Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B

Percentage Accurate: 85.1% → 95.6%

Time: 5.6s

Alternatives: 8

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.6% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- a t))) (t_2 (+ x (/ (* y (- z t)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     (+ x (* (* t_1 (- 1.0 (/ t z))) z))
     (if (<= t_2 5e+306) t_2 (* (- z t) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a - t);
	double t_2 = x + ((y * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = x + ((t_1 * (1.0 - (t / z))) * z);
	} else if (t_2 <= 5e+306) {
		tmp = t_2;
	} else {
		tmp = (z - t) * t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a - t);
	double t_2 = x + ((y * (z - t)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = x + ((t_1 * (1.0 - (t / z))) * z);
	} else if (t_2 <= 5e+306) {
		tmp = t_2;
	} else {
		tmp = (z - t) * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a - t)
	t_2 = x + ((y * (z - t)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = x + ((t_1 * (1.0 - (t / z))) * z)
	elif t_2 <= 5e+306:
		tmp = t_2
	else:
		tmp = (z - t) * t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a - t))
	t_2 = Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(t_1 * Float64(1.0 - Float64(t / z))) * z));
	elseif (t_2 <= 5e+306)
		tmp = t_2;
	else
		tmp = Float64(Float64(z - t) * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a - t);
	t_2 = x + ((y * (z - t)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = x + ((t_1 * (1.0 - (t / z))) * z);
	elseif (t_2 <= 5e+306)
		tmp = t_2;
	else
		tmp = (z - t) * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(x + N[(N[(t$95$1 * N[(1.0 - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+306], t$95$2, N[(N[(z - t), $MachinePrecision] * t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 46.7%

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

   3. Taylor expanded in z around inf

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

      1. distribute-rgt-in N/A

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

      2. fp-cancel-sign-sub-inv N/A

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

      3. mul-1-neg N/A

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

      4. fp-cancel-sub-sign-inv N/A

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

      5. *-commutative N/A

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

      6. mul-1-neg N/A

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

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

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

      8. distribute-lft-neg-in N/A

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

      9. distribute-neg-in N/A

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

      10. *-commutative N/A

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

      11. distribute-rgt-in N/A

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

      12. +-commutative N/A

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

   5. Applied rewrites 95.8%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))) < 4.99999999999999993e306

   1. Initial program 99.4%

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

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

   1. Initial program 39.2%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 91.8

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

   5. Applied rewrites 91.8%

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

Alternative 2: 96.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+306}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y (- z t)) (- a t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+306)))
     (* (- z t) (/ y (- a t)))
     t_1)))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+306)) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * (z - t)) / (a - t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+306)) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * (z - t)) / (a - t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+306):
		tmp = (z - t) * (y / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(a - t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+306))
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * (z - t)) / (a - t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+306)))
		tmp = (z - t) * (y / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+306]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))) < -inf.0 or 4.99999999999999993e306 < (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))

   1. Initial program 42.1%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 90.0

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

   5. Applied rewrites 90.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))) < 4.99999999999999993e306

   1. Initial program 99.4%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - t\right)}{a - t} \leq -\infty \lor \neg \left(x + \frac{y \cdot \left(z - t\right)}{a - t} \leq 5 \cdot 10^{+306}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+181} \lor \neg \left(t\_1 \leq 10^{+183}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- a t))))
   (if (or (<= t_1 -2e+181) (not (<= t_1 1e+183)))
     (* (- z t) (/ y (- a t)))
     (- x (* y (/ t (- a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (a - t);
	double tmp;
	if ((t_1 <= -2e+181) || !(t_1 <= 1e+183)) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = x - (y * (t / (a - t)));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / (a - t)
    if ((t_1 <= (-2d+181)) .or. (.not. (t_1 <= 1d+183))) then
        tmp = (z - t) * (y / (a - t))
    else
        tmp = x - (y * (t / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (a - t);
	double tmp;
	if ((t_1 <= -2e+181) || !(t_1 <= 1e+183)) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = x - (y * (t / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / (a - t)
	tmp = 0
	if (t_1 <= -2e+181) or not (t_1 <= 1e+183):
		tmp = (z - t) * (y / (a - t))
	else:
		tmp = x - (y * (t / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(a - t))
	tmp = 0.0
	if ((t_1 <= -2e+181) || !(t_1 <= 1e+183))
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	else
		tmp = Float64(x - Float64(y * Float64(t / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / (a - t);
	tmp = 0.0;
	if ((t_1 <= -2e+181) || ~((t_1 <= 1e+183)))
		tmp = (z - t) * (y / (a - t));
	else
		tmp = x - (y * (t / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+181], N[Not[LessEqual[t$95$1, 1e+183]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -1.9999999999999998e181 or 9.99999999999999947e182 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 56.5%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 84.4

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

   5. Applied rewrites 84.4%

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

   if -1.9999999999999998e181 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 9.99999999999999947e182

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

         \[\leadsto x - \color{blue}{1} \cdot \frac{t \cdot y}{a - t} \]

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 89.9

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

   5. Applied rewrites 89.9%

      \[\leadsto \color{blue}{x - y \cdot \frac{t}{a - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \leq -2 \cdot 10^{+181} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a - t} \leq 10^{+183}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;\frac{z}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (+ x (/ (* y (- z t)) (- a t))) (- INFINITY)) (* (/ z a) y) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x + ((y * (z - t)) / (a - t))) <= -((double) INFINITY)) {
		tmp = (z / a) * y;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x + ((y * (z - t)) / (a - t))) <= -Double.POSITIVE_INFINITY) {
		tmp = (z / a) * y;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x + ((y * (z - t)) / (a - t))) <= -math.inf:
		tmp = (z / a) * y
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(a - t))) <= Float64(-Inf))
		tmp = Float64(Float64(z / a) * y);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x + ((y * (z - t)) / (a - t))) <= -Inf)
		tmp = (z / a) * y;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 46.7%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 70.1

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

   5. Applied rewrites 70.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 41.0%

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

   10. Applied rewrites 61.6%

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

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

   1. Initial program 89.9%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-+.f64 67.5

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

   5. Applied rewrites 67.5%

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

Alternative 5: 59.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - t\right)}{a - t} \leq -\infty:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (+ x (/ (* y (- z t)) (- a t))) (- INFINITY)) (* (/ y a) z) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x + ((y * (z - t)) / (a - t))) <= -((double) INFINITY)) {
		tmp = (y / a) * z;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x + ((y * (z - t)) / (a - t))) <= -Double.POSITIVE_INFINITY) {
		tmp = (y / a) * z;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x + ((y * (z - t)) / (a - t))) <= -math.inf:
		tmp = (y / a) * z
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(a - t))) <= Float64(-Inf))
		tmp = Float64(Float64(y / a) * z);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x + ((y * (z - t)) / (a - t))) <= -Inf)
		tmp = (y / a) * z;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 46.7%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 70.1

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

   5. Applied rewrites 70.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 41.0%

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

   10. Applied rewrites 61.5%

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

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

   1. Initial program 89.9%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-+.f64 67.5

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

   5. Applied rewrites 67.5%

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

Alternative 6: 76.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+41} \lor \neg \left(t \leq 8.2 \cdot 10^{+58}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.15e+41) (not (<= t 8.2e+58))) (+ y x) (fma (/ z a) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e+41) || !(t <= 8.2e+58)) {
		tmp = y + x;
	} else {
		tmp = fma((z / a), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.15e+41) || !(t <= 8.2e+58))
		tmp = Float64(y + x);
	else
		tmp = fma(Float64(z / a), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.15e+41], N[Not[LessEqual[t, 8.2e+58]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1499999999999999e41 or 8.2e58 < t

   1. Initial program 79.0%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-+.f64 84.2

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

   5. Applied rewrites 84.2%

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

   if -1.1499999999999999e41 < t < 8.2e58

   1. Initial program 92.3%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 79.8

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

   5. Applied rewrites 79.8%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+41} \lor \neg \left(t \leq 8.2 \cdot 10^{+58}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+41} \lor \neg \left(t \leq 225000000000\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.15e+41) (not (<= t 225000000000.0)))
   (+ y x)
   (fma z (/ y a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e+41) || !(t <= 225000000000.0)) {
		tmp = y + x;
	} else {
		tmp = fma(z, (y / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.15e+41) || !(t <= 225000000000.0))
		tmp = Float64(y + x);
	else
		tmp = fma(z, Float64(y / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.15e+41], N[Not[LessEqual[t, 225000000000.0]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(z * N[(y / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1499999999999999e41 or 2.25e11 < t

   1. Initial program 79.5%

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

   3. Taylor expanded in t around inf

      \[\leadsto \color{blue}{x + y} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. lower-+.f64 82.0

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

   5. Applied rewrites 82.0%

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

   if -1.1499999999999999e41 < t < 2.25e11

   1. Initial program 92.5%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 81.6

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

   5. Applied rewrites 81.6%

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

   7. Applied rewrites 79.0%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+41} \lor \neg \left(t \leq 225000000000\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.7% accurate, 6.5× speedup

Math

\[\begin{array}{l} \\ y + x \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(y + x), $MachinePrecision]

Derivation

1. Initial program 86.0%

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

3. Taylor expanded in t around inf

   \[\leadsto \color{blue}{x + y} \]
4. Step-by-step derivation

   1. +-commutative N/A

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

   2. lower-+.f64 62.8

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

5. Applied rewrites 62.8%

   \[\leadsto \color{blue}{y + x} \]
6. Add Preprocessing

Developer Target 1: 98.1% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2025015 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (/ y (/ (- a t) (- z t)))))

  (+ x (/ (* y (- z t)) (- a t))))