Rosa's DopplerBench

Percentage Accurate: 73.3% → 97.9%

Time: 5.9s

Alternatives: 12

Speedup: 0.8×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \end{array} \]

FPCore

(FPCore (u v t1) :precision binary64 (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))

C

double code(double u, double v, double t1) {
	return (-t1 * v) / ((t1 + u) * (t1 + u));
}

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(u, v, t1)
use fmin_fmax_functions
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    code = (-t1 * v) / ((t1 + u) * (t1 + u))
end function

Java

public static double code(double u, double v, double t1) {
	return (-t1 * v) / ((t1 + u) * (t1 + u));
}

Python

def code(u, v, t1):
	return (-t1 * v) / ((t1 + u) * (t1 + u))

Julia

function code(u, v, t1)
	return Float64(Float64(Float64(-t1) * v) / Float64(Float64(t1 + u) * Float64(t1 + u)))
end

MATLAB

function tmp = code(u, v, t1)
	tmp = (-t1 * v) / ((t1 + u) * (t1 + u));
end

Wolfram

code[u_, v_, t1_] := N[(N[((-t1) * v), $MachinePrecision] / N[(N[(t1 + u), $MachinePrecision] * N[(t1 + u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \end{array} \]

FPCore

(FPCore (u v t1) :precision binary64 (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))

C

double code(double u, double v, double t1) {
	return (-t1 * v) / ((t1 + u) * (t1 + u));
}

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(u, v, t1)
use fmin_fmax_functions
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    code = (-t1 * v) / ((t1 + u) * (t1 + u))
end function

Java

public static double code(double u, double v, double t1) {
	return (-t1 * v) / ((t1 + u) * (t1 + u));
}

Python

def code(u, v, t1):
	return (-t1 * v) / ((t1 + u) * (t1 + u))

Julia

function code(u, v, t1)
	return Float64(Float64(Float64(-t1) * v) / Float64(Float64(t1 + u) * Float64(t1 + u)))
end

MATLAB

function tmp = code(u, v, t1)
	tmp = (-t1 * v) / ((t1 + u) * (t1 + u));
end

Wolfram

code[u_, v_, t1_] := N[(N[((-t1) * v), $MachinePrecision] / N[(N[(t1 + u), $MachinePrecision] * N[(t1 + u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{t1 \cdot \frac{v}{u + t1}}{\left(-u\right) - t1} \end{array} \]

FPCore

(FPCore (u v t1) :precision binary64 (/ (* t1 (/ v (+ u t1))) (- (- u) t1)))

C

double code(double u, double v, double t1) {
	return (t1 * (v / (u + t1))) / (-u - t1);
}

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(u, v, t1)
use fmin_fmax_functions
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    code = (t1 * (v / (u + t1))) / (-u - t1)
end function

Java

public static double code(double u, double v, double t1) {
	return (t1 * (v / (u + t1))) / (-u - t1);
}

Python

def code(u, v, t1):
	return (t1 * (v / (u + t1))) / (-u - t1)

Julia

function code(u, v, t1)
	return Float64(Float64(t1 * Float64(v / Float64(u + t1))) / Float64(Float64(-u) - t1))
end

MATLAB

function tmp = code(u, v, t1)
	tmp = (t1 * (v / (u + t1))) / (-u - t1);
end

Wolfram

code[u_, v_, t1_] := N[(N[(t1 * N[(v / N[(u + t1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[((-u) - t1), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.5%

   \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
2. Add Preprocessing

3. Taylor expanded in v around 0

   \[\leadsto \color{blue}{-1 \cdot \frac{t1 \cdot v}{{\left(t1 + u\right)}^{2}}} \]
4. Step-by-step derivation

5. Applied rewrites 70.8%

   \[\leadsto \color{blue}{\frac{v}{{\left(u + t1\right)}^{2}} \cdot \left(-t1\right)} \]
6. Step-by-step derivation

7. Applied rewrites 98.8%

   \[\leadsto \frac{\left(-t1\right) \cdot \frac{v}{u + t1}}{\color{blue}{u + t1}} \]

8. Final simplification 98.8%

   \[\leadsto \frac{t1 \cdot \frac{v}{u + t1}}{\left(-u\right) - t1} \]
9. Add Preprocessing

Alternative 2: 87.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -1.45 \cdot 10^{+30}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq -3.4 \cdot 10^{-162}:\\ \;\;\;\;\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\\ \mathbf{elif}\;t1 \leq 6.7 \cdot 10^{-164}:\\ \;\;\;\;\frac{t1 \cdot \frac{-v}{u}}{u}\\ \mathbf{elif}\;t1 \leq 2.05 \cdot 10^{+108}:\\ \;\;\;\;\frac{-v}{\left(u + t1\right) \cdot \left(u + t1\right)} \cdot t1\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u + t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= t1 -1.45e+30)
   (/ v (- u t1))
   (if (<= t1 -3.4e-162)
     (/ (* (- t1) v) (* (+ t1 u) (+ t1 u)))
     (if (<= t1 6.7e-164)
       (/ (* t1 (/ (- v) u)) u)
       (if (<= t1 2.05e+108)
         (* (/ (- v) (* (+ u t1) (+ u t1))) t1)
         (/ (- v) (+ u t1)))))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -1.45e+30) {
		tmp = v / (u - t1);
	} else if (t1 <= -3.4e-162) {
		tmp = (-t1 * v) / ((t1 + u) * (t1 + u));
	} else if (t1 <= 6.7e-164) {
		tmp = (t1 * (-v / u)) / u;
	} else if (t1 <= 2.05e+108) {
		tmp = (-v / ((u + t1) * (u + t1))) * t1;
	} else {
		tmp = -v / (u + t1);
	}
	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(u, v, t1)
use fmin_fmax_functions
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if (t1 <= (-1.45d+30)) then
        tmp = v / (u - t1)
    else if (t1 <= (-3.4d-162)) then
        tmp = (-t1 * v) / ((t1 + u) * (t1 + u))
    else if (t1 <= 6.7d-164) then
        tmp = (t1 * (-v / u)) / u
    else if (t1 <= 2.05d+108) then
        tmp = (-v / ((u + t1) * (u + t1))) * t1
    else
        tmp = -v / (u + t1)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -1.45e+30) {
		tmp = v / (u - t1);
	} else if (t1 <= -3.4e-162) {
		tmp = (-t1 * v) / ((t1 + u) * (t1 + u));
	} else if (t1 <= 6.7e-164) {
		tmp = (t1 * (-v / u)) / u;
	} else if (t1 <= 2.05e+108) {
		tmp = (-v / ((u + t1) * (u + t1))) * t1;
	} else {
		tmp = -v / (u + t1);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -1.45e+30:
		tmp = v / (u - t1)
	elif t1 <= -3.4e-162:
		tmp = (-t1 * v) / ((t1 + u) * (t1 + u))
	elif t1 <= 6.7e-164:
		tmp = (t1 * (-v / u)) / u
	elif t1 <= 2.05e+108:
		tmp = (-v / ((u + t1) * (u + t1))) * t1
	else:
		tmp = -v / (u + t1)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -1.45e+30)
		tmp = Float64(v / Float64(u - t1));
	elseif (t1 <= -3.4e-162)
		tmp = Float64(Float64(Float64(-t1) * v) / Float64(Float64(t1 + u) * Float64(t1 + u)));
	elseif (t1 <= 6.7e-164)
		tmp = Float64(Float64(t1 * Float64(Float64(-v) / u)) / u);
	elseif (t1 <= 2.05e+108)
		tmp = Float64(Float64(Float64(-v) / Float64(Float64(u + t1) * Float64(u + t1))) * t1);
	else
		tmp = Float64(Float64(-v) / Float64(u + t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (t1 <= -1.45e+30)
		tmp = v / (u - t1);
	elseif (t1 <= -3.4e-162)
		tmp = (-t1 * v) / ((t1 + u) * (t1 + u));
	elseif (t1 <= 6.7e-164)
		tmp = (t1 * (-v / u)) / u;
	elseif (t1 <= 2.05e+108)
		tmp = (-v / ((u + t1) * (u + t1))) * t1;
	else
		tmp = -v / (u + t1);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -1.45e+30], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, -3.4e-162], N[(N[((-t1) * v), $MachinePrecision] / N[(N[(t1 + u), $MachinePrecision] * N[(t1 + u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 6.7e-164], N[(N[(t1 * N[((-v) / u), $MachinePrecision]), $MachinePrecision] / u), $MachinePrecision], If[LessEqual[t1, 2.05e+108], N[(N[((-v) / N[(N[(u + t1), $MachinePrecision] * N[(u + t1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t1), $MachinePrecision], N[((-v) / N[(u + t1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t1 < -1.4499999999999999e30

   1. Initial program 52.4%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   4. Applied rewrites 99.3%

      \[\leadsto \color{blue}{\frac{\frac{t1}{u - t1} \cdot \left(-v\right)}{u - t1}} \]

   5. Taylor expanded in u around 0

      \[\leadsto \frac{\color{blue}{v}}{u - t1} \]
   6. Step-by-step derivation

   7. Applied rewrites 93.2%

      \[\leadsto \frac{\color{blue}{v}}{u - t1} \]

   if -1.4499999999999999e30 < t1 < -3.4e-162

   1. Initial program 94.3%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   if -3.4e-162 < t1 < 6.69999999999999999e-164

   1. Initial program 72.0%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in u around inf

      \[\leadsto \color{blue}{\frac{-1 \cdot \left(t1 \cdot v\right) + 2 \cdot \frac{{t1}^{2} \cdot v}{u}}{{u}^{2}}} \]
   4. Step-by-step derivation

   5. Applied rewrites 83.8%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\frac{\left(v \cdot t1\right) \cdot t1}{u}, 2, \left(-t1\right) \cdot v\right)}{u}}{u}} \]

   6. Taylor expanded in u around inf

      \[\leadsto \frac{-1 \cdot \frac{t1 \cdot v}{u}}{u} \]
   7. Step-by-step derivation

   8. Applied rewrites 88.6%

      \[\leadsto \frac{t1 \cdot \frac{-v}{u}}{u} \]

   if 6.69999999999999999e-164 < t1 < 2.05e108

   1. Initial program 84.0%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in v around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{t1 \cdot v}{{\left(t1 + u\right)}^{2}}} \]
   4. Step-by-step derivation

   5. Applied rewrites 84.9%

      \[\leadsto \color{blue}{\frac{v}{{\left(u + t1\right)}^{2}} \cdot \left(-t1\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 84.9%

      \[\leadsto \frac{v}{\left(u + t1\right) \cdot \left(u + t1\right)} \cdot \left(-t1\right) \]

   if 2.05e108 < t1

   1. Initial program 55.0%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in v around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{t1 \cdot v}{{\left(t1 + u\right)}^{2}}} \]
   4. Step-by-step derivation

   5. Applied rewrites 54.5%

      \[\leadsto \color{blue}{\frac{v}{{\left(u + t1\right)}^{2}} \cdot \left(-t1\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 99.9%

      \[\leadsto \frac{\left(-t1\right) \cdot \frac{v}{u + t1}}{\color{blue}{u + t1}} \]

   8. Taylor expanded in u around 0

      \[\leadsto \frac{-1 \cdot v}{\color{blue}{u} + t1} \]
   9. Step-by-step derivation

   10. Applied rewrites 91.8%

       \[\leadsto \frac{-v}{\color{blue}{u} + t1} \]
3. Recombined 5 regimes into one program.

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -1.45 \cdot 10^{+30}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq -3.4 \cdot 10^{-162}:\\ \;\;\;\;\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)}\\ \mathbf{elif}\;t1 \leq 6.7 \cdot 10^{-164}:\\ \;\;\;\;\frac{t1 \cdot \frac{-v}{u}}{u}\\ \mathbf{elif}\;t1 \leq 2.05 \cdot 10^{+108}:\\ \;\;\;\;\frac{-v}{\left(u + t1\right) \cdot \left(u + t1\right)} \cdot t1\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u + t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-v}{\left(u + t1\right) \cdot \left(u + t1\right)} \cdot t1\\ \mathbf{if}\;t1 \leq -1.3 \cdot 10^{+121}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq -1.8 \cdot 10^{-140}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t1 \leq 6.7 \cdot 10^{-164}:\\ \;\;\;\;\frac{t1 \cdot \frac{-v}{u}}{u}\\ \mathbf{elif}\;t1 \leq 2.05 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u + t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (let* ((t_1 (* (/ (- v) (* (+ u t1) (+ u t1))) t1)))
   (if (<= t1 -1.3e+121)
     (/ v (- u t1))
     (if (<= t1 -1.8e-140)
       t_1
       (if (<= t1 6.7e-164)
         (/ (* t1 (/ (- v) u)) u)
         (if (<= t1 2.05e+108) t_1 (/ (- v) (+ u t1))))))))

C

double code(double u, double v, double t1) {
	double t_1 = (-v / ((u + t1) * (u + t1))) * t1;
	double tmp;
	if (t1 <= -1.3e+121) {
		tmp = v / (u - t1);
	} else if (t1 <= -1.8e-140) {
		tmp = t_1;
	} else if (t1 <= 6.7e-164) {
		tmp = (t1 * (-v / u)) / u;
	} else if (t1 <= 2.05e+108) {
		tmp = t_1;
	} else {
		tmp = -v / (u + t1);
	}
	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(u, v, t1)
use fmin_fmax_functions
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-v / ((u + t1) * (u + t1))) * t1
    if (t1 <= (-1.3d+121)) then
        tmp = v / (u - t1)
    else if (t1 <= (-1.8d-140)) then
        tmp = t_1
    else if (t1 <= 6.7d-164) then
        tmp = (t1 * (-v / u)) / u
    else if (t1 <= 2.05d+108) then
        tmp = t_1
    else
        tmp = -v / (u + t1)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double t_1 = (-v / ((u + t1) * (u + t1))) * t1;
	double tmp;
	if (t1 <= -1.3e+121) {
		tmp = v / (u - t1);
	} else if (t1 <= -1.8e-140) {
		tmp = t_1;
	} else if (t1 <= 6.7e-164) {
		tmp = (t1 * (-v / u)) / u;
	} else if (t1 <= 2.05e+108) {
		tmp = t_1;
	} else {
		tmp = -v / (u + t1);
	}
	return tmp;
}

Python

def code(u, v, t1):
	t_1 = (-v / ((u + t1) * (u + t1))) * t1
	tmp = 0
	if t1 <= -1.3e+121:
		tmp = v / (u - t1)
	elif t1 <= -1.8e-140:
		tmp = t_1
	elif t1 <= 6.7e-164:
		tmp = (t1 * (-v / u)) / u
	elif t1 <= 2.05e+108:
		tmp = t_1
	else:
		tmp = -v / (u + t1)
	return tmp

Julia

function code(u, v, t1)
	t_1 = Float64(Float64(Float64(-v) / Float64(Float64(u + t1) * Float64(u + t1))) * t1)
	tmp = 0.0
	if (t1 <= -1.3e+121)
		tmp = Float64(v / Float64(u - t1));
	elseif (t1 <= -1.8e-140)
		tmp = t_1;
	elseif (t1 <= 6.7e-164)
		tmp = Float64(Float64(t1 * Float64(Float64(-v) / u)) / u);
	elseif (t1 <= 2.05e+108)
		tmp = t_1;
	else
		tmp = Float64(Float64(-v) / Float64(u + t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	t_1 = (-v / ((u + t1) * (u + t1))) * t1;
	tmp = 0.0;
	if (t1 <= -1.3e+121)
		tmp = v / (u - t1);
	elseif (t1 <= -1.8e-140)
		tmp = t_1;
	elseif (t1 <= 6.7e-164)
		tmp = (t1 * (-v / u)) / u;
	elseif (t1 <= 2.05e+108)
		tmp = t_1;
	else
		tmp = -v / (u + t1);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := Block[{t$95$1 = N[(N[((-v) / N[(N[(u + t1), $MachinePrecision] * N[(u + t1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t1), $MachinePrecision]}, If[LessEqual[t1, -1.3e+121], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, -1.8e-140], t$95$1, If[LessEqual[t1, 6.7e-164], N[(N[(t1 * N[((-v) / u), $MachinePrecision]), $MachinePrecision] / u), $MachinePrecision], If[LessEqual[t1, 2.05e+108], t$95$1, N[((-v) / N[(u + t1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t1 < -1.2999999999999999e121

   1. Initial program 46.4%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   4. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\frac{\frac{t1}{u - t1} \cdot \left(-v\right)}{u - t1}} \]

   5. Taylor expanded in u around 0

      \[\leadsto \frac{\color{blue}{v}}{u - t1} \]
   6. Step-by-step derivation

   7. Applied rewrites 100.0%

      \[\leadsto \frac{\color{blue}{v}}{u - t1} \]

   if -1.2999999999999999e121 < t1 < -1.8e-140 or 6.69999999999999999e-164 < t1 < 2.05e108

   1. Initial program 85.0%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in v around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{t1 \cdot v}{{\left(t1 + u\right)}^{2}}} \]
   4. Step-by-step derivation

   5. Applied rewrites 86.3%

      \[\leadsto \color{blue}{\frac{v}{{\left(u + t1\right)}^{2}} \cdot \left(-t1\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 86.3%

      \[\leadsto \frac{v}{\left(u + t1\right) \cdot \left(u + t1\right)} \cdot \left(-t1\right) \]

   if -1.8e-140 < t1 < 6.69999999999999999e-164

   1. Initial program 72.5%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in u around inf

      \[\leadsto \color{blue}{\frac{-1 \cdot \left(t1 \cdot v\right) + 2 \cdot \frac{{t1}^{2} \cdot v}{u}}{{u}^{2}}} \]
   4. Step-by-step derivation

   5. Applied rewrites 83.3%

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(\frac{\left(v \cdot t1\right) \cdot t1}{u}, 2, \left(-t1\right) \cdot v\right)}{u}}{u}} \]

   6. Taylor expanded in u around inf

      \[\leadsto \frac{-1 \cdot \frac{t1 \cdot v}{u}}{u} \]
   7. Step-by-step derivation

   8. Applied rewrites 87.9%

      \[\leadsto \frac{t1 \cdot \frac{-v}{u}}{u} \]

   if 2.05e108 < t1

   1. Initial program 55.0%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in v around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{t1 \cdot v}{{\left(t1 + u\right)}^{2}}} \]
   4. Step-by-step derivation

   5. Applied rewrites 54.5%

      \[\leadsto \color{blue}{\frac{v}{{\left(u + t1\right)}^{2}} \cdot \left(-t1\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 99.9%

      \[\leadsto \frac{\left(-t1\right) \cdot \frac{v}{u + t1}}{\color{blue}{u + t1}} \]

   8. Taylor expanded in u around 0

      \[\leadsto \frac{-1 \cdot v}{\color{blue}{u} + t1} \]
   9. Step-by-step derivation

   10. Applied rewrites 91.8%

       \[\leadsto \frac{-v}{\color{blue}{u} + t1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -1.3 \cdot 10^{+121}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq -1.8 \cdot 10^{-140}:\\ \;\;\;\;\frac{-v}{\left(u + t1\right) \cdot \left(u + t1\right)} \cdot t1\\ \mathbf{elif}\;t1 \leq 6.7 \cdot 10^{-164}:\\ \;\;\;\;\frac{t1 \cdot \frac{-v}{u}}{u}\\ \mathbf{elif}\;t1 \leq 2.05 \cdot 10^{+108}:\\ \;\;\;\;\frac{-v}{\left(u + t1\right) \cdot \left(u + t1\right)} \cdot t1\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u + t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-v}{\left(u + t1\right) \cdot \left(u + t1\right)} \cdot t1\\ \mathbf{if}\;t1 \leq -1.3 \cdot 10^{+121}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq -4.5 \cdot 10^{-142}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t1 \leq 6.7 \cdot 10^{-164}:\\ \;\;\;\;\frac{t1}{u} \cdot \frac{-v}{u}\\ \mathbf{elif}\;t1 \leq 2.05 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u + t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (let* ((t_1 (* (/ (- v) (* (+ u t1) (+ u t1))) t1)))
   (if (<= t1 -1.3e+121)
     (/ v (- u t1))
     (if (<= t1 -4.5e-142)
       t_1
       (if (<= t1 6.7e-164)
         (* (/ t1 u) (/ (- v) u))
         (if (<= t1 2.05e+108) t_1 (/ (- v) (+ u t1))))))))

C

double code(double u, double v, double t1) {
	double t_1 = (-v / ((u + t1) * (u + t1))) * t1;
	double tmp;
	if (t1 <= -1.3e+121) {
		tmp = v / (u - t1);
	} else if (t1 <= -4.5e-142) {
		tmp = t_1;
	} else if (t1 <= 6.7e-164) {
		tmp = (t1 / u) * (-v / u);
	} else if (t1 <= 2.05e+108) {
		tmp = t_1;
	} else {
		tmp = -v / (u + t1);
	}
	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(u, v, t1)
use fmin_fmax_functions
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-v / ((u + t1) * (u + t1))) * t1
    if (t1 <= (-1.3d+121)) then
        tmp = v / (u - t1)
    else if (t1 <= (-4.5d-142)) then
        tmp = t_1
    else if (t1 <= 6.7d-164) then
        tmp = (t1 / u) * (-v / u)
    else if (t1 <= 2.05d+108) then
        tmp = t_1
    else
        tmp = -v / (u + t1)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double t_1 = (-v / ((u + t1) * (u + t1))) * t1;
	double tmp;
	if (t1 <= -1.3e+121) {
		tmp = v / (u - t1);
	} else if (t1 <= -4.5e-142) {
		tmp = t_1;
	} else if (t1 <= 6.7e-164) {
		tmp = (t1 / u) * (-v / u);
	} else if (t1 <= 2.05e+108) {
		tmp = t_1;
	} else {
		tmp = -v / (u + t1);
	}
	return tmp;
}

Python

def code(u, v, t1):
	t_1 = (-v / ((u + t1) * (u + t1))) * t1
	tmp = 0
	if t1 <= -1.3e+121:
		tmp = v / (u - t1)
	elif t1 <= -4.5e-142:
		tmp = t_1
	elif t1 <= 6.7e-164:
		tmp = (t1 / u) * (-v / u)
	elif t1 <= 2.05e+108:
		tmp = t_1
	else:
		tmp = -v / (u + t1)
	return tmp

Julia

function code(u, v, t1)
	t_1 = Float64(Float64(Float64(-v) / Float64(Float64(u + t1) * Float64(u + t1))) * t1)
	tmp = 0.0
	if (t1 <= -1.3e+121)
		tmp = Float64(v / Float64(u - t1));
	elseif (t1 <= -4.5e-142)
		tmp = t_1;
	elseif (t1 <= 6.7e-164)
		tmp = Float64(Float64(t1 / u) * Float64(Float64(-v) / u));
	elseif (t1 <= 2.05e+108)
		tmp = t_1;
	else
		tmp = Float64(Float64(-v) / Float64(u + t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	t_1 = (-v / ((u + t1) * (u + t1))) * t1;
	tmp = 0.0;
	if (t1 <= -1.3e+121)
		tmp = v / (u - t1);
	elseif (t1 <= -4.5e-142)
		tmp = t_1;
	elseif (t1 <= 6.7e-164)
		tmp = (t1 / u) * (-v / u);
	elseif (t1 <= 2.05e+108)
		tmp = t_1;
	else
		tmp = -v / (u + t1);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := Block[{t$95$1 = N[(N[((-v) / N[(N[(u + t1), $MachinePrecision] * N[(u + t1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t1), $MachinePrecision]}, If[LessEqual[t1, -1.3e+121], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, -4.5e-142], t$95$1, If[LessEqual[t1, 6.7e-164], N[(N[(t1 / u), $MachinePrecision] * N[((-v) / u), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 2.05e+108], t$95$1, N[((-v) / N[(u + t1), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t1 < -1.2999999999999999e121

   1. Initial program 46.4%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   4. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\frac{\frac{t1}{u - t1} \cdot \left(-v\right)}{u - t1}} \]

   5. Taylor expanded in u around 0

      \[\leadsto \frac{\color{blue}{v}}{u - t1} \]
   6. Step-by-step derivation

   7. Applied rewrites 100.0%

      \[\leadsto \frac{\color{blue}{v}}{u - t1} \]

   if -1.2999999999999999e121 < t1 < -4.50000000000000019e-142 or 6.69999999999999999e-164 < t1 < 2.05e108

   1. Initial program 85.0%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in v around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{t1 \cdot v}{{\left(t1 + u\right)}^{2}}} \]
   4. Step-by-step derivation

   5. Applied rewrites 86.3%

      \[\leadsto \color{blue}{\frac{v}{{\left(u + t1\right)}^{2}} \cdot \left(-t1\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 86.3%

      \[\leadsto \frac{v}{\left(u + t1\right) \cdot \left(u + t1\right)} \cdot \left(-t1\right) \]

   if -4.50000000000000019e-142 < t1 < 6.69999999999999999e-164

   1. Initial program 72.5%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in u around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{t1 \cdot v}{{u}^{2}}} \]
   4. Step-by-step derivation

   5. Applied rewrites 87.8%

      \[\leadsto \color{blue}{\frac{-t1}{u} \cdot \frac{v}{u}} \]

   if 2.05e108 < t1

   1. Initial program 55.0%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in v around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{t1 \cdot v}{{\left(t1 + u\right)}^{2}}} \]
   4. Step-by-step derivation

   5. Applied rewrites 54.5%

      \[\leadsto \color{blue}{\frac{v}{{\left(u + t1\right)}^{2}} \cdot \left(-t1\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 99.9%

      \[\leadsto \frac{\left(-t1\right) \cdot \frac{v}{u + t1}}{\color{blue}{u + t1}} \]

   8. Taylor expanded in u around 0

      \[\leadsto \frac{-1 \cdot v}{\color{blue}{u} + t1} \]
   9. Step-by-step derivation

   10. Applied rewrites 91.8%

       \[\leadsto \frac{-v}{\color{blue}{u} + t1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -1.3 \cdot 10^{+121}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq -4.5 \cdot 10^{-142}:\\ \;\;\;\;\frac{-v}{\left(u + t1\right) \cdot \left(u + t1\right)} \cdot t1\\ \mathbf{elif}\;t1 \leq 6.7 \cdot 10^{-164}:\\ \;\;\;\;\frac{t1}{u} \cdot \frac{-v}{u}\\ \mathbf{elif}\;t1 \leq 2.05 \cdot 10^{+108}:\\ \;\;\;\;\frac{-v}{\left(u + t1\right) \cdot \left(u + t1\right)} \cdot t1\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u + t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 90.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -1.45 \cdot 10^{+142}:\\ \;\;\;\;\frac{v}{-t1}\\ \mathbf{elif}\;t1 \leq 4.6 \cdot 10^{+138}:\\ \;\;\;\;\frac{\frac{v}{u + t1}}{u + t1} \cdot \left(-t1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u + t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= t1 -1.45e+142)
   (/ v (- t1))
   (if (<= t1 4.6e+138)
     (* (/ (/ v (+ u t1)) (+ u t1)) (- t1))
     (/ (- v) (+ u t1)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -1.45e+142) {
		tmp = v / -t1;
	} else if (t1 <= 4.6e+138) {
		tmp = ((v / (u + t1)) / (u + t1)) * -t1;
	} else {
		tmp = -v / (u + t1);
	}
	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(u, v, t1)
use fmin_fmax_functions
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if (t1 <= (-1.45d+142)) then
        tmp = v / -t1
    else if (t1 <= 4.6d+138) then
        tmp = ((v / (u + t1)) / (u + t1)) * -t1
    else
        tmp = -v / (u + t1)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -1.45e+142) {
		tmp = v / -t1;
	} else if (t1 <= 4.6e+138) {
		tmp = ((v / (u + t1)) / (u + t1)) * -t1;
	} else {
		tmp = -v / (u + t1);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -1.45e+142:
		tmp = v / -t1
	elif t1 <= 4.6e+138:
		tmp = ((v / (u + t1)) / (u + t1)) * -t1
	else:
		tmp = -v / (u + t1)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -1.45e+142)
		tmp = Float64(v / Float64(-t1));
	elseif (t1 <= 4.6e+138)
		tmp = Float64(Float64(Float64(v / Float64(u + t1)) / Float64(u + t1)) * Float64(-t1));
	else
		tmp = Float64(Float64(-v) / Float64(u + t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (t1 <= -1.45e+142)
		tmp = v / -t1;
	elseif (t1 <= 4.6e+138)
		tmp = ((v / (u + t1)) / (u + t1)) * -t1;
	else
		tmp = -v / (u + t1);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -1.45e+142], N[(v / (-t1)), $MachinePrecision], If[LessEqual[t1, 4.6e+138], N[(N[(N[(v / N[(u + t1), $MachinePrecision]), $MachinePrecision] / N[(u + t1), $MachinePrecision]), $MachinePrecision] * (-t1)), $MachinePrecision], N[((-v) / N[(u + t1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -1.45000000000000007e142

   1. Initial program 41.9%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in u around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{v}{t1}} \]
   4. Step-by-step derivation

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\frac{v}{-t1}} \]

   if -1.45000000000000007e142 < t1 < 4.60000000000000015e138

   1. Initial program 80.0%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in v around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{t1 \cdot v}{{\left(t1 + u\right)}^{2}}} \]
   4. Step-by-step derivation

   5. Applied rewrites 80.9%

      \[\leadsto \color{blue}{\frac{v}{{\left(u + t1\right)}^{2}} \cdot \left(-t1\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 87.2%

      \[\leadsto \frac{\frac{v}{u + t1}}{u + t1} \cdot \left(-\color{blue}{t1}\right) \]

   if 4.60000000000000015e138 < t1

   1. Initial program 53.1%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in v around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{t1 \cdot v}{{\left(t1 + u\right)}^{2}}} \]
   4. Step-by-step derivation

   5. Applied rewrites 54.7%

      \[\leadsto \color{blue}{\frac{v}{{\left(u + t1\right)}^{2}} \cdot \left(-t1\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 100.0%

      \[\leadsto \frac{\left(-t1\right) \cdot \frac{v}{u + t1}}{\color{blue}{u + t1}} \]

   8. Taylor expanded in u around 0

      \[\leadsto \frac{-1 \cdot v}{\color{blue}{u} + t1} \]
   9. Step-by-step derivation

   10. Applied rewrites 95.4%

       \[\leadsto \frac{-v}{\color{blue}{u} + t1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 86.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -1.3 \cdot 10^{+121}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 2.05 \cdot 10^{+108}:\\ \;\;\;\;\frac{-v}{\left(u + t1\right) \cdot \left(u + t1\right)} \cdot t1\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u + t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (<= t1 -1.3e+121)
   (/ v (- u t1))
   (if (<= t1 2.05e+108)
     (* (/ (- v) (* (+ u t1) (+ u t1))) t1)
     (/ (- v) (+ u t1)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -1.3e+121) {
		tmp = v / (u - t1);
	} else if (t1 <= 2.05e+108) {
		tmp = (-v / ((u + t1) * (u + t1))) * t1;
	} else {
		tmp = -v / (u + t1);
	}
	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(u, v, t1)
use fmin_fmax_functions
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if (t1 <= (-1.3d+121)) then
        tmp = v / (u - t1)
    else if (t1 <= 2.05d+108) then
        tmp = (-v / ((u + t1) * (u + t1))) * t1
    else
        tmp = -v / (u + t1)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if (t1 <= -1.3e+121) {
		tmp = v / (u - t1);
	} else if (t1 <= 2.05e+108) {
		tmp = (-v / ((u + t1) * (u + t1))) * t1;
	} else {
		tmp = -v / (u + t1);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if t1 <= -1.3e+121:
		tmp = v / (u - t1)
	elif t1 <= 2.05e+108:
		tmp = (-v / ((u + t1) * (u + t1))) * t1
	else:
		tmp = -v / (u + t1)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if (t1 <= -1.3e+121)
		tmp = Float64(v / Float64(u - t1));
	elseif (t1 <= 2.05e+108)
		tmp = Float64(Float64(Float64(-v) / Float64(Float64(u + t1) * Float64(u + t1))) * t1);
	else
		tmp = Float64(Float64(-v) / Float64(u + t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if (t1 <= -1.3e+121)
		tmp = v / (u - t1);
	elseif (t1 <= 2.05e+108)
		tmp = (-v / ((u + t1) * (u + t1))) * t1;
	else
		tmp = -v / (u + t1);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[LessEqual[t1, -1.3e+121], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t1, 2.05e+108], N[(N[((-v) / N[(N[(u + t1), $MachinePrecision] * N[(u + t1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t1), $MachinePrecision], N[((-v) / N[(u + t1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t1 < -1.2999999999999999e121

   1. Initial program 46.4%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   4. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\frac{\frac{t1}{u - t1} \cdot \left(-v\right)}{u - t1}} \]

   5. Taylor expanded in u around 0

      \[\leadsto \frac{\color{blue}{v}}{u - t1} \]
   6. Step-by-step derivation

   7. Applied rewrites 100.0%

      \[\leadsto \frac{\color{blue}{v}}{u - t1} \]

   if -1.2999999999999999e121 < t1 < 2.05e108

   1. Initial program 80.1%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in v around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{t1 \cdot v}{{\left(t1 + u\right)}^{2}}} \]
   4. Step-by-step derivation

   5. Applied rewrites 81.6%

      \[\leadsto \color{blue}{\frac{v}{{\left(u + t1\right)}^{2}} \cdot \left(-t1\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 81.6%

      \[\leadsto \frac{v}{\left(u + t1\right) \cdot \left(u + t1\right)} \cdot \left(-t1\right) \]

   if 2.05e108 < t1

   1. Initial program 55.0%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in v around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{t1 \cdot v}{{\left(t1 + u\right)}^{2}}} \]
   4. Step-by-step derivation

   5. Applied rewrites 54.5%

      \[\leadsto \color{blue}{\frac{v}{{\left(u + t1\right)}^{2}} \cdot \left(-t1\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 99.9%

      \[\leadsto \frac{\left(-t1\right) \cdot \frac{v}{u + t1}}{\color{blue}{u + t1}} \]

   8. Taylor expanded in u around 0

      \[\leadsto \frac{-1 \cdot v}{\color{blue}{u} + t1} \]
   9. Step-by-step derivation

   10. Applied rewrites 91.8%

       \[\leadsto \frac{-v}{\color{blue}{u} + t1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -1.3 \cdot 10^{+121}:\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{elif}\;t1 \leq 2.05 \cdot 10^{+108}:\\ \;\;\;\;\frac{-v}{\left(u + t1\right) \cdot \left(u + t1\right)} \cdot t1\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u + t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -5.1 \cdot 10^{-108} \lor \neg \left(t1 \leq 4.5 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u \cdot u} \cdot t1\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -5.1e-108) (not (<= t1 4.5e-19)))
   (/ v (- u t1))
   (* (/ (- v) (* u u)) t1)))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -5.1e-108) || !(t1 <= 4.5e-19)) {
		tmp = v / (u - t1);
	} else {
		tmp = (-v / (u * u)) * t1;
	}
	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(u, v, t1)
use fmin_fmax_functions
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((t1 <= (-5.1d-108)) .or. (.not. (t1 <= 4.5d-19))) then
        tmp = v / (u - t1)
    else
        tmp = (-v / (u * u)) * t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -5.1e-108) || !(t1 <= 4.5e-19)) {
		tmp = v / (u - t1);
	} else {
		tmp = (-v / (u * u)) * t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -5.1e-108) or not (t1 <= 4.5e-19):
		tmp = v / (u - t1)
	else:
		tmp = (-v / (u * u)) * t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -5.1e-108) || !(t1 <= 4.5e-19))
		tmp = Float64(v / Float64(u - t1));
	else
		tmp = Float64(Float64(Float64(-v) / Float64(u * u)) * t1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -5.1e-108) || ~((t1 <= 4.5e-19)))
		tmp = v / (u - t1);
	else
		tmp = (-v / (u * u)) * t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -5.1e-108], N[Not[LessEqual[t1, 4.5e-19]], $MachinePrecision]], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision], N[(N[((-v) / N[(u * u), $MachinePrecision]), $MachinePrecision] * t1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -5.1000000000000002e-108 or 4.50000000000000013e-19 < t1

   1. Initial program 66.3%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   4. Applied rewrites 98.5%

      \[\leadsto \color{blue}{\frac{\frac{t1}{u - t1} \cdot \left(-v\right)}{u - t1}} \]

   5. Taylor expanded in u around 0

      \[\leadsto \frac{\color{blue}{v}}{u - t1} \]
   6. Step-by-step derivation

   7. Applied rewrites 83.1%

      \[\leadsto \frac{\color{blue}{v}}{u - t1} \]

   if -5.1000000000000002e-108 < t1 < 4.50000000000000013e-19

   1. Initial program 77.2%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in u around inf

      \[\leadsto \frac{\left(-t1\right) \cdot v}{\color{blue}{{u}^{2}}} \]
   4. Step-by-step derivation

   5. Applied rewrites 70.3%

      \[\leadsto \frac{\left(-t1\right) \cdot v}{\color{blue}{u \cdot u}} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(-t1\right) \cdot v}{u \cdot u}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(-t1\right) \cdot v}}{u \cdot u} \]

      3. associate-/l* N/A

         \[\leadsto \color{blue}{\left(-t1\right) \cdot \frac{v}{u \cdot u}} \]

      4. *-commutative N/A

         \[\leadsto \color{blue}{\frac{v}{u \cdot u} \cdot \left(-t1\right)} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{v}{u \cdot u} \cdot \left(-t1\right)} \]

      6. lower-/.f64 71.8

         \[\leadsto \color{blue}{\frac{v}{u \cdot u}} \cdot \left(-t1\right) \]

   7. Applied rewrites 71.8%

      \[\leadsto \color{blue}{\frac{v}{u \cdot u} \cdot \left(-t1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -5.1 \cdot 10^{-108} \lor \neg \left(t1 \leq 4.5 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{else}:\\ \;\;\;\;\frac{-v}{u \cdot u} \cdot t1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t1 \leq -5.1 \cdot 10^{-108} \lor \neg \left(t1 \leq 4.5 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{else}:\\ \;\;\;\;v \cdot \frac{-t1}{u \cdot u}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= t1 -5.1e-108) (not (<= t1 4.5e-19)))
   (/ v (- u t1))
   (* v (/ (- t1) (* u u)))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -5.1e-108) || !(t1 <= 4.5e-19)) {
		tmp = v / (u - t1);
	} else {
		tmp = v * (-t1 / (u * u));
	}
	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(u, v, t1)
use fmin_fmax_functions
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((t1 <= (-5.1d-108)) .or. (.not. (t1 <= 4.5d-19))) then
        tmp = v / (u - t1)
    else
        tmp = v * (-t1 / (u * u))
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((t1 <= -5.1e-108) || !(t1 <= 4.5e-19)) {
		tmp = v / (u - t1);
	} else {
		tmp = v * (-t1 / (u * u));
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (t1 <= -5.1e-108) or not (t1 <= 4.5e-19):
		tmp = v / (u - t1)
	else:
		tmp = v * (-t1 / (u * u))
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((t1 <= -5.1e-108) || !(t1 <= 4.5e-19))
		tmp = Float64(v / Float64(u - t1));
	else
		tmp = Float64(v * Float64(Float64(-t1) / Float64(u * u)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((t1 <= -5.1e-108) || ~((t1 <= 4.5e-19)))
		tmp = v / (u - t1);
	else
		tmp = v * (-t1 / (u * u));
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[t1, -5.1e-108], N[Not[LessEqual[t1, 4.5e-19]], $MachinePrecision]], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision], N[(v * N[((-t1) / N[(u * u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t1 < -5.1000000000000002e-108 or 4.50000000000000013e-19 < t1

   1. Initial program 66.3%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   4. Applied rewrites 98.5%

      \[\leadsto \color{blue}{\frac{\frac{t1}{u - t1} \cdot \left(-v\right)}{u - t1}} \]

   5. Taylor expanded in u around 0

      \[\leadsto \frac{\color{blue}{v}}{u - t1} \]
   6. Step-by-step derivation

   7. Applied rewrites 83.1%

      \[\leadsto \frac{\color{blue}{v}}{u - t1} \]

   if -5.1000000000000002e-108 < t1 < 4.50000000000000013e-19

   1. Initial program 77.2%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in u around inf

      \[\leadsto \frac{\left(-t1\right) \cdot v}{\color{blue}{{u}^{2}}} \]
   4. Step-by-step derivation

   5. Applied rewrites 70.3%

      \[\leadsto \frac{\left(-t1\right) \cdot v}{\color{blue}{u \cdot u}} \]
   6. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\left(-t1\right) \cdot v}{u \cdot u}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{\color{blue}{\left(-t1\right) \cdot v}}{u \cdot u} \]

      3. *-commutative N/A

         \[\leadsto \frac{\color{blue}{v \cdot \left(-t1\right)}}{u \cdot u} \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{v \cdot \frac{-t1}{u \cdot u}} \]

      5. lower-*.f64 N/A

         \[\leadsto \color{blue}{v \cdot \frac{-t1}{u \cdot u}} \]

      6. lower-/.f64 71.7

         \[\leadsto v \cdot \color{blue}{\frac{-t1}{u \cdot u}} \]

   7. Applied rewrites 71.7%

      \[\leadsto \color{blue}{v \cdot \frac{-t1}{u \cdot u}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t1 \leq -5.1 \cdot 10^{-108} \lor \neg \left(t1 \leq 4.5 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{v}{u - t1}\\ \mathbf{else}:\\ \;\;\;\;v \cdot \frac{-t1}{u \cdot u}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -7.4 \cdot 10^{+130} \lor \neg \left(u \leq 3.5 \cdot 10^{+121}\right):\\ \;\;\;\;v \cdot \frac{t1}{u \cdot u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u - t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -7.4e+130) (not (<= u 3.5e+121)))
   (* v (/ t1 (* u u)))
   (/ v (- u t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -7.4e+130) || !(u <= 3.5e+121)) {
		tmp = v * (t1 / (u * u));
	} else {
		tmp = v / (u - t1);
	}
	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(u, v, t1)
use fmin_fmax_functions
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-7.4d+130)) .or. (.not. (u <= 3.5d+121))) then
        tmp = v * (t1 / (u * u))
    else
        tmp = v / (u - t1)
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -7.4e+130) || !(u <= 3.5e+121)) {
		tmp = v * (t1 / (u * u));
	} else {
		tmp = v / (u - t1);
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -7.4e+130) or not (u <= 3.5e+121):
		tmp = v * (t1 / (u * u))
	else:
		tmp = v / (u - t1)
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -7.4e+130) || !(u <= 3.5e+121))
		tmp = Float64(v * Float64(t1 / Float64(u * u)));
	else
		tmp = Float64(v / Float64(u - t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -7.4e+130) || ~((u <= 3.5e+121)))
		tmp = v * (t1 / (u * u));
	else
		tmp = v / (u - t1);
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -7.4e+130], N[Not[LessEqual[u, 3.5e+121]], $MachinePrecision]], N[(v * N[(t1 / N[(u * u), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -7.4000000000000003e130 or 3.5e121 < u

   1. Initial program 77.0%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   4. Applied rewrites 98.3%

      \[\leadsto \color{blue}{\frac{\frac{t1}{u - t1} \cdot \left(-v\right)}{u - t1}} \]

   5. Taylor expanded in u around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{t1 \cdot v}{{u}^{2}}} \]
   6. Step-by-step derivation

   7. Applied rewrites 92.4%

      \[\leadsto \color{blue}{\frac{v}{u} \cdot \frac{-t1}{u}} \]
   8. Step-by-step derivation

   9. Applied rewrites 74.4%

      \[\leadsto v \cdot \color{blue}{\frac{t1}{u \cdot u}} \]

   if -7.4000000000000003e130 < u < 3.5e121

   1. Initial program 68.3%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   4. Applied rewrites 95.8%

      \[\leadsto \color{blue}{\frac{\frac{t1}{u - t1} \cdot \left(-v\right)}{u - t1}} \]

   5. Taylor expanded in u around 0

      \[\leadsto \frac{\color{blue}{v}}{u - t1} \]
   6. Step-by-step derivation

   7. Applied rewrites 68.9%

      \[\leadsto \frac{\color{blue}{v}}{u - t1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -7.4 \cdot 10^{+130} \lor \neg \left(u \leq 3.5 \cdot 10^{+121}\right):\\ \;\;\;\;v \cdot \frac{t1}{u \cdot u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{u - t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 57.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;u \leq -2.4 \cdot 10^{+132} \lor \neg \left(u \leq 1.36 \cdot 10^{+221}\right):\\ \;\;\;\;\frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \end{array} \]

FPCore

(FPCore (u v t1)
 :precision binary64
 (if (or (<= u -2.4e+132) (not (<= u 1.36e+221))) (/ v u) (/ v (- t1))))

C

double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -2.4e+132) || !(u <= 1.36e+221)) {
		tmp = v / u;
	} else {
		tmp = v / -t1;
	}
	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(u, v, t1)
use fmin_fmax_functions
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    real(8) :: tmp
    if ((u <= (-2.4d+132)) .or. (.not. (u <= 1.36d+221))) then
        tmp = v / u
    else
        tmp = v / -t1
    end if
    code = tmp
end function

Java

public static double code(double u, double v, double t1) {
	double tmp;
	if ((u <= -2.4e+132) || !(u <= 1.36e+221)) {
		tmp = v / u;
	} else {
		tmp = v / -t1;
	}
	return tmp;
}

Python

def code(u, v, t1):
	tmp = 0
	if (u <= -2.4e+132) or not (u <= 1.36e+221):
		tmp = v / u
	else:
		tmp = v / -t1
	return tmp

Julia

function code(u, v, t1)
	tmp = 0.0
	if ((u <= -2.4e+132) || !(u <= 1.36e+221))
		tmp = Float64(v / u);
	else
		tmp = Float64(v / Float64(-t1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(u, v, t1)
	tmp = 0.0;
	if ((u <= -2.4e+132) || ~((u <= 1.36e+221)))
		tmp = v / u;
	else
		tmp = v / -t1;
	end
	tmp_2 = tmp;
end

Wolfram

code[u_, v_, t1_] := If[Or[LessEqual[u, -2.4e+132], N[Not[LessEqual[u, 1.36e+221]], $MachinePrecision]], N[(v / u), $MachinePrecision], N[(v / (-t1)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if u < -2.4000000000000001e132 or 1.36e221 < u

   1. Initial program 89.0%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   4. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\frac{\frac{t1}{u - t1} \cdot \left(-v\right)}{u - t1}} \]

   5. Taylor expanded in u around 0

      \[\leadsto \frac{\color{blue}{v}}{u - t1} \]
   6. Step-by-step derivation

   7. Applied rewrites 46.0%

      \[\leadsto \frac{\color{blue}{v}}{u - t1} \]

   8. Taylor expanded in u around inf

      \[\leadsto \frac{v}{\color{blue}{u}} \]
   9. Step-by-step derivation

   10. Applied rewrites 46.0%

       \[\leadsto \frac{v}{\color{blue}{u}} \]

   if -2.4000000000000001e132 < u < 1.36e221

   1. Initial program 66.6%

      \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in u around 0

      \[\leadsto \color{blue}{-1 \cdot \frac{v}{t1}} \]
   4. Step-by-step derivation

   5. Applied rewrites 63.6%

      \[\leadsto \color{blue}{\frac{v}{-t1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;u \leq -2.4 \cdot 10^{+132} \lor \neg \left(u \leq 1.36 \cdot 10^{+221}\right):\\ \;\;\;\;\frac{v}{u}\\ \mathbf{else}:\\ \;\;\;\;\frac{v}{-t1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \frac{v}{u - t1} \end{array} \]

FPCore

(FPCore (u v t1) :precision binary64 (/ v (- u t1)))

C

double code(double u, double v, double t1) {
	return v / (u - t1);
}

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(u, v, t1)
use fmin_fmax_functions
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    code = v / (u - t1)
end function

Java

public static double code(double u, double v, double t1) {
	return v / (u - t1);
}

Python

def code(u, v, t1):
	return v / (u - t1)

Julia

function code(u, v, t1)
	return Float64(v / Float64(u - t1))
end

MATLAB

function tmp = code(u, v, t1)
	tmp = v / (u - t1);
end

Wolfram

code[u_, v_, t1_] := N[(v / N[(u - t1), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.5%

   \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
2. Add Preprocessing

4. Applied rewrites 96.4%

   \[\leadsto \color{blue}{\frac{\frac{t1}{u - t1} \cdot \left(-v\right)}{u - t1}} \]

5. Taylor expanded in u around 0

   \[\leadsto \frac{\color{blue}{v}}{u - t1} \]
6. Step-by-step derivation

7. Applied rewrites 61.8%

   \[\leadsto \frac{\color{blue}{v}}{u - t1} \]
8. Add Preprocessing

Alternative 12: 17.0% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \frac{v}{u} \end{array} \]

FPCore

(FPCore (u v t1) :precision binary64 (/ v u))

C

double code(double u, double v, double t1) {
	return v / u;
}

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(u, v, t1)
use fmin_fmax_functions
    real(8), intent (in) :: u
    real(8), intent (in) :: v
    real(8), intent (in) :: t1
    code = v / u
end function

Java

public static double code(double u, double v, double t1) {
	return v / u;
}

Python

def code(u, v, t1):
	return v / u

Julia

function code(u, v, t1)
	return Float64(v / u)
end

MATLAB

function tmp = code(u, v, t1)
	tmp = v / u;
end

Wolfram

code[u_, v_, t1_] := N[(v / u), $MachinePrecision]

Derivation

1. Initial program 70.5%

   \[\frac{\left(-t1\right) \cdot v}{\left(t1 + u\right) \cdot \left(t1 + u\right)} \]
2. Add Preprocessing

4. Applied rewrites 96.4%

   \[\leadsto \color{blue}{\frac{\frac{t1}{u - t1} \cdot \left(-v\right)}{u - t1}} \]

5. Taylor expanded in u around 0

   \[\leadsto \frac{\color{blue}{v}}{u - t1} \]
6. Step-by-step derivation

7. Applied rewrites 61.8%

   \[\leadsto \frac{\color{blue}{v}}{u - t1} \]

8. Taylor expanded in u around inf

   \[\leadsto \frac{v}{\color{blue}{u}} \]
9. Step-by-step derivation

10. Applied rewrites 13.4%

    \[\leadsto \frac{v}{\color{blue}{u}} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2025019 
(FPCore (u v t1)
  :name "Rosa's DopplerBench"
  :precision binary64
  (/ (* (- t1) v) (* (+ t1 u) (+ t1 u))))