Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2

Percentage Accurate: 86.3% → 99.2%

Time: 7.5s

Alternatives: 16

Speedup: 0.7×

• 23.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Python

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Python

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+301}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{\frac{2}{z}}{t} - 2, y, x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))))
   (if (<= t_1 2e+301) t_1 (/ (fma (- (/ (/ 2.0 z) t) 2.0) y x) y))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
	double tmp;
	if (t_1 <= 2e+301) {
		tmp = t_1;
	} else {
		tmp = fma((((2.0 / z) / t) - 2.0), y, x) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
	tmp = 0.0
	if (t_1 <= 2e+301)
		tmp = t_1;
	else
		tmp = Float64(fma(Float64(Float64(Float64(2.0 / z) / t) - 2.0), y, x) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+301], t$95$1, N[(N[(N[(N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision] * y + x), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 x y) (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))) < 2.00000000000000011e301

   1. Initial program 99.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   if 2.00000000000000011e301 < (+.f64 (/.f64 x y) (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)))

   1. Initial program 37.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{1 - t}{t \cdot x} + \left(\frac{1}{y} + \frac{2}{t \cdot \left(x \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 99.8%

      \[\leadsto \color{blue}{\left(\frac{\frac{\frac{2}{z} - -2}{t} - 2}{x} + \frac{1}{y}\right) \cdot x} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x + y \cdot \left(2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}\right)}{y}} \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x + y \cdot \left(2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}\right)}{y}} \]

   8. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{\frac{2}{z} - -2}{t} - 2, y, x\right)}{y}} \]

   9. Taylor expanded in z around 0

      \[\leadsto \frac{\mathsf{fma}\left(\frac{\frac{2}{z}}{t} - 2, y, x\right)}{y} \]
   10. Step-by-step derivation

   11. Applied rewrites 100.0%

       \[\leadsto \frac{\mathsf{fma}\left(\frac{\frac{2}{z}}{t} - 2, y, x\right)}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 70.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+276}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+90} \lor \neg \left(t\_1 \leq \infty\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (<= t_1 -1e+276)
     (/ (/ 2.0 z) t)
     (if (<= t_1 -5e+104)
       (- (/ 2.0 t) 2.0)
       (if (or (<= t_1 2e+90) (not (<= t_1 INFINITY)))
         (+ (/ x y) -2.0)
         (/ (/ 2.0 t) z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_1 <= -1e+276) {
		tmp = (2.0 / z) / t;
	} else if (t_1 <= -5e+104) {
		tmp = (2.0 / t) - 2.0;
	} else if ((t_1 <= 2e+90) || !(t_1 <= ((double) INFINITY))) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (2.0 / t) / z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_1 <= -1e+276) {
		tmp = (2.0 / z) / t;
	} else if (t_1 <= -5e+104) {
		tmp = (2.0 / t) - 2.0;
	} else if ((t_1 <= 2e+90) || !(t_1 <= Double.POSITIVE_INFINITY)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (2.0 / t) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if t_1 <= -1e+276:
		tmp = (2.0 / z) / t
	elif t_1 <= -5e+104:
		tmp = (2.0 / t) - 2.0
	elif (t_1 <= 2e+90) or not (t_1 <= math.inf):
		tmp = (x / y) + -2.0
	else:
		tmp = (2.0 / t) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if (t_1 <= -1e+276)
		tmp = Float64(Float64(2.0 / z) / t);
	elseif (t_1 <= -5e+104)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	elseif ((t_1 <= 2e+90) || !(t_1 <= Inf))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(Float64(2.0 / t) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if (t_1 <= -1e+276)
		tmp = (2.0 / z) / t;
	elseif (t_1 <= -5e+104)
		tmp = (2.0 / t) - 2.0;
	elseif ((t_1 <= 2e+90) || ~((t_1 <= Inf)))
		tmp = (x / y) + -2.0;
	else
		tmp = (2.0 / t) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+276], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, -5e+104], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], If[Or[LessEqual[t$95$1, 2e+90], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.0000000000000001e276

   1. Initial program 96.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} + 2}}{t} \]

      3. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} + \color{blue}{2 \cdot 1}}{t} \]

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

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - \left(\mathsf{neg}\left(2\right)\right) \cdot 1}}{t} \]

      5. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2} \cdot 1}{t} \]

      6. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2}}{t} \]

      7. lower--.f64 N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - -2}}{t} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\color{blue}{\frac{2 \cdot 1}{z}} - -2}{t} \]

      9. metadata-eval N/A

         \[\leadsto \frac{\frac{\color{blue}{2}}{z} - -2}{t} \]

      10. lower-/.f64 100.0

          \[\leadsto \frac{\color{blue}{\frac{2}{z}} - -2}{t} \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t}} \]

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\frac{2}{z}}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 89.8%

      \[\leadsto \frac{\frac{2}{z}}{t} \]

   if -1.0000000000000001e276 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -4.9999999999999997e104

   1. Initial program 99.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 80.4%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t} - 2} \]

   6. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \frac{1}{t} - \color{blue}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 48.6%

      \[\leadsto \frac{2}{t} - \color{blue}{2} \]

   if -4.9999999999999997e104 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.99999999999999993e90 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 71.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Applied rewrites 84.1%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]

   if 1.99999999999999993e90 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 97.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{1 - t}{t \cdot x} + \left(\frac{1}{y} + \frac{2}{t \cdot \left(x \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 80.5%

      \[\leadsto \color{blue}{\left(\frac{\frac{\frac{2}{z} - -2}{t} - 2}{x} + \frac{1}{y}\right) \cdot x} \]

   6. Taylor expanded in z around 0

      \[\leadsto \frac{2}{\color{blue}{t \cdot z}} \]
   7. Step-by-step derivation

   8. Applied rewrites 59.0%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -1 \cdot 10^{+276}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq 2 \cdot 10^{+90} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq \infty\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+276}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+90} \lor \neg \left(t\_1 \leq \infty\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (<= t_1 -1e+276)
     (/ 2.0 (* t z))
     (if (<= t_1 -5e+104)
       (- (/ 2.0 t) 2.0)
       (if (or (<= t_1 2e+90) (not (<= t_1 INFINITY)))
         (+ (/ x y) -2.0)
         (/ (/ 2.0 t) z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_1 <= -1e+276) {
		tmp = 2.0 / (t * z);
	} else if (t_1 <= -5e+104) {
		tmp = (2.0 / t) - 2.0;
	} else if ((t_1 <= 2e+90) || !(t_1 <= ((double) INFINITY))) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (2.0 / t) / z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_1 <= -1e+276) {
		tmp = 2.0 / (t * z);
	} else if (t_1 <= -5e+104) {
		tmp = (2.0 / t) - 2.0;
	} else if ((t_1 <= 2e+90) || !(t_1 <= Double.POSITIVE_INFINITY)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (2.0 / t) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if t_1 <= -1e+276:
		tmp = 2.0 / (t * z)
	elif t_1 <= -5e+104:
		tmp = (2.0 / t) - 2.0
	elif (t_1 <= 2e+90) or not (t_1 <= math.inf):
		tmp = (x / y) + -2.0
	else:
		tmp = (2.0 / t) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if (t_1 <= -1e+276)
		tmp = Float64(2.0 / Float64(t * z));
	elseif (t_1 <= -5e+104)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	elseif ((t_1 <= 2e+90) || !(t_1 <= Inf))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(Float64(2.0 / t) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if (t_1 <= -1e+276)
		tmp = 2.0 / (t * z);
	elseif (t_1 <= -5e+104)
		tmp = (2.0 / t) - 2.0;
	elseif ((t_1 <= 2e+90) || ~((t_1 <= Inf)))
		tmp = (x / y) + -2.0;
	else
		tmp = (2.0 / t) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+276], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+104], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], If[Or[LessEqual[t$95$1, 2e+90], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.0000000000000001e276

   1. Initial program 96.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{1 - t}{t \cdot x} + \left(\frac{1}{y} + \frac{2}{t \cdot \left(x \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 77.8%

      \[\leadsto \color{blue}{\left(\frac{\frac{\frac{2}{z} - -2}{t} - 2}{x} + \frac{1}{y}\right) \cdot x} \]

   6. Taylor expanded in z around 0

      \[\leadsto \frac{2}{\color{blue}{t \cdot z}} \]
   7. Step-by-step derivation

   8. Applied rewrites 89.7%

      \[\leadsto \frac{\frac{2}{t}}{\color{blue}{z}} \]
   9. Step-by-step derivation

   10. Applied rewrites 89.7%

       \[\leadsto \frac{2}{t \cdot \color{blue}{z}} \]

   if -1.0000000000000001e276 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -4.9999999999999997e104

   1. Initial program 99.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 80.4%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t} - 2} \]

   6. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \frac{1}{t} - \color{blue}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 48.6%

      \[\leadsto \frac{2}{t} - \color{blue}{2} \]

   if -4.9999999999999997e104 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.99999999999999993e90 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 71.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Applied rewrites 84.1%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]

   if 1.99999999999999993e90 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 97.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{1 - t}{t \cdot x} + \left(\frac{1}{y} + \frac{2}{t \cdot \left(x \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 80.5%

      \[\leadsto \color{blue}{\left(\frac{\frac{\frac{2}{z} - -2}{t} - 2}{x} + \frac{1}{y}\right) \cdot x} \]

   6. Taylor expanded in z around 0

      \[\leadsto \frac{2}{\color{blue}{t \cdot z}} \]
   7. Step-by-step derivation

   8. Applied rewrites 59.0%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -1 \cdot 10^{+276}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq 2 \cdot 10^{+90} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq \infty\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+276}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+90} \lor \neg \left(t\_2 \leq \infty\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z)))
        (t_2 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (<= t_2 -1e+276)
     t_1
     (if (<= t_2 -5e+104)
       (- (/ 2.0 t) 2.0)
       (if (or (<= t_2 2e+90) (not (<= t_2 INFINITY)))
         (+ (/ x y) -2.0)
         t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_2 <= -1e+276) {
		tmp = t_1;
	} else if (t_2 <= -5e+104) {
		tmp = (2.0 / t) - 2.0;
	} else if ((t_2 <= 2e+90) || !(t_2 <= ((double) INFINITY))) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_2 <= -1e+276) {
		tmp = t_1;
	} else if (t_2 <= -5e+104) {
		tmp = (2.0 / t) - 2.0;
	} else if ((t_2 <= 2e+90) || !(t_2 <= Double.POSITIVE_INFINITY)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if t_2 <= -1e+276:
		tmp = t_1
	elif t_2 <= -5e+104:
		tmp = (2.0 / t) - 2.0
	elif (t_2 <= 2e+90) or not (t_2 <= math.inf):
		tmp = (x / y) + -2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if (t_2 <= -1e+276)
		tmp = t_1;
	elseif (t_2 <= -5e+104)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	elseif ((t_2 <= 2e+90) || !(t_2 <= Inf))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if (t_2 <= -1e+276)
		tmp = t_1;
	elseif (t_2 <= -5e+104)
		tmp = (2.0 / t) - 2.0;
	elseif ((t_2 <= 2e+90) || ~((t_2 <= Inf)))
		tmp = (x / y) + -2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+276], t$95$1, If[LessEqual[t$95$2, -5e+104], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], If[Or[LessEqual[t$95$2, 2e+90], N[Not[LessEqual[t$95$2, Infinity]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.0000000000000001e276 or 1.99999999999999993e90 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 97.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{1 - t}{t \cdot x} + \left(\frac{1}{y} + \frac{2}{t \cdot \left(x \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 79.6%

      \[\leadsto \color{blue}{\left(\frac{\frac{\frac{2}{z} - -2}{t} - 2}{x} + \frac{1}{y}\right) \cdot x} \]

   6. Taylor expanded in z around 0

      \[\leadsto \frac{2}{\color{blue}{t \cdot z}} \]
   7. Step-by-step derivation

   8. Applied rewrites 69.0%

      \[\leadsto \frac{\frac{2}{t}}{\color{blue}{z}} \]
   9. Step-by-step derivation

   10. Applied rewrites 69.0%

       \[\leadsto \frac{2}{t \cdot \color{blue}{z}} \]

   if -1.0000000000000001e276 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -4.9999999999999997e104

   1. Initial program 99.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 80.4%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t} - 2} \]

   6. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \frac{1}{t} - \color{blue}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 48.6%

      \[\leadsto \frac{2}{t} - \color{blue}{2} \]

   if -4.9999999999999997e104 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.99999999999999993e90 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 71.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Applied rewrites 84.1%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -1 \cdot 10^{+276}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -5 \cdot 10^{+104}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq 2 \cdot 10^{+90} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq \infty\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+35} \lor \neg \left(t\_1 \leq 100000000 \lor \neg \left(t\_1 \leq \infty\right)\right):\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (or (<= t_1 -5e+35)
           (not (or (<= t_1 100000000.0) (not (<= t_1 INFINITY)))))
     (/ (- (/ 2.0 z) -2.0) t)
     (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if ((t_1 <= -5e+35) || !((t_1 <= 100000000.0) || !(t_1 <= ((double) INFINITY)))) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if ((t_1 <= -5e+35) || !((t_1 <= 100000000.0) || !(t_1 <= Double.POSITIVE_INFINITY))) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if (t_1 <= -5e+35) or not ((t_1 <= 100000000.0) or not (t_1 <= math.inf)):
		tmp = ((2.0 / z) - -2.0) / t
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if ((t_1 <= -5e+35) || !((t_1 <= 100000000.0) || !(t_1 <= Inf)))
		tmp = Float64(Float64(Float64(2.0 / z) - -2.0) / t);
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if ((t_1 <= -5e+35) || ~(((t_1 <= 100000000.0) || ~((t_1 <= Inf)))))
		tmp = ((2.0 / z) - -2.0) / t;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+35], N[Not[Or[LessEqual[t$95$1, 100000000.0], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]]], $MachinePrecision]], N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -5.00000000000000021e35 or 1e8 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 98.3%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} + 2}}{t} \]

      3. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} + \color{blue}{2 \cdot 1}}{t} \]

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

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - \left(\mathsf{neg}\left(2\right)\right) \cdot 1}}{t} \]

      5. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2} \cdot 1}{t} \]

      6. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2}}{t} \]

      7. lower--.f64 N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - -2}}{t} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\color{blue}{\frac{2 \cdot 1}{z}} - -2}{t} \]

      9. metadata-eval N/A

         \[\leadsto \frac{\frac{\color{blue}{2}}{z} - -2}{t} \]

      10. lower-/.f64 80.0

          \[\leadsto \frac{\color{blue}{\frac{2}{z}} - -2}{t} \]

   5. Applied rewrites 80.0%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t}} \]

   if -5.00000000000000021e35 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1e8 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 64.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Applied rewrites 95.1%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -5 \cdot 10^{+35} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq 100000000 \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq \infty\right)\right):\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{z} - -2}{t}\\ t_2 := t\_1 - 2\\ \mathbf{if}\;\frac{x}{y} \leq -20000000:\\ \;\;\;\;\frac{x}{y} + t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-62}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t\_2, y, x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- (/ 2.0 z) -2.0) t)) (t_2 (- t_1 2.0)))
   (if (<= (/ x y) -20000000.0)
     (+ (/ x y) t_1)
     (if (<= (/ x y) 4e-62) t_2 (/ (fma t_2 y x) y)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / z) - -2.0) / t;
	double t_2 = t_1 - 2.0;
	double tmp;
	if ((x / y) <= -20000000.0) {
		tmp = (x / y) + t_1;
	} else if ((x / y) <= 4e-62) {
		tmp = t_2;
	} else {
		tmp = fma(t_2, y, x) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(2.0 / z) - -2.0) / t)
	t_2 = Float64(t_1 - 2.0)
	tmp = 0.0
	if (Float64(x / y) <= -20000000.0)
		tmp = Float64(Float64(x / y) + t_1);
	elseif (Float64(x / y) <= 4e-62)
		tmp = t_2;
	else
		tmp = Float64(fma(t_2, y, x) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - 2.0), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -20000000.0], N[(N[(x / y), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4e-62], t$95$2, N[(N[(t$95$2 * y + x), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e7

   1. Initial program 82.3%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{2 + 2 \cdot z}{t \cdot z}} \]

   5. Applied rewrites 97.1%

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{\frac{2}{z} - -2}{t}} \]

   if -2e7 < (/.f64 x y) < 4.0000000000000002e-62

   1. Initial program 79.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t} - 2} \]

   if 4.0000000000000002e-62 < (/.f64 x y)

   1. Initial program 92.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{1 - t}{t \cdot x} + \left(\frac{1}{y} + \frac{2}{t \cdot \left(x \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 96.6%

      \[\leadsto \color{blue}{\left(\frac{\frac{\frac{2}{z} - -2}{t} - 2}{x} + \frac{1}{y}\right) \cdot x} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x + y \cdot \left(2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}\right)}{y}} \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x + y \cdot \left(2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}\right)}{y}} \]

   8. Applied rewrites 99.9%

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

Alternative 7: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{z} - -2}{t}\\ \mathbf{if}\;\frac{x}{y} \leq -20000000 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{x}{y} + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- (/ 2.0 z) -2.0) t)))
   (if (or (<= (/ x y) -20000000.0) (not (<= (/ x y) 4e-24)))
     (+ (/ x y) t_1)
     (- t_1 2.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / z) - -2.0) / t;
	double tmp;
	if (((x / y) <= -20000000.0) || !((x / y) <= 4e-24)) {
		tmp = (x / y) + t_1;
	} else {
		tmp = t_1 - 2.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((2.0d0 / z) - (-2.0d0)) / t
    if (((x / y) <= (-20000000.0d0)) .or. (.not. ((x / y) <= 4d-24))) then
        tmp = (x / y) + t_1
    else
        tmp = t_1 - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / z) - -2.0) / t;
	double tmp;
	if (((x / y) <= -20000000.0) || !((x / y) <= 4e-24)) {
		tmp = (x / y) + t_1;
	} else {
		tmp = t_1 - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((2.0 / z) - -2.0) / t
	tmp = 0
	if ((x / y) <= -20000000.0) or not ((x / y) <= 4e-24):
		tmp = (x / y) + t_1
	else:
		tmp = t_1 - 2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(2.0 / z) - -2.0) / t)
	tmp = 0.0
	if ((Float64(x / y) <= -20000000.0) || !(Float64(x / y) <= 4e-24))
		tmp = Float64(Float64(x / y) + t_1);
	else
		tmp = Float64(t_1 - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((2.0 / z) - -2.0) / t;
	tmp = 0.0;
	if (((x / y) <= -20000000.0) || ~(((x / y) <= 4e-24)))
		tmp = (x / y) + t_1;
	else
		tmp = t_1 - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision]}, If[Or[LessEqual[N[(x / y), $MachinePrecision], -20000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e-24]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e7 or 3.99999999999999969e-24 < (/.f64 x y)

   1. Initial program 89.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{2 + 2 \cdot z}{t \cdot z}} \]

   5. Applied rewrites 97.4%

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{\frac{2}{z} - -2}{t}} \]

   if -2e7 < (/.f64 x y) < 3.99999999999999969e-24

   1. Initial program 79.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 99.9%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -20000000 \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -20000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{\frac{2}{z}}{t} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -20000000.0) (not (<= (/ x y) 5e+30)))
   (+ (/ (/ 2.0 z) t) (/ x y))
   (- (/ (- (/ 2.0 z) -2.0) t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -20000000.0) || !((x / y) <= 5e+30)) {
		tmp = ((2.0 / z) / t) + (x / y);
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-20000000.0d0)) .or. (.not. ((x / y) <= 5d+30))) then
        tmp = ((2.0d0 / z) / t) + (x / y)
    else
        tmp = (((2.0d0 / z) - (-2.0d0)) / t) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -20000000.0) || !((x / y) <= 5e+30)) {
		tmp = ((2.0 / z) / t) + (x / y);
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -20000000.0) or not ((x / y) <= 5e+30):
		tmp = ((2.0 / z) / t) + (x / y)
	else:
		tmp = (((2.0 / z) - -2.0) / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -20000000.0) || !(Float64(x / y) <= 5e+30))
		tmp = Float64(Float64(Float64(2.0 / z) / t) + Float64(x / y));
	else
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -20000000.0) || ~(((x / y) <= 5e+30)))
		tmp = ((2.0 / z) / t) + (x / y);
	else
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -20000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e+30]], $MachinePrecision]], N[(N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e7 or 4.9999999999999998e30 < (/.f64 x y)

   1. Initial program 88.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{2}}{t \cdot z} \]
   4. Step-by-step derivation

   5. Applied rewrites 90.7%

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{2}}{t \cdot z} \]
   6. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{y} + \frac{2}{t \cdot z}} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\frac{2}{t \cdot z} + \frac{x}{y}} \]

      3. lower-+.f64 90.7

         \[\leadsto \color{blue}{\frac{2}{t \cdot z} + \frac{x}{y}} \]

      4. lift-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2}{t \cdot z}} + \frac{x}{y} \]

      5. lift-*.f64 N/A

         \[\leadsto \frac{2}{\color{blue}{t \cdot z}} + \frac{x}{y} \]

      6. *-commutative N/A

         \[\leadsto \frac{2}{\color{blue}{z \cdot t}} + \frac{x}{y} \]

      7. associate-/r* N/A

         \[\leadsto \color{blue}{\frac{\frac{2}{z}}{t}} + \frac{x}{y} \]

      8. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{\frac{2}{z}}{t}} + \frac{x}{y} \]

      9. lower-/.f64 90.8

         \[\leadsto \frac{\color{blue}{\frac{2}{z}}}{t} + \frac{x}{y} \]

   7. Applied rewrites 90.8%

      \[\leadsto \color{blue}{\frac{\frac{2}{z}}{t} + \frac{x}{y}} \]

   if -2e7 < (/.f64 x y) < 4.9999999999999998e30

   1. Initial program 80.2%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 98.1%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -20000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{\frac{2}{z}}{t} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -20000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -20000000.0) (not (<= (/ x y) 5e+30)))
   (+ (/ x y) (/ 2.0 (* t z)))
   (- (/ (- (/ 2.0 z) -2.0) t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -20000000.0) || !((x / y) <= 5e+30)) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-20000000.0d0)) .or. (.not. ((x / y) <= 5d+30))) then
        tmp = (x / y) + (2.0d0 / (t * z))
    else
        tmp = (((2.0d0 / z) - (-2.0d0)) / t) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -20000000.0) || !((x / y) <= 5e+30)) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -20000000.0) or not ((x / y) <= 5e+30):
		tmp = (x / y) + (2.0 / (t * z))
	else:
		tmp = (((2.0 / z) - -2.0) / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -20000000.0) || !(Float64(x / y) <= 5e+30))
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	else
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -20000000.0) || ~(((x / y) <= 5e+30)))
		tmp = (x / y) + (2.0 / (t * z));
	else
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -20000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e+30]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e7 or 4.9999999999999998e30 < (/.f64 x y)

   1. Initial program 88.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{2}}{t \cdot z} \]
   4. Step-by-step derivation

   5. Applied rewrites 90.7%

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{2}}{t \cdot z} \]

   if -2e7 < (/.f64 x y) < 4.9999999999999998e30

   1. Initial program 80.2%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 98.1%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -20000000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+56} \lor \neg \left(\frac{x}{y} \leq 10^{+23}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4e+56) (not (<= (/ x y) 1e+23)))
   (+ (/ x y) (- -2.0 (/ -2.0 t)))
   (- (/ (- (/ 2.0 z) -2.0) t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4e+56) || !((x / y) <= 1e+23)) {
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-4d+56)) .or. (.not. ((x / y) <= 1d+23))) then
        tmp = (x / y) + ((-2.0d0) - ((-2.0d0) / t))
    else
        tmp = (((2.0d0 / z) - (-2.0d0)) / t) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4e+56) || !((x / y) <= 1e+23)) {
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -4e+56) or not ((x / y) <= 1e+23):
		tmp = (x / y) + (-2.0 - (-2.0 / t))
	else:
		tmp = (((2.0 / z) - -2.0) / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4e+56) || !(Float64(x / y) <= 1e+23))
		tmp = Float64(Float64(x / y) + Float64(-2.0 - Float64(-2.0 / t)));
	else
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -4e+56) || ~(((x / y) <= 1e+23)))
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	else
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -4e+56], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e+23]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.00000000000000037e56 or 9.9999999999999992e22 < (/.f64 x y)

   1. Initial program 88.1%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \frac{x}{y} + \color{blue}{2 \cdot \frac{1 - t}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{x}{y} + \color{blue}{\frac{2 \cdot \left(1 - t\right)}{t}} \]

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

         \[\leadsto \frac{x}{y} + \frac{\color{blue}{2 \cdot 1 - 2 \cdot t}}{t} \]

      3. metadata-eval N/A

         \[\leadsto \frac{x}{y} + \frac{\color{blue}{2} - 2 \cdot t}{t} \]

      4. metadata-eval N/A

         \[\leadsto \frac{x}{y} + \frac{2 - \color{blue}{\left(\mathsf{neg}\left(-2\right)\right)} \cdot t}{t} \]

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

         \[\leadsto \frac{x}{y} + \frac{\color{blue}{2 + -2 \cdot t}}{t} \]

      6. +-commutative N/A

         \[\leadsto \frac{x}{y} + \frac{\color{blue}{-2 \cdot t + 2}}{t} \]

      7. metadata-eval N/A

         \[\leadsto \frac{x}{y} + \frac{-2 \cdot t + \color{blue}{2 \cdot 1}}{t} \]

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

         \[\leadsto \frac{x}{y} + \frac{\color{blue}{-2 \cdot t - \left(\mathsf{neg}\left(2\right)\right) \cdot 1}}{t} \]

      9. metadata-eval N/A

         \[\leadsto \frac{x}{y} + \frac{-2 \cdot t - \color{blue}{-2} \cdot 1}{t} \]

      10. metadata-eval N/A

          \[\leadsto \frac{x}{y} + \frac{-2 \cdot t - \color{blue}{-2}}{t} \]

      11. div-sub N/A

          \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{-2 \cdot t}{t} - \frac{-2}{t}\right)} \]

      12. associate-*r/ N/A

          \[\leadsto \frac{x}{y} + \left(\color{blue}{-2 \cdot \frac{t}{t}} - \frac{-2}{t}\right) \]

      13. metadata-eval N/A

          \[\leadsto \frac{x}{y} + \left(\color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot \frac{t}{t} - \frac{-2}{t}\right) \]

      14. *-inverses N/A

          \[\leadsto \frac{x}{y} + \left(\left(\mathsf{neg}\left(2\right)\right) \cdot \color{blue}{1} - \frac{-2}{t}\right) \]

      15. metadata-eval N/A

          \[\leadsto \frac{x}{y} + \left(\color{blue}{-2} \cdot 1 - \frac{-2}{t}\right) \]

      16. metadata-eval N/A

          \[\leadsto \frac{x}{y} + \left(\color{blue}{-2} - \frac{-2}{t}\right) \]

      17. metadata-eval N/A

          \[\leadsto \frac{x}{y} + \left(-2 - \frac{\color{blue}{-2 \cdot 1}}{t}\right) \]

      18. associate-*r/ N/A

          \[\leadsto \frac{x}{y} + \left(-2 - \color{blue}{-2 \cdot \frac{1}{t}}\right) \]

      19. metadata-eval N/A

          \[\leadsto \frac{x}{y} + \left(-2 - \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot \frac{1}{t}\right) \]

      20. lower--.f64 N/A

          \[\leadsto \frac{x}{y} + \color{blue}{\left(-2 - \left(\mathsf{neg}\left(2\right)\right) \cdot \frac{1}{t}\right)} \]

      21. metadata-eval N/A

          \[\leadsto \frac{x}{y} + \left(-2 - \color{blue}{-2} \cdot \frac{1}{t}\right) \]

      22. associate-*r/ N/A

          \[\leadsto \frac{x}{y} + \left(-2 - \color{blue}{\frac{-2 \cdot 1}{t}}\right) \]

      23. metadata-eval N/A

          \[\leadsto \frac{x}{y} + \left(-2 - \frac{\color{blue}{-2}}{t}\right) \]

      24. lower-/.f64 82.9

          \[\leadsto \frac{x}{y} + \left(-2 - \color{blue}{\frac{-2}{t}}\right) \]

   5. Applied rewrites 82.9%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(-2 - \frac{-2}{t}\right)} \]

   if -4.00000000000000037e56 < (/.f64 x y) < 9.9999999999999992e22

   1. Initial program 81.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 95.3%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+56} \lor \neg \left(\frac{x}{y} \leq 10^{+23}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 85.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+56} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4e+56) (not (<= (/ x y) 5e+30)))
   (/ x y)
   (- (/ (- (/ 2.0 z) -2.0) t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4e+56) || !((x / y) <= 5e+30)) {
		tmp = x / y;
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-4d+56)) .or. (.not. ((x / y) <= 5d+30))) then
        tmp = x / y
    else
        tmp = (((2.0d0 / z) - (-2.0d0)) / t) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4e+56) || !((x / y) <= 5e+30)) {
		tmp = x / y;
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -4e+56) or not ((x / y) <= 5e+30):
		tmp = x / y
	else:
		tmp = (((2.0 / z) - -2.0) / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4e+56) || !(Float64(x / y) <= 5e+30))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -4e+56) || ~(((x / y) <= 5e+30)))
		tmp = x / y;
	else
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -4e+56], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e+30]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.00000000000000037e56 or 4.9999999999999998e30 < (/.f64 x y)

   1. Initial program 87.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{1 - t}{t \cdot x} + \left(\frac{1}{y} + \frac{2}{t \cdot \left(x \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 98.0%

      \[\leadsto \color{blue}{\left(\frac{\frac{\frac{2}{z} - -2}{t} - 2}{x} + \frac{1}{y}\right) \cdot x} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x + y \cdot \left(2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}\right)}{y}} \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x + y \cdot \left(2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}\right)}{y}} \]

   8. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{\frac{2}{z} - -2}{t} - 2, y, x\right)}{y}} \]

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 75.1%

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

   if -4.00000000000000037e56 < (/.f64 x y) < 4.9999999999999998e30

   1. Initial program 81.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 94.8%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+56} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 70.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+56}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+23}:\\ \;\;\;\;\frac{\frac{2}{z}}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -4e+56)
   (/ x y)
   (if (<= (/ x y) 5e+23) (- (/ (/ 2.0 z) t) 2.0) (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4e+56) {
		tmp = x / y;
	} else if ((x / y) <= 5e+23) {
		tmp = ((2.0 / z) / t) - 2.0;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-4d+56)) then
        tmp = x / y
    else if ((x / y) <= 5d+23) then
        tmp = ((2.0d0 / z) / t) - 2.0d0
    else
        tmp = (x / y) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4e+56) {
		tmp = x / y;
	} else if ((x / y) <= 5e+23) {
		tmp = ((2.0 / z) / t) - 2.0;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -4e+56:
		tmp = x / y
	elif (x / y) <= 5e+23:
		tmp = ((2.0 / z) / t) - 2.0
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -4e+56)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 5e+23)
		tmp = Float64(Float64(Float64(2.0 / z) / t) - 2.0);
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -4e+56)
		tmp = x / y;
	elseif ((x / y) <= 5e+23)
		tmp = ((2.0 / z) / t) - 2.0;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -4e+56], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e+23], N[(N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.00000000000000037e56

   1. Initial program 76.3%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{1 - t}{t \cdot x} + \left(\frac{1}{y} + \frac{2}{t \cdot \left(x \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\frac{\frac{\frac{2}{z} - -2}{t} - 2}{x} + \frac{1}{y}\right) \cdot x} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x + y \cdot \left(2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}\right)}{y}} \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x + y \cdot \left(2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}\right)}{y}} \]

   8. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{\frac{2}{z} - -2}{t} - 2, y, x\right)}{y}} \]

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 89.6%

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

   if -4.00000000000000037e56 < (/.f64 x y) < 4.9999999999999999e23

   1. Initial program 81.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 95.4%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t} - 2} \]

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\frac{2}{z}}{t} - 2 \]
   7. Step-by-step derivation

   8. Applied rewrites 71.7%

      \[\leadsto \frac{\frac{2}{z}}{t} - 2 \]

   if 4.9999999999999999e23 < (/.f64 x y)

   1. Initial program 95.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Applied rewrites 65.6%

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

Alternative 13: 65.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -7200 \lor \neg \left(\frac{x}{y} \leq 0.008\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -7200.0) (not (<= (/ x y) 0.008)))
   (+ (/ x y) -2.0)
   (- (/ 2.0 t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -7200.0) || !((x / y) <= 0.008)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-7200.0d0)) .or. (.not. ((x / y) <= 0.008d0))) then
        tmp = (x / y) + (-2.0d0)
    else
        tmp = (2.0d0 / t) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -7200.0) || !((x / y) <= 0.008)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -7200.0) or not ((x / y) <= 0.008):
		tmp = (x / y) + -2.0
	else:
		tmp = (2.0 / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -7200.0) || !(Float64(x / y) <= 0.008))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(Float64(2.0 / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -7200.0) || ~(((x / y) <= 0.008)))
		tmp = (x / y) + -2.0;
	else
		tmp = (2.0 / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -7200.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.008]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -7200 or 0.0080000000000000002 < (/.f64 x y)

   1. Initial program 89.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Applied rewrites 66.1%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]

   if -7200 < (/.f64 x y) < 0.0080000000000000002

   1. Initial program 79.2%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t} - 2} \]

   6. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \frac{1}{t} - \color{blue}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 65.1%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -7200 \lor \neg \left(\frac{x}{y} \leq 0.008\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.65 \cdot 10^{+25} \lor \neg \left(\frac{x}{y} \leq 4.3 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1.65e+25) (not (<= (/ x y) 4.3e+30)))
   (/ x y)
   (- (/ 2.0 t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.65e+25) || !((x / y) <= 4.3e+30)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1.65d+25)) .or. (.not. ((x / y) <= 4.3d+30))) then
        tmp = x / y
    else
        tmp = (2.0d0 / t) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.65e+25) || !((x / y) <= 4.3e+30)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1.65e+25) or not ((x / y) <= 4.3e+30):
		tmp = x / y
	else:
		tmp = (2.0 / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1.65e+25) || !(Float64(x / y) <= 4.3e+30))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(2.0 / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1.65e+25) || ~(((x / y) <= 4.3e+30)))
		tmp = x / y;
	else
		tmp = (2.0 / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1.65e+25], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4.3e+30]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.6500000000000001e25 or 4.3e30 < (/.f64 x y)

   1. Initial program 88.2%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{1 - t}{t \cdot x} + \left(\frac{1}{y} + \frac{2}{t \cdot \left(x \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 97.4%

      \[\leadsto \color{blue}{\left(\frac{\frac{\frac{2}{z} - -2}{t} - 2}{x} + \frac{1}{y}\right) \cdot x} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x + y \cdot \left(2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}\right)}{y}} \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x + y \cdot \left(2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}\right)}{y}} \]

   8. Applied rewrites 97.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{\frac{2}{z} - -2}{t} - 2, y, x\right)}{y}} \]

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 70.2%

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

   if -1.6500000000000001e25 < (/.f64 x y) < 4.3e30

   1. Initial program 81.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

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

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

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

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 96.9%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t} - 2} \]

   6. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \frac{1}{t} - \color{blue}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 61.7%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.65 \cdot 10^{+25} \lor \neg \left(\frac{x}{y} \leq 4.3 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 47.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -88000 \lor \neg \left(\frac{x}{y} \leq 4.3 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -88000.0) (not (<= (/ x y) 4.3e+30))) (/ x y) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -88000.0) || !((x / y) <= 4.3e+30)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-88000.0d0)) .or. (.not. ((x / y) <= 4.3d+30))) then
        tmp = x / y
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -88000.0) || !((x / y) <= 4.3e+30)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -88000.0) or not ((x / y) <= 4.3e+30):
		tmp = x / y
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -88000.0) || !(Float64(x / y) <= 4.3e+30))
		tmp = Float64(x / y);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -88000.0) || ~(((x / y) <= 4.3e+30)))
		tmp = x / y;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -88000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4.3e+30]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -88000 or 4.3e30 < (/.f64 x y)

   1. Initial program 88.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{1 - t}{t \cdot x} + \left(\frac{1}{y} + \frac{2}{t \cdot \left(x \cdot z\right)}\right)\right)} \]

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\left(\frac{\frac{\frac{2}{z} - -2}{t} - 2}{x} + \frac{1}{y}\right) \cdot x} \]

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x + y \cdot \left(2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}\right)}{y}} \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x + y \cdot \left(2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}\right)}{y}} \]

   8. Applied rewrites 96.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{\frac{2}{z} - -2}{t} - 2, y, x\right)}{y}} \]

   9. Taylor expanded in x around inf

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

   11. Applied rewrites 67.8%

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

   if -88000 < (/.f64 x y) < 4.3e30

   1. Initial program 80.2%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} + 2}}{t} \]

      3. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} + \color{blue}{2 \cdot 1}}{t} \]

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

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - \left(\mathsf{neg}\left(2\right)\right) \cdot 1}}{t} \]

      5. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2} \cdot 1}{t} \]

      6. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2}}{t} \]

      7. lower--.f64 N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - -2}}{t} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\color{blue}{\frac{2 \cdot 1}{z}} - -2}{t} \]

      9. metadata-eval N/A

         \[\leadsto \frac{\frac{\color{blue}{2}}{z} - -2}{t} \]

      10. lower-/.f64 60.7

          \[\leadsto \frac{\color{blue}{\frac{2}{z}} - -2}{t} \]

   5. Applied rewrites 60.7%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t}} \]

   6. Taylor expanded in z around inf

      \[\leadsto \frac{2}{\color{blue}{t}} \]
   7. Step-by-step derivation

   8. Applied rewrites 27.1%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -88000 \lor \neg \left(\frac{x}{y} \leq 4.3 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 35.4% accurate, 3.9× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.2%

   \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{1 - t}{t \cdot x} + \left(\frac{1}{y} + \frac{2}{t \cdot \left(x \cdot z\right)}\right)\right)} \]

5. Applied rewrites 87.5%

   \[\leadsto \color{blue}{\left(\frac{\frac{\frac{2}{z} - -2}{t} - 2}{x} + \frac{1}{y}\right) \cdot x} \]

6. Taylor expanded in y around 0

   \[\leadsto \color{blue}{\frac{x + y \cdot \left(2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}\right)}{y}} \]
7. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{x + y \cdot \left(2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}\right)}{y}} \]

8. Applied rewrites 90.8%

   \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{\frac{2}{z} - -2}{t} - 2, y, x\right)}{y}} \]

9. Taylor expanded in x around inf

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

11. Applied rewrites 33.2%

    \[\leadsto \frac{x}{\color{blue}{y}} \]
12. Add Preprocessing

Developer Target 1: 99.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y))))

C

double code(double x, double y, double z, double t) {
	return (((2.0 / z) + 2.0) / t) - (2.0 - (x / y));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((2.0d0 / z) + 2.0d0) / t) - (2.0d0 - (x / y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((2.0 / z) + 2.0) / t) - (2.0 - (x / y));
}

Python

def code(x, y, z, t):
	return (((2.0 / z) + 2.0) / t) - (2.0 - (x / y))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(2.0 / z) + 2.0) / t) - Float64(2.0 - Float64(x / y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((2.0 / z) + 2.0) / t) - (2.0 - (x / y));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(2.0 / z), $MachinePrecision] + 2.0), $MachinePrecision] / t), $MachinePrecision] - N[(2.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2025015 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y))))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))