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

Percentage Accurate: 85.9% → 96.4%

Time: 6.6s

Alternatives: 9

Speedup: 0.3×

Specification

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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)) / (z - a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+301}\right):\\ \;\;\;\;\frac{y}{z - a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y (- z t)) (- z a)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+301)))
     (* (/ y (- z a)) (- z t))
     t_1)))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * (z - t)) / (z - a));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+301)) {
		tmp = (y / (z - a)) * (z - 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)) / (z - a));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+301)) {
		tmp = (y / (z - a)) * (z - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * (z - t)) / (z - a))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+301):
		tmp = (y / (z - a)) * (z - 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(z - a)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+301))
		tmp = Float64(Float64(y / Float64(z - a)) * Float64(z - 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)) / (z - a));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+301)))
		tmp = (y / (z - a)) * (z - 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[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+301]], $MachinePrecision]], N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))) < -inf.0 or 5.0000000000000004e301 < (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

   1. Initial program 34.3%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-add-rev N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

      11. associate-*r* N/A

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

      12. distribute-rgt-out N/A

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

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

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

      14. metadata-eval N/A

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

      15. *-lft-identity N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower--.f64 94.0

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

   5. Applied rewrites 94.0%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))) < 5.0000000000000004e301

   1. Initial program 99.3%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - t\right)}{z - a} \leq -\infty \lor \neg \left(x + \frac{y \cdot \left(z - t\right)}{z - a} \leq 5 \cdot 10^{+301}\right):\\ \;\;\;\;\frac{y}{z - a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{z - a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 83.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{z - a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+56} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-34}\right):\\ \;\;\;\;\frac{y}{z - a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) (- z a))))
   (if (or (<= t_1 -2e+56) (not (<= t_1 2e-34)))
     (* (/ y (- z a)) (- z t))
     (fma (/ z (- z a)) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / (z - a);
	double tmp;
	if ((t_1 <= -2e+56) || !(t_1 <= 2e-34)) {
		tmp = (y / (z - a)) * (z - t);
	} else {
		tmp = fma((z / (z - a)), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / Float64(z - a))
	tmp = 0.0
	if ((t_1 <= -2e+56) || !(t_1 <= 2e-34))
		tmp = Float64(Float64(y / Float64(z - a)) * Float64(z - t));
	else
		tmp = fma(Float64(z / Float64(z - a)), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+56], N[Not[LessEqual[t$95$1, 2e-34]], $MachinePrecision]], N[(N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < -2.00000000000000018e56 or 1.99999999999999986e-34 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

   1. Initial program 62.9%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-add-rev N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. associate-/l* N/A

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

      11. associate-*r* N/A

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

      12. distribute-rgt-out N/A

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

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

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

      14. metadata-eval N/A

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

      15. *-lft-identity N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. lower--.f64 N/A

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

      19. lower--.f64 83.8

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

   5. Applied rewrites 83.8%

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

   if -2.00000000000000018e56 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)) < 1.99999999999999986e-34

   1. Initial program 99.2%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 87.2

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

   5. Applied rewrites 87.2%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{z - a} \leq -2 \cdot 10^{+56} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{z - a} \leq 2 \cdot 10^{-34}\right):\\ \;\;\;\;\frac{y}{z - a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+29} \lor \neg \left(z \leq 10^{-35}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{z}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7e+29) (not (<= z 1e-35)))
   (fma (/ (- z t) z) y x)
   (fma (/ y a) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7e+29) || !(z <= 1e-35)) {
		tmp = fma(((z - t) / z), y, x);
	} else {
		tmp = fma((y / a), t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7e+29) || !(z <= 1e-35))
		tmp = fma(Float64(Float64(z - t) / z), y, x);
	else
		tmp = fma(Float64(y / a), t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7e+29], N[Not[LessEqual[z, 1e-35]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.99999999999999958e29 or 1.00000000000000001e-35 < z

   1. Initial program 72.9%

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

   3. Taylor expanded in a around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 89.6

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

   5. Applied rewrites 89.6%

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

   if -6.99999999999999958e29 < z < 1.00000000000000001e-35

   1. Initial program 89.3%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 79.1

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

   5. Applied rewrites 79.1%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+29} \lor \neg \left(z \leq 10^{-35}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{z}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+50} \lor \neg \left(z \leq 9.2 \cdot 10^{-43}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.5e+50) (not (<= z 9.2e-43)))
   (fma (/ z (- z a)) y x)
   (fma (/ y a) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e+50) || !(z <= 9.2e-43)) {
		tmp = fma((z / (z - a)), y, x);
	} else {
		tmp = fma((y / a), t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.5e+50) || !(z <= 9.2e-43))
		tmp = fma(Float64(z / Float64(z - a)), y, x);
	else
		tmp = fma(Float64(y / a), t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.5e+50], N[Not[LessEqual[z, 9.2e-43]], $MachinePrecision]], N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.50000000000000006e50 or 9.1999999999999995e-43 < z

   1. Initial program 73.4%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 85.3

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

   5. Applied rewrites 85.3%

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

   if -3.50000000000000006e50 < z < 9.1999999999999995e-43

   1. Initial program 88.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 78.6

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

   5. Applied rewrites 78.6%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+50} \lor \neg \left(z \leq 9.2 \cdot 10^{-43}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{z - a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+50} \lor \neg \left(z \leq 6.7 \cdot 10^{-43}\right):\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{z - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.5e+50) (not (<= z 6.7e-43)))
   (fma z (/ y (- z a)) x)
   (fma (/ y a) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.5e+50) || !(z <= 6.7e-43)) {
		tmp = fma(z, (y / (z - a)), x);
	} else {
		tmp = fma((y / a), t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.5e+50) || !(z <= 6.7e-43))
		tmp = fma(z, Float64(y / Float64(z - a)), x);
	else
		tmp = fma(Float64(y / a), t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.5e+50], N[Not[LessEqual[z, 6.7e-43]], $MachinePrecision]], N[(z * N[(y / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.50000000000000006e50 or 6.6999999999999998e-43 < z

   1. Initial program 73.4%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 85.3

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

   5. Applied rewrites 85.3%

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

   7. Applied rewrites 82.2%

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

   if -3.50000000000000006e50 < z < 6.6999999999999998e-43

   1. Initial program 88.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 78.6

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

   5. Applied rewrites 78.6%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+50} \lor \neg \left(z \leq 6.7 \cdot 10^{-43}\right):\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{z - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+50} \lor \neg \left(z \leq 6.2 \cdot 10^{+90}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.4e+50) (not (<= z 6.2e+90))) (+ y x) (fma (/ y a) t x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.4e+50) || !(z <= 6.2e+90)) {
		tmp = y + x;
	} else {
		tmp = fma((y / a), t, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.4e+50) || !(z <= 6.2e+90))
		tmp = Float64(y + x);
	else
		tmp = fma(Float64(y / a), t, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.4e+50], N[Not[LessEqual[z, 6.2e+90]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4e50 or 6.19999999999999977e90 < z

   1. Initial program 67.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 79.9

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

   5. Applied rewrites 79.9%

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

   if -5.4e50 < z < 6.19999999999999977e90

   1. Initial program 89.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 77.0

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

   5. Applied rewrites 77.0%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+50} \lor \neg \left(z \leq 6.2 \cdot 10^{+90}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+50} \lor \neg \left(z \leq 6.2 \cdot 10^{+90}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.4e+50) (not (<= z 6.2e+90))) (+ y x) (fma y (/ t a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.4e+50) || !(z <= 6.2e+90)) {
		tmp = y + x;
	} else {
		tmp = fma(y, (t / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.4e+50) || !(z <= 6.2e+90))
		tmp = Float64(y + x);
	else
		tmp = fma(y, Float64(t / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.4e+50], N[Not[LessEqual[z, 6.2e+90]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4e50 or 6.19999999999999977e90 < z

   1. Initial program 67.9%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 79.9

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

   5. Applied rewrites 79.9%

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

   if -5.4e50 < z < 6.19999999999999977e90

   1. Initial program 89.8%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-/l* N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 77.0

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

   5. Applied rewrites 77.0%

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

   7. Applied rewrites 73.4%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+50} \lor \neg \left(z \leq 6.2 \cdot 10^{+90}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+121}:\\ \;\;\;\;\left(-x\right) \cdot -1\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -7.2e+121) (* (- x) -1.0) (+ y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.2e+121) {
		tmp = -x * -1.0;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-7.2d+121)) then
        tmp = -x * (-1.0d0)
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.2e+121) {
		tmp = -x * -1.0;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -7.2e+121:
		tmp = -x * -1.0
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.2e+121)
		tmp = Float64(Float64(-x) * -1.0);
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -7.2e+121)
		tmp = -x * -1.0;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.2e+121], N[((-x) * -1.0), $MachinePrecision], N[(y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.19999999999999963e121

   1. Initial program 78.3%

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

   3. Taylor expanded in x around -inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 N/A

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

   5. Applied rewrites 86.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 79.5%

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

   9. Taylor expanded in x around inf

      \[\leadsto \left(-x\right) \cdot -1 \]
   10. Step-by-step derivation

   11. Applied rewrites 56.8%

       \[\leadsto \left(-x\right) \cdot -1 \]

   if -7.19999999999999963e121 < a

   1. Initial program 82.2%

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

   3. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 61.4

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

   5. Applied rewrites 61.4%

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

Alternative 9: 60.0% 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 81.5%

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

3. Taylor expanded in z around inf

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

   1. +-commutative N/A

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

   2. lower-+.f64 58.0

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

5. Applied rewrites 58.0%

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

Developer Target 1: 98.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024363 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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