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

Percentage Accurate: 86.3% → 99.4%

Time: 8.1s

Alternatives: 12

Speedup: 1.1×

• 23.0% 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: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.0%

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

3. Taylor expanded in x around 0

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

   1. associate-+r+ N/A

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

   2. +-commutative N/A

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

   3. associate-*r/ N/A

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

   4. *-commutative N/A

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

   5. associate-/l* N/A

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

   6. metadata-eval N/A

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

   7. associate-*r/ N/A

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

   8. associate-/r* N/A

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

   9. associate-*r/ N/A

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

   10. metadata-eval N/A

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

   11. associate-*r* N/A

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

   12. associate-*l/ N/A

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

   13. distribute-rgt-out N/A

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

   14. lower-fma.f64 N/A

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

5. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{2}{t}, \frac{1 + z}{z} - t, \frac{x}{y}\right)} \]
6. Add Preprocessing

Alternative 2: 69.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_3 := \frac{\left(1 - t\right) \cdot 2}{t}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+154}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+291}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0))
        (t_2 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))
        (t_3 (/ (* (- 1.0 t) 2.0) t)))
   (if (<= t_2 (- INFINITY))
     (/ 2.0 (* t z))
     (if (<= t_2 -2e+154)
       t_3
       (if (<= t_2 2e+127)
         t_1
         (if (<= t_2 5e+291)
           t_3
           (if (<= t_2 INFINITY) (/ (/ 2.0 z) t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_3 = ((1.0 - t) * 2.0) / t;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = 2.0 / (t * z);
	} else if (t_2 <= -2e+154) {
		tmp = t_3;
	} else if (t_2 <= 2e+127) {
		tmp = t_1;
	} else if (t_2 <= 5e+291) {
		tmp = t_3;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (2.0 / z) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_3 = ((1.0 - t) * 2.0) / t;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = 2.0 / (t * z);
	} else if (t_2 <= -2e+154) {
		tmp = t_3;
	} else if (t_2 <= 2e+127) {
		tmp = t_1;
	} else if (t_2 <= 5e+291) {
		tmp = t_3;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (2.0 / z) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	t_3 = ((1.0 - t) * 2.0) / t
	tmp = 0
	if t_2 <= -math.inf:
		tmp = 2.0 / (t * z)
	elif t_2 <= -2e+154:
		tmp = t_3
	elif t_2 <= 2e+127:
		tmp = t_1
	elif t_2 <= 5e+291:
		tmp = t_3
	elif t_2 <= math.inf:
		tmp = (2.0 / z) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	t_2 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	t_3 = Float64(Float64(Float64(1.0 - t) * 2.0) / t)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(2.0 / Float64(t * z));
	elseif (t_2 <= -2e+154)
		tmp = t_3;
	elseif (t_2 <= 2e+127)
		tmp = t_1;
	elseif (t_2 <= 5e+291)
		tmp = t_3;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(2.0 / z) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	t_3 = ((1.0 - t) * 2.0) / t;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = 2.0 / (t * z);
	elseif (t_2 <= -2e+154)
		tmp = t_3;
	elseif (t_2 <= 2e+127)
		tmp = t_1;
	elseif (t_2 <= 5e+291)
		tmp = t_3;
	elseif (t_2 <= Inf)
		tmp = (2.0 / z) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + -2.0), $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]}, Block[{t$95$3 = N[(N[(N[(1.0 - t), $MachinePrecision] * 2.0), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e+154], t$95$3, If[LessEqual[t$95$2, 2e+127], t$95$1, If[LessEqual[t$95$2, 5e+291], t$95$3, If[LessEqual[t$95$2, Infinity], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]]]]]]

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)) < -inf.0

   1. Initial program 96.3%

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

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 96.3

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

   8. Applied rewrites 96.3%

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

   if -inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -2.00000000000000007e154 or 1.99999999999999991e127 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 5.0000000000000001e291

   1. Initial program 99.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-/l* N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

   5. Applied rewrites 79.0%

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

   6. Taylor expanded in z around inf

      \[\leadsto \frac{2 \cdot \left(1 - t\right)}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 48.5%

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

   if -2.00000000000000007e154 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.99999999999999991e127 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 73.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 88.9%

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

   if 5.0000000000000001e291 < (/.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 95.2%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-/l* N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

   5. Applied rewrites 90.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 90.5%

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

Alternative 3: 69.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{x}{y} + -2\\ t_3 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_4 := \frac{\left(1 - t\right) \cdot 2}{t}\\ \mathbf{if}\;t\_3 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq -2 \cdot 10^{+154}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+127}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+291}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z)))
        (t_2 (+ (/ x y) -2.0))
        (t_3 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))
        (t_4 (/ (* (- 1.0 t) 2.0) t)))
   (if (<= t_3 (- INFINITY))
     t_1
     (if (<= t_3 -2e+154)
       t_4
       (if (<= t_3 2e+127)
         t_2
         (if (<= t_3 5e+291) t_4 (if (<= t_3 INFINITY) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) + -2.0;
	double t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_4 = ((1.0 - t) * 2.0) / t;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_3 <= -2e+154) {
		tmp = t_4;
	} else if (t_3 <= 2e+127) {
		tmp = t_2;
	} else if (t_3 <= 5e+291) {
		tmp = t_4;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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 = (x / y) + -2.0;
	double t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_4 = ((1.0 - t) * 2.0) / t;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_3 <= -2e+154) {
		tmp = t_4;
	} else if (t_3 <= 2e+127) {
		tmp = t_2;
	} else if (t_3 <= 5e+291) {
		tmp = t_4;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (x / y) + -2.0
	t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	t_4 = ((1.0 - t) * 2.0) / t
	tmp = 0
	if t_3 <= -math.inf:
		tmp = t_1
	elif t_3 <= -2e+154:
		tmp = t_4
	elif t_3 <= 2e+127:
		tmp = t_2
	elif t_3 <= 5e+291:
		tmp = t_4
	elif t_3 <= math.inf:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(x / y) + -2.0)
	t_3 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	t_4 = Float64(Float64(Float64(1.0 - t) * 2.0) / t)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_3 <= -2e+154)
		tmp = t_4;
	elseif (t_3 <= 2e+127)
		tmp = t_2;
	elseif (t_3 <= 5e+291)
		tmp = t_4;
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = (x / y) + -2.0;
	t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	t_4 = ((1.0 - t) * 2.0) / t;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = t_1;
	elseif (t_3 <= -2e+154)
		tmp = t_4;
	elseif (t_3 <= 2e+127)
		tmp = t_2;
	elseif (t_3 <= 5e+291)
		tmp = t_4;
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_2;
	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[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(1.0 - t), $MachinePrecision] * 2.0), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], t$95$1, If[LessEqual[t$95$3, -2e+154], t$95$4, If[LessEqual[t$95$3, 2e+127], t$95$2, If[LessEqual[t$95$3, 5e+291], t$95$4, If[LessEqual[t$95$3, Infinity], t$95$1, t$95$2]]]]]]]]]

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)) < -inf.0 or 5.0000000000000001e291 < (/.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 95.8%

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

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 93.6

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

   8. Applied rewrites 93.6%

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

   if -inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -2.00000000000000007e154 or 1.99999999999999991e127 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 5.0000000000000001e291

   1. Initial program 99.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-/l* N/A

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

      5. div-add-rev N/A

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

      6. lower-/.f64 N/A

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

   5. Applied rewrites 79.0%

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

   6. Taylor expanded in z around inf

      \[\leadsto \frac{2 \cdot \left(1 - t\right)}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 48.5%

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

   if -2.00000000000000007e154 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.99999999999999991e127 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 73.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 88.9%

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

Alternative 4: 69.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_3 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -2 \cdot 10^{+154}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+127}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+291}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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)))
        (t_3 (+ (/ x y) -2.0)))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e+154)
       (/ 2.0 t)
       (if (<= t_2 2e+127)
         t_3
         (if (<= t_2 5e+291) (/ 2.0 t) (if (<= t_2 INFINITY) t_1 t_3)))))))

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 t_3 = (x / y) + -2.0;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e+154) {
		tmp = 2.0 / t;
	} else if (t_2 <= 2e+127) {
		tmp = t_3;
	} else if (t_2 <= 5e+291) {
		tmp = 2.0 / t;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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 t_3 = (x / y) + -2.0;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e+154) {
		tmp = 2.0 / t;
	} else if (t_2 <= 2e+127) {
		tmp = t_3;
	} else if (t_2 <= 5e+291) {
		tmp = 2.0 / t;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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)
	t_3 = (x / y) + -2.0
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e+154:
		tmp = 2.0 / t
	elif t_2 <= 2e+127:
		tmp = t_3
	elif t_2 <= 5e+291:
		tmp = 2.0 / t
	elif t_2 <= math.inf:
		tmp = t_1
	else:
		tmp = t_3
	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))
	t_3 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e+154)
		tmp = Float64(2.0 / t);
	elseif (t_2 <= 2e+127)
		tmp = t_3;
	elseif (t_2 <= 5e+291)
		tmp = Float64(2.0 / t);
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	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);
	t_3 = (x / y) + -2.0;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e+154)
		tmp = 2.0 / t;
	elseif (t_2 <= 2e+127)
		tmp = t_3;
	elseif (t_2 <= 5e+291)
		tmp = 2.0 / t;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	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]}, Block[{t$95$3 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e+154], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$2, 2e+127], t$95$3, If[LessEqual[t$95$2, 5e+291], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$1, t$95$3]]]]]]]]

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)) < -inf.0 or 5.0000000000000001e291 < (/.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 95.8%

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

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 93.6

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

   8. Applied rewrites 93.6%

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

   if -inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -2.00000000000000007e154 or 1.99999999999999991e127 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 5.0000000000000001e291

   1. Initial program 99.6%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

   5. Applied rewrites 79.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 48.3%

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

   if -2.00000000000000007e154 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.99999999999999991e127 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 73.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 88.9%

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

Alternative 5: 80.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+152} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+127} \lor \neg \left(t\_1 \leq \infty\right)\right):\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

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 -2e+152) (not (or (<= t_1 2e+127) (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 <= -2e+152) || !((t_1 <= 2e+127) || !(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 <= -2e+152) || !((t_1 <= 2e+127) || !(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 <= -2e+152) or not ((t_1 <= 2e+127) 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 <= -2e+152) || !((t_1 <= 2e+127) || !(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 <= -2e+152) || ~(((t_1 <= 2e+127) || ~((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, -2e+152], N[Not[Or[LessEqual[t$95$1, 2e+127], 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)) < -2.0000000000000001e152 or 1.99999999999999991e127 < (/.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 98.1%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

   5. Applied rewrites 85.7%

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

   if -2.0000000000000001e152 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.99999999999999991e127 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 73.3%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 89.5%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -2 \cdot 10^{+152} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq 2 \cdot 10^{+127} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq \infty\right)\right):\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{x}{y} + \frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} + 2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5000.0) (not (<= (/ x y) 5e+15)))
   (+ (/ x y) (/ (fma 2.0 z 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) <= -5000.0) || !((x / y) <= 5e+15)) {
		tmp = (x / y) + (fma(2.0, z, 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) <= -5000.0) || !(Float64(x / y) <= 5e+15))
		tmp = Float64(Float64(x / y) + Float64(fma(2.0, z, 2.0) / Float64(t * z)));
	else
		tmp = Float64(Float64(Float64(Float64(2.0 / z) + 2.0) / t) - 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e+15]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 * z + 2.0), $MachinePrecision] / 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) < -5e3 or 5e15 < (/.f64 x y)

   1. Initial program 91.7%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 98.6

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

   5. Applied rewrites 98.6%

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

   if -5e3 < (/.f64 x y) < 5e15

   1. Initial program 79.1%

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

   3. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 99.3%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5000 \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{x}{y} + \frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} + 2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+78} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+51}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} + 2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4e+78) (not (<= (/ x y) 4e+51)))
   (+ (/ 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) <= -4e+78) || !((x / y) <= 4e+51)) {
		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) <= (-4d+78)) .or. (.not. ((x / y) <= 4d+51))) 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) <= -4e+78) || !((x / y) <= 4e+51)) {
		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) <= -4e+78) or not ((x / y) <= 4e+51):
		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) <= -4e+78) || !(Float64(x / y) <= 4e+51))
		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) <= -4e+78) || ~(((x / y) <= 4e+51)))
		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], -4e+78], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e+51]], $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) < -4.00000000000000003e78 or 4e51 < (/.f64 x y)

   1. Initial program 90.5%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 90.1%

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

   if -4.00000000000000003e78 < (/.f64 x y) < 4e51

   1. Initial program 81.2%

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

   3. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 97.5%

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

4. Final simplification 94.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+78} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+51}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} + 2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 88.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+93} \lor \neg \left(\frac{x}{y} \leq 10^{+41}\right):\\ \;\;\;\;\left(\frac{x}{y} - \frac{-2}{t}\right) - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} + 2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+93) (not (<= (/ x y) 1e+41)))
   (- (- (/ x y) (/ -2.0 t)) 2.0)
   (- (/ (+ (/ 2.0 z) 2.0) t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+93) || !((x / y) <= 1e+41)) {
		tmp = ((x / y) - (-2.0 / t)) - 2.0;
	} 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) <= (-5d+93)) .or. (.not. ((x / y) <= 1d+41))) then
        tmp = ((x / y) - ((-2.0d0) / t)) - 2.0d0
    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) <= -5e+93) || !((x / y) <= 1e+41)) {
		tmp = ((x / y) - (-2.0 / t)) - 2.0;
	} else {
		tmp = (((2.0 / z) + 2.0) / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e+93) or not ((x / y) <= 1e+41):
		tmp = ((x / y) - (-2.0 / t)) - 2.0
	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) <= -5e+93) || !(Float64(x / y) <= 1e+41))
		tmp = Float64(Float64(Float64(x / y) - Float64(-2.0 / t)) - 2.0);
	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) <= -5e+93) || ~(((x / y) <= 1e+41)))
		tmp = ((x / y) - (-2.0 / t)) - 2.0;
	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], -5e+93], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e+41]], $MachinePrecision]], N[(N[(N[(x / y), $MachinePrecision] - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision] - 2.0), $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) < -5.0000000000000001e93 or 1.00000000000000001e41 < (/.f64 x y)

   1. Initial program 91.0%

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

   3. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 99.0%

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

   6. Taylor expanded in z around inf

      \[\leadsto \left(\frac{x}{y} - \frac{-2}{t}\right) - 2 \]
   7. Step-by-step derivation

   8. Applied rewrites 87.8%

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

   if -5.0000000000000001e93 < (/.f64 x y) < 1.00000000000000001e41

   1. Initial program 81.1%

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

   3. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 99.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 95.8%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+93} \lor \neg \left(\frac{x}{y} \leq 10^{+41}\right):\\ \;\;\;\;\left(\frac{x}{y} - \frac{-2}{t}\right) - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} + 2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 84.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+177} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+51}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} + 2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4e+177) (not (<= (/ x y) 4e+51)))
   (+ (/ x y) -2.0)
   (- (/ (+ (/ 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+177) || !((x / y) <= 4e+51)) {
		tmp = (x / y) + -2.0;
	} 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+177)) .or. (.not. ((x / y) <= 4d+51))) then
        tmp = (x / y) + (-2.0d0)
    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+177) || !((x / y) <= 4e+51)) {
		tmp = (x / y) + -2.0;
	} 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+177) or not ((x / y) <= 4e+51):
		tmp = (x / y) + -2.0
	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+177) || !(Float64(x / y) <= 4e+51))
		tmp = Float64(Float64(x / y) + -2.0);
	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+177) || ~(((x / y) <= 4e+51)))
		tmp = (x / y) + -2.0;
	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+177], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e+51]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $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) < -4e177 or 4e51 < (/.f64 x y)

   1. Initial program 89.7%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 83.7%

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

   if -4e177 < (/.f64 x y) < 4e51

   1. Initial program 82.6%

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

   3. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 93.3%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+177} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+51}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} + 2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

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) / t)) - 2.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.0%

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

3. Taylor expanded in t around inf

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

   1. lower--.f64 N/A

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

5. Applied rewrites 99.6%

   \[\leadsto \color{blue}{\left(\frac{x}{y} - \frac{\frac{-2}{z} - 2}{t}\right) - 2} \]
6. Add Preprocessing

Alternative 11: 61.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-86} \lor \neg \left(t \leq 4.2 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8e-86) (not (<= t 4.2e-80))) (+ (/ x y) -2.0) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8e-86) || !(t <= 4.2e-80)) {
		tmp = (x / y) + -2.0;
	} 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 ((t <= (-8d-86)) .or. (.not. (t <= 4.2d-80))) then
        tmp = (x / y) + (-2.0d0)
    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 ((t <= -8e-86) || !(t <= 4.2e-80)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8e-86) or not (t <= 4.2e-80):
		tmp = (x / y) + -2.0
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8e-86) || !(t <= 4.2e-80))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8e-86) || ~((t <= 4.2e-80)))
		tmp = (x / y) + -2.0;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8e-86], N[Not[LessEqual[t, 4.2e-80]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.00000000000000068e-86 or 4.20000000000000003e-80 < t

   1. Initial program 75.1%

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

   3. Taylor expanded in 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 -8.00000000000000068e-86 < t < 4.20000000000000003e-80

   1. Initial program 98.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

   5. Applied rewrites 87.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 37.7%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-86} \lor \neg \left(t \leq 4.2 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 19.7% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \frac{2}{t} \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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 / t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(2.0 / t), $MachinePrecision]

Derivation

1. Initial program 85.0%

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

3. Taylor expanded in t around 0

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

   1. lower-/.f64 N/A

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

5. Applied rewrites 46.8%

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

6. Taylor expanded in z around inf

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

8. Applied rewrites 18.7%

   \[\leadsto \frac{2}{t} \]
9. 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 2024358 
(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))))