Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E

Percentage Accurate: 93.4% → 98.6%

Time: 4.2s

Alternatives: 12

Speedup: 0.5×

• 26.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+238} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+70}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (or (<= t_1 -4e+238) (not (<= t_1 5e+70)))
     (fma (/ (- z t) a) y x)
     (+ x (/ t_1 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if ((t_1 <= -4e+238) || !(t_1 <= 5e+70)) {
		tmp = fma(((z - t) / a), y, x);
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if ((t_1 <= -4e+238) || !(t_1 <= 5e+70))
		tmp = fma(Float64(Float64(z - t) / a), y, x);
	else
		tmp = Float64(x + Float64(t_1 / a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+238], N[Not[LessEqual[t$95$1, 5e+70]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -4.0000000000000002e238 or 5.0000000000000002e70 < (*.f64 y (-.f64 z t))

   1. Initial program 87.8%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-/l* N/A

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

      7. sub-div N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   if -4.0000000000000002e238 < (*.f64 y (-.f64 z t)) < 5.0000000000000002e70

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -4 \cdot 10^{+238} \lor \neg \left(y \cdot \left(z - t\right) \leq 5 \cdot 10^{+70}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{z - t}{a} \cdot y\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{+76} \lor \neg \left(t\_1 \leq 4 \cdot 10^{+121}\right):\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (<= t_1 (- INFINITY))
     (* (/ (- z t) a) y)
     (if (or (<= t_1 -2e+76) (not (<= t_1 4e+121)))
       (/ (* (- z t) y) a)
       (- x (* y (/ t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((z - t) / a) * y;
	} else if ((t_1 <= -2e+76) || !(t_1 <= 4e+121)) {
		tmp = ((z - t) * y) / a;
	} else {
		tmp = x - (y * (t / a));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = ((z - t) / a) * y;
	} else if ((t_1 <= -2e+76) || !(t_1 <= 4e+121)) {
		tmp = ((z - t) * y) / a;
	} else {
		tmp = x - (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if t_1 <= -math.inf:
		tmp = ((z - t) / a) * y
	elif (t_1 <= -2e+76) or not (t_1 <= 4e+121):
		tmp = ((z - t) * y) / a
	else:
		tmp = x - (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(z - t) / a) * y);
	elseif ((t_1 <= -2e+76) || !(t_1 <= 4e+121))
		tmp = Float64(Float64(Float64(z - t) * y) / a);
	else
		tmp = Float64(x - Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = ((z - t) / a) * y;
	elseif ((t_1 <= -2e+76) || ~((t_1 <= 4e+121)))
		tmp = ((z - t) * y) / a;
	else
		tmp = x - (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], If[Or[LessEqual[t$95$1, -2e+76], N[Not[LessEqual[t$95$1, 4e+121]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 80.6%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-/l* N/A

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

      7. sub-div N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-*l/ N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 73.3

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

   7. Applied rewrites 73.3%

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

   8. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. +-commutative N/A

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

      4. lower-/.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lower--.f64 80.6

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

   10. Applied rewrites 80.6%

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

       1. lift-/.f64 N/A

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

       2. lift--.f64 N/A

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

       3. lift-*.f64 N/A

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

       4. associate-*l/ N/A

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

       5. lower-*.f64 N/A

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

       6. lower-/.f64 N/A

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

       7. lift--.f64 95.5

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

   12. Applied rewrites 95.5%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) a) < -2.0000000000000001e76 or 4.00000000000000015e121 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 95.1%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 88.0

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

   5. Applied rewrites 88.0%

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

   if -2.0000000000000001e76 < (/.f64 (*.f64 y (-.f64 z t)) a) < 4.00000000000000015e121

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. cancel-sign-sub N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 88.4

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

   5. Applied rewrites 88.4%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -\infty:\\ \;\;\;\;\frac{z - t}{a} \cdot y\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq -2 \cdot 10^{+76} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \leq 4 \cdot 10^{+121}\right):\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+76} \lor \neg \left(t\_1 \leq 4 \cdot 10^{+121}\right):\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (or (<= t_1 -2e+76) (not (<= t_1 4e+121)))
     (/ (* (- z t) y) a)
     (- x (* y (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if ((t_1 <= -2e+76) || !(t_1 <= 4e+121)) {
		tmp = ((z - t) * y) / a;
	} else {
		tmp = x - (y * (t / a));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / a
    if ((t_1 <= (-2d+76)) .or. (.not. (t_1 <= 4d+121))) then
        tmp = ((z - t) * y) / a
    else
        tmp = x - (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if ((t_1 <= -2e+76) || !(t_1 <= 4e+121)) {
		tmp = ((z - t) * y) / a;
	} else {
		tmp = x - (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if (t_1 <= -2e+76) or not (t_1 <= 4e+121):
		tmp = ((z - t) * y) / a
	else:
		tmp = x - (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if ((t_1 <= -2e+76) || !(t_1 <= 4e+121))
		tmp = Float64(Float64(Float64(z - t) * y) / a);
	else
		tmp = Float64(x - Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	tmp = 0.0;
	if ((t_1 <= -2e+76) || ~((t_1 <= 4e+121)))
		tmp = ((z - t) * y) / a;
	else
		tmp = x - (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+76], N[Not[LessEqual[t$95$1, 4e+121]], $MachinePrecision]], N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -2.0000000000000001e76 or 4.00000000000000015e121 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 90.7%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lift--.f64 85.8

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

   5. Applied rewrites 85.8%

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

   if -2.0000000000000001e76 < (/.f64 (*.f64 y (-.f64 z t)) a) < 4.00000000000000015e121

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

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

      1. cancel-sign-sub N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 88.4

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

   5. Applied rewrites 88.4%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -2 \cdot 10^{+76} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \leq 4 \cdot 10^{+121}\right):\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 57.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+184} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+276}\right):\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (or (<= t_1 -1e+184) (not (<= t_1 2e+276))) (* (/ y a) z) x)))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if ((t_1 <= -1e+184) || !(t_1 <= 2e+276)) {
		tmp = (y / a) * z;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / a
    if ((t_1 <= (-1d+184)) .or. (.not. (t_1 <= 2d+276))) then
        tmp = (y / a) * z
    else
        tmp = x
    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;
	double tmp;
	if ((t_1 <= -1e+184) || !(t_1 <= 2e+276)) {
		tmp = (y / a) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if (t_1 <= -1e+184) or not (t_1 <= 2e+276):
		tmp = (y / a) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if ((t_1 <= -1e+184) || !(t_1 <= 2e+276))
		tmp = Float64(Float64(y / a) * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	tmp = 0.0;
	if ((t_1 <= -1e+184) || ~((t_1 <= 2e+276)))
		tmp = (y / a) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+184], N[Not[LessEqual[t$95$1, 2e+276]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -1.00000000000000002e184 or 2.0000000000000001e276 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 88.1%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-/l* N/A

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

      7. sub-div N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 91.8

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

   4. Applied rewrites 91.8%

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

   5. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-*l/ N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 60.3

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

   7. Applied rewrites 60.3%

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

   if -1.00000000000000002e184 < (/.f64 (*.f64 y (-.f64 z t)) a) < 2.0000000000000001e276

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 64.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -1 \cdot 10^{+184} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \leq 2 \cdot 10^{+276}\right):\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 57.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+184}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (<= t_1 -1e+184) (* (/ y a) z) (if (<= t_1 2e+154) x (/ (* y z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -1e+184) {
		tmp = (y / a) * z;
	} else if (t_1 <= 2e+154) {
		tmp = x;
	} else {
		tmp = (y * z) / a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / a
    if (t_1 <= (-1d+184)) then
        tmp = (y / a) * z
    else if (t_1 <= 2d+154) then
        tmp = x
    else
        tmp = (y * z) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -1e+184) {
		tmp = (y / a) * z;
	} else if (t_1 <= 2e+154) {
		tmp = x;
	} else {
		tmp = (y * z) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if t_1 <= -1e+184:
		tmp = (y / a) * z
	elif t_1 <= 2e+154:
		tmp = x
	else:
		tmp = (y * z) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if (t_1 <= -1e+184)
		tmp = Float64(Float64(y / a) * z);
	elseif (t_1 <= 2e+154)
		tmp = x;
	else
		tmp = Float64(Float64(y * z) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	tmp = 0.0;
	if (t_1 <= -1e+184)
		tmp = (y / a) * z;
	elseif (t_1 <= 2e+154)
		tmp = x;
	else
		tmp = (y * z) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+184], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 2e+154], x, N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -1.00000000000000002e184

   1. Initial program 85.4%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-/l* N/A

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

      7. sub-div N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 90.4

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

   4. Applied rewrites 90.4%

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

   5. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-*l/ N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 63.5

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

   7. Applied rewrites 63.5%

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

   if -1.00000000000000002e184 < (/.f64 (*.f64 y (-.f64 z t)) a) < 2.00000000000000007e154

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 69.2%

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

   if 2.00000000000000007e154 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 92.8%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-/l* N/A

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

      7. sub-div N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 90.2

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

   4. Applied rewrites 90.2%

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

   5. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-*l/ N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 48.7

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

   7. Applied rewrites 48.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 49.8

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

   9. Applied rewrites 49.8%

      \[\leadsto \frac{y \cdot z}{\color{blue}{a}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -1 \cdot 10^{+184}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq 2 \cdot 10^{+154}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+184}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+172}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (<= t_1 -1e+184) (* (/ y a) z) (if (<= t_1 5e+172) x (* (/ z a) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -1e+184) {
		tmp = (y / a) * z;
	} else if (t_1 <= 5e+172) {
		tmp = x;
	} else {
		tmp = (z / a) * y;
	}
	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
    if (t_1 <= (-1d+184)) then
        tmp = (y / a) * z
    else if (t_1 <= 5d+172) then
        tmp = x
    else
        tmp = (z / a) * y
    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;
	double tmp;
	if (t_1 <= -1e+184) {
		tmp = (y / a) * z;
	} else if (t_1 <= 5e+172) {
		tmp = x;
	} else {
		tmp = (z / a) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if t_1 <= -1e+184:
		tmp = (y / a) * z
	elif t_1 <= 5e+172:
		tmp = x
	else:
		tmp = (z / a) * y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if (t_1 <= -1e+184)
		tmp = Float64(Float64(y / a) * z);
	elseif (t_1 <= 5e+172)
		tmp = x;
	else
		tmp = Float64(Float64(z / a) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	tmp = 0.0;
	if (t_1 <= -1e+184)
		tmp = (y / a) * z;
	elseif (t_1 <= 5e+172)
		tmp = x;
	else
		tmp = (z / a) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+184], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 5e+172], x, N[(N[(z / a), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -1.00000000000000002e184

   1. Initial program 85.4%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-/l* N/A

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

      7. sub-div N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 90.4

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

   4. Applied rewrites 90.4%

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

   5. Taylor expanded in z around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. associate-*l/ N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 63.5

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

   7. Applied rewrites 63.5%

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

   if -1.00000000000000002e184 < (/.f64 (*.f64 y (-.f64 z t)) a) < 5.0000000000000001e172

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 68.1%

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

   if 5.0000000000000001e172 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 92.4%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 50.7

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

   5. Applied rewrites 50.7%

      \[\leadsto \color{blue}{\frac{z}{a} \cdot y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -1 \cdot 10^{+184}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq 5 \cdot 10^{+172}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -10000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+54}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -10000000000.0)
   (fma (/ y a) z x)
   (if (<= z 1.9e+54) (- x (* y (/ t a))) (fma (/ z a) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -10000000000.0) {
		tmp = fma((y / a), z, x);
	} else if (z <= 1.9e+54) {
		tmp = x - (y * (t / a));
	} else {
		tmp = fma((z / a), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -10000000000.0)
		tmp = fma(Float64(y / a), z, x);
	elseif (z <= 1.9e+54)
		tmp = Float64(x - Float64(y * Float64(t / a)));
	else
		tmp = fma(Float64(z / a), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -10000000000.0], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision], If[LessEqual[z, 1.9e+54], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1e10

   1. Initial program 96.4%

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

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

      2. associate-*l/ N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 91.1

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

   5. Applied rewrites 91.1%

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

   if -1e10 < z < 1.9000000000000001e54

   1. Initial program 96.0%

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

   3. Taylor expanded in z around 0

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

      1. cancel-sign-sub N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. lower-/.f64 82.3

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

   5. Applied rewrites 82.3%

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

   if 1.9000000000000001e54 < z

   1. Initial program 89.4%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-/l* N/A

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

      7. sub-div N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 96.4

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

   4. Applied rewrites 96.4%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 87.5

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

   7. Applied rewrites 87.5%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -10000000000:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+54}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+119} \lor \neg \left(t \leq 9.4 \cdot 10^{+86}\right):\\ \;\;\;\;\frac{-y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.15e+119) (not (<= t 9.4e+86)))
   (* (/ (- y) a) t)
   (fma (/ y a) z x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.15e+119) || !(t <= 9.4e+86)) {
		tmp = (-y / a) * t;
	} else {
		tmp = fma((y / a), z, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.15e+119) || !(t <= 9.4e+86))
		tmp = Float64(Float64(Float64(-y) / a) * t);
	else
		tmp = fma(Float64(y / a), z, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.15e+119], N[Not[LessEqual[t, 9.4e+86]], $MachinePrecision]], N[(N[((-y) / a), $MachinePrecision] * t), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.15e119 or 9.4000000000000004e86 < t

   1. Initial program 90.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. mul-1-neg N/A

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

      9. lower-neg.f64 66.4

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

   5. Applied rewrites 66.4%

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

   if -1.15e119 < t < 9.4000000000000004e86

   1. Initial program 97.1%

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

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

      2. associate-*l/ N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 82.3

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

   5. Applied rewrites 82.3%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+119} \lor \neg \left(t \leq 9.4 \cdot 10^{+86}\right):\\ \;\;\;\;\frac{-y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 6.4 \cdot 10^{+87}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{a} \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 6.4e+87) (fma (/ y a) z x) (* (/ (- t) a) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 6.4e+87) {
		tmp = fma((y / a), z, x);
	} else {
		tmp = (-t / a) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 6.4e+87)
		tmp = fma(Float64(y / a), z, x);
	else
		tmp = Float64(Float64(Float64(-t) / a) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 6.4e+87], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision], N[(N[((-t) / a), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 6.4000000000000001e87

   1. Initial program 96.1%

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

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

      2. associate-*l/ N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 75.9

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

   5. Applied rewrites 75.9%

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

   if 6.4000000000000001e87 < t

   1. Initial program 89.5%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. +-commutative N/A

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

      6. associate-/l* N/A

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

      7. sub-div N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 88.0

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

   4. Applied rewrites 88.0%

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

   5. Taylor expanded in t around inf

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-*r/ N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 N/A

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

      10. lift-/.f64 56.3

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

   7. Applied rewrites 56.3%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6.4 \cdot 10^{+87}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{a} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 93.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.7%

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

   1. lift-+.f64 N/A

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

   2. lift-/.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. +-commutative N/A

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

   6. associate-/l* N/A

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

   7. sub-div N/A

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

   8. *-commutative N/A

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

   9. lower-fma.f64 N/A

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

   10. sub-div N/A

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

   11. lower-/.f64 N/A

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

   12. lift--.f64 92.1

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

4. Applied rewrites 92.1%

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

Alternative 11: 70.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{y}{a}, z, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.7%

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

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

   2. associate-*l/ N/A

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

   3. lower-fma.f64 N/A

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

   4. lower-/.f64 68.9

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

5. Applied rewrites 68.9%

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

6. Final simplification 68.9%

   \[\leadsto \mathsf{fma}\left(\frac{y}{a}, z, x\right) \]
7. Add Preprocessing

Alternative 12: 38.6% accurate, 23.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 94.7%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 38.6%

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

6. Final simplification 38.6%

   \[\leadsto x \]
7. Add Preprocessing

Developer Target 1: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{t\_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- z t))))
   (if (< y -1.0761266216389975e-10)
     (+ x (/ 1.0 (/ t_1 y)))
     (if (< y 2.894426862792089e-49)
       (+ x (/ (* y (- z t)) a))
       (+ x (/ y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x + (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (z - t)
    if (y < (-1.0761266216389975d-10)) then
        tmp = x + (1.0d0 / (t_1 / y))
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) / a)
    else
        tmp = x + (y / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x + (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (z - t)
	tmp = 0
	if y < -1.0761266216389975e-10:
		tmp = x + (1.0 / (t_1 / y))
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) / a)
	else:
		tmp = x + (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(z - t))
	tmp = 0.0
	if (y < -1.0761266216389975e-10)
		tmp = Float64(x + Float64(1.0 / Float64(t_1 / y)));
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x + Float64(y / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (z - t);
	tmp = 0.0;
	if (y < -1.0761266216389975e-10)
		tmp = x + (1.0 / (t_1 / y));
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) / a);
	else
		tmp = x + (y / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -1.0761266216389975e-10], N[(x + N[(1.0 / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Reproduce

herbie shell --seed 2025037 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -430450648655599/4000000000000000000000000) (+ x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2894426862792089/10000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t)))))))

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