 2e-15) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2.0) {
		tmp = (1.0 - (x / y)) * t;
	} else {
		tmp = (x / (z - y)) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -200.0:
		tmp = x * (t / (z - y))
	elif t_1 <= 2e-15:
		tmp = ((x - y) * t) / z
	elif t_1 <= 2.0:
		tmp = (1.0 - (x / y)) * t
	else:
		tmp = (x / (z - y)) * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -200.0)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (t_1 <= 2e-15)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (t_1 <= 2.0)
		tmp = Float64(Float64(1.0 - Float64(x / y)) * t);
	else
		tmp = Float64(Float64(x / Float64(z - y)) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -200.0)
		tmp = x * (t / (z - y));
	elseif (t_1 <= 2e-15)
		tmp = ((x - y) * t) / z;
	elseif (t_1 <= 2.0)
		tmp = (1.0 - (x / y)) * t;
	else
		tmp = (x / (z - y)) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -200.0], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-15], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -200

   1. Initial program 94.3%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 90.2

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

   3. Applied rewrites 90.2%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 89.4%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 90.1

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

   8. Applied rewrites 90.1%

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

   if -200 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2.0000000000000002e-15

   1. Initial program 95.6%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 88.3

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

   4. Applied rewrites 88.3%

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

   if 2.0000000000000002e-15 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 71.2

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

   4. Applied rewrites 71.2%

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

   5. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 95.4

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

   7. Applied rewrites 95.4%

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

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.4%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 93.6%

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

Alternative 6: 91.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := x \cdot \frac{t}{z - y}\\ \mathbf{if}\;t\_1 \leq -200:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-15}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 50000000:\\ \;\;\;\;\frac{y - x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* x (/ t (- z y)))))
   (if (<= t_1 -200.0)
     t_2
     (if (<= t_1 2e-15)
       (/ (* (- x y) t) z)
       (if (<= t_1 50000000.0) (* (/ (- y x) y) t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = x * (t / (z - y));
	double tmp;
	if (t_1 <= -200.0) {
		tmp = t_2;
	} else if (t_1 <= 2e-15) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 50000000.0) {
		tmp = ((y - x) / y) * t;
	} 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)
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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = x * (t / (z - y))
    if (t_1 <= (-200.0d0)) then
        tmp = t_2
    else if (t_1 <= 2d-15) then
        tmp = ((x - y) * t) / z
    else if (t_1 <= 50000000.0d0) then
        tmp = ((y - x) / y) * t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = x * (t / (z - y));
	double tmp;
	if (t_1 <= -200.0) {
		tmp = t_2;
	} else if (t_1 <= 2e-15) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 50000000.0) {
		tmp = ((y - x) / y) * t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = x * (t / (z - y))
	tmp = 0
	if t_1 <= -200.0:
		tmp = t_2
	elif t_1 <= 2e-15:
		tmp = ((x - y) * t) / z
	elif t_1 <= 50000000.0:
		tmp = ((y - x) / y) * t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(x * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= -200.0)
		tmp = t_2;
	elseif (t_1 <= 2e-15)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (t_1 <= 50000000.0)
		tmp = Float64(Float64(Float64(y - x) / y) * t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = x * (t / (z - y));
	tmp = 0.0;
	if (t_1 <= -200.0)
		tmp = t_2;
	elseif (t_1 <= 2e-15)
		tmp = ((x - y) * t) / z;
	elseif (t_1 <= 50000000.0)
		tmp = ((y - x) / y) * t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -200.0], t$95$2, If[LessEqual[t$95$1, 2e-15], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 50000000.0], N[(N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision] * t), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -200 or 5e7 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 94.8%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-/.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift--.f64 89.8

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

   3. Applied rewrites 89.8%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 89.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 90.3

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

   8. Applied rewrites 90.3%

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

   if -200 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2.0000000000000002e-15

   1. Initial program 95.6%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 88.3

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

   4. Applied rewrites 88.3%

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

   if 2.0000000000000002e-15 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5e7

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 71.1

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

   4. Applied rewrites 71.1%

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

   5. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 95.0

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

   7. Applied rewrites 95.0%

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

   8. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 95.0

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

   10. Applied rewrites 95.0%

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

Alternative 7: 79.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-15}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+86}:\\ \;\;\;\;\frac{y - x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 2e-15)
     (/ (* (- x y) t) z)
     (if (<= t_1 2e+86) (* (/ (- y x) y) t) (* (/ x z) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 2e-15) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2e+86) {
		tmp = ((y - x) / y) * t;
	} else {
		tmp = (x / z) * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 2d-15) then
        tmp = ((x - y) * t) / z
    else if (t_1 <= 2d+86) then
        tmp = ((y - x) / y) * t
    else
        tmp = (x / z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 2e-15) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 2e+86) {
		tmp = ((y - x) / y) * t;
	} else {
		tmp = (x / z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 2e-15:
		tmp = ((x - y) * t) / z
	elif t_1 <= 2e+86:
		tmp = ((y - x) / y) * t
	else:
		tmp = (x / z) * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 2e-15)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (t_1 <= 2e+86)
		tmp = Float64(Float64(Float64(y - x) / y) * t);
	else
		tmp = Float64(Float64(x / z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 2e-15)
		tmp = ((x - y) * t) / z;
	elseif (t_1 <= 2e+86)
		tmp = ((y - x) / y) * t;
	else
		tmp = (x / z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e-15], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2e+86], N[(N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision] * t), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 2.0000000000000002e-15

   1. Initial program 95.2%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 75.9

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

   4. Applied rewrites 75.9%

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

   if 2.0000000000000002e-15 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e86

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 67.5

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

   4. Applied rewrites 67.5%

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

   5. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 89.6

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

   7. Applied rewrites 89.6%

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

   8. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 89.6

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

   10. Applied rewrites 89.6%

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

   if 2e86 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 93.1%

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

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 54.1

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

   4. Applied rewrites 54.1%

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

Alternative 8: 79.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-10}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+86}:\\ \;\;\;\;\frac{y - x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 5e-10)
     (* (- x y) (/ t z))
     (if (<= t_1 2e+86) (* (/ (- y x) y) t) (* (/ x z) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e-10) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 2e+86) {
		tmp = ((y - x) / y) * t;
	} else {
		tmp = (x / z) * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 5d-10) then
        tmp = (x - y) * (t / z)
    else if (t_1 <= 2d+86) then
        tmp = ((y - x) / y) * t
    else
        tmp = (x / z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e-10) {
		tmp = (x - y) * (t / z);
	} else if (t_1 <= 2e+86) {
		tmp = ((y - x) / y) * t;
	} else {
		tmp = (x / z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 5e-10:
		tmp = (x - y) * (t / z)
	elif t_1 <= 2e+86:
		tmp = ((y - x) / y) * t
	else:
		tmp = (x / z) * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 5e-10)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (t_1 <= 2e+86)
		tmp = Float64(Float64(Float64(y - x) / y) * t);
	else
		tmp = Float64(Float64(x / z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 5e-10)
		tmp = (x - y) * (t / z);
	elseif (t_1 <= 2e+86)
		tmp = ((y - x) / y) * t;
	else
		tmp = (x / z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-10], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+86], N[(N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision] * t), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 5.00000000000000031e-10

   1. Initial program 95.2%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 76.0

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

   4. Applied rewrites 76.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. associate-/l* N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lower-/.f64 76.8

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

   6. Applied rewrites 76.8%

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

   if 5.00000000000000031e-10 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e86

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 68.2

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

   4. Applied rewrites 68.2%

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

   5. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 90.4

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

   7. Applied rewrites 90.4%

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

   8. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 90.4

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

   10. Applied rewrites 90.4%

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

   if 2e86 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 93.1%

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

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 54.1

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

   4. Applied rewrites 54.1%

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

Alternative 9: 69.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-16}:\\ \;\;\;\;\frac{t}{z} \cdot x\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+86}:\\ \;\;\;\;\frac{y - x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 5e-16)
     (* (/ t z) x)
     (if (<= t_1 2e+86) (* (/ (- y x) y) t) (* (/ x z) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e-16) {
		tmp = (t / z) * x;
	} else if (t_1 <= 2e+86) {
		tmp = ((y - x) / y) * t;
	} else {
		tmp = (x / z) * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 5d-16) then
        tmp = (t / z) * x
    else if (t_1 <= 2d+86) then
        tmp = ((y - x) / y) * t
    else
        tmp = (x / z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e-16) {
		tmp = (t / z) * x;
	} else if (t_1 <= 2e+86) {
		tmp = ((y - x) / y) * t;
	} else {
		tmp = (x / z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 5e-16:
		tmp = (t / z) * x
	elif t_1 <= 2e+86:
		tmp = ((y - x) / y) * t
	else:
		tmp = (x / z) * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 5e-16)
		tmp = Float64(Float64(t / z) * x);
	elseif (t_1 <= 2e+86)
		tmp = Float64(Float64(Float64(y - x) / y) * t);
	else
		tmp = Float64(Float64(x / z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 5e-16)
		tmp = (t / z) * x;
	elseif (t_1 <= 2e+86)
		tmp = ((y - x) / y) * t;
	else
		tmp = (x / z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-16], N[(N[(t / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 2e+86], N[(N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision] * t), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 5.0000000000000004e-16

   1. Initial program 95.2%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-/l* N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift--.f64 86.1

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

   4. Applied rewrites 86.1%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 55.6

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

   7. Applied rewrites 55.6%

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

   if 5.0000000000000004e-16 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2e86

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 67.5

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

   4. Applied rewrites 67.5%

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

   5. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 89.5

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

   7. Applied rewrites 89.5%

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

   8. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 89.5

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

   10. Applied rewrites 89.5%

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

   if 2e86 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 93.1%

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

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 54.1

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

   4. Applied rewrites 54.1%

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

Alternative 10: 68.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-16}:\\ \;\;\;\;\frac{t}{z} \cdot x\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 5e-16) (* (/ t z) x) (if (<= t_1 2.0) t (* (/ x z) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e-16) {
		tmp = (t / z) * x;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = (x / z) * t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 5d-16) then
        tmp = (t / z) * x
    else if (t_1 <= 2.0d0) then
        tmp = t
    else
        tmp = (x / z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e-16) {
		tmp = (t / z) * x;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = (x / z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 5e-16:
		tmp = (t / z) * x
	elif t_1 <= 2.0:
		tmp = t
	else:
		tmp = (x / z) * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 5e-16)
		tmp = Float64(Float64(t / z) * x);
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = Float64(Float64(x / z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 5e-16)
		tmp = (t / z) * x;
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = (x / z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-16], N[(N[(t / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 2.0], t, N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 5.0000000000000004e-16

   1. Initial program 95.2%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-/l* N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift--.f64 86.1

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

   4. Applied rewrites 86.1%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 55.6

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

   7. Applied rewrites 55.6%

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

   if 5.0000000000000004e-16 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 93.9%

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

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.4%

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

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 52.7

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

   4. Applied rewrites 52.7%

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

Alternative 11: 67.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-16}:\\ \;\;\;\;\frac{t}{z} \cdot x\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 5e-16) (* (/ t z) x) (if (<= t_1 2.0) t (/ (* t x) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e-16) {
		tmp = (t / z) * x;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 5d-16) then
        tmp = (t / z) * x
    else if (t_1 <= 2.0d0) then
        tmp = t
    else
        tmp = (t * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e-16) {
		tmp = (t / z) * x;
	} else if (t_1 <= 2.0) {
		tmp = t;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 5e-16:
		tmp = (t / z) * x
	elif t_1 <= 2.0:
		tmp = t
	else:
		tmp = (t * x) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 5e-16)
		tmp = Float64(Float64(t / z) * x);
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = Float64(Float64(t * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 5e-16)
		tmp = (t / z) * x;
	elseif (t_1 <= 2.0)
		tmp = t;
	else
		tmp = (t * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-16], N[(N[(t / z), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 2.0], t, N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 5.0000000000000004e-16

   1. Initial program 95.2%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-/l* N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift--.f64 86.1

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

   4. Applied rewrites 86.1%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 55.6

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

   7. Applied rewrites 55.6%

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

   if 5.0000000000000004e-16 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 93.9%

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

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.4%

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

   2. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 49.6

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

   4. Applied rewrites 49.6%

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

Alternative 12: 67.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{t}{z} \cdot x\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 100000000:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ t z) x)))
   (if (<= t_1 5e-16) t_2 (if (<= t_1 100000000.0) t t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / z) * x;
	double tmp;
	if (t_1 <= 5e-16) {
		tmp = t_2;
	} else if (t_1 <= 100000000.0) {
		tmp = t;
	} 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)
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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (t / z) * x
    if (t_1 <= 5d-16) then
        tmp = t_2
    else if (t_1 <= 100000000.0d0) then
        tmp = t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (t / z) * x;
	double tmp;
	if (t_1 <= 5e-16) {
		tmp = t_2;
	} else if (t_1 <= 100000000.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (t / z) * x
	tmp = 0
	if t_1 <= 5e-16:
		tmp = t_2
	elif t_1 <= 100000000.0:
		tmp = t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(t / z) * x)
	tmp = 0.0
	if (t_1 <= 5e-16)
		tmp = t_2;
	elseif (t_1 <= 100000000.0)
		tmp = t;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (t / z) * x;
	tmp = 0.0;
	if (t_1 <= 5e-16)
		tmp = t_2;
	elseif (t_1 <= 100000000.0)
		tmp = t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t / z), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$1, 5e-16], t$95$2, If[LessEqual[t$95$1, 100000000.0], t, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 5.0000000000000004e-16 or 1e8 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 95.2%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift--.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. associate-/l* N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. lift--.f64 86.9

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

   4. Applied rewrites 86.9%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 54.5

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

   7. Applied rewrites 54.5%

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

   if 5.0000000000000004e-16 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e8

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 92.6%

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

Alternative 13: 35.0% accurate, 12.6× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 96.8%

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

2. Taylor expanded in y around inf

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

4. Applied rewrites 35.0%

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

Reproduce

herbie shell --seed 2025120 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64
  (* (/ (- x y) (- z y)) t))