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

Percentage Accurate: 87.4% → 99.5%

Time: 5.1s

Alternatives: 10

Speedup: 1.0×

• 77.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z t)
  :precision binary64
  (+ (/ x y) (/ (+ 2 (* (* z 2) (- 1 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 + N[(N[(z * 2), $MachinePrecision] * N[(1 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 87.4% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t)
  :precision binary64
  (+ (/ x y) (/ (+ 2 (* (* z 2) (- 1 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 + N[(N[(z * 2), $MachinePrecision] * N[(1 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.5% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t)
  :precision binary64
  (+ (/ x y) (/ (- (* (- 1 t) 2) (/ -2 z)) t)))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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) + ((((1.0d0 - t) * 2.0d0) - ((-2.0d0) / z)) / t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(N[(N[(1 - t), $MachinePrecision] * 2), $MachinePrecision] - N[(-2 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 87.4%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. associate-/r* N/A

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

   5. lower-/.f64 N/A

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

   6. lift-+.f64 N/A

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

   7. +-commutative N/A

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

   8. add-flip N/A

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

   9. lift-*.f64 N/A

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

   10. lift-*.f64 N/A

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

   11. associate-*l* N/A

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

   12. *-commutative N/A

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

   13. sub-to-fraction-rev N/A

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

   14. lower--.f64 N/A

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

   15. *-commutative N/A

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

   16. lower-*.f64 N/A

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

   17. lower-/.f64 N/A

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

   18. metadata-eval 99.1%

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

3. Applied rewrites 99.1%

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

Alternative 2: 99.1% accurate, 0.5× speedup

Math

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

FPCore

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

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 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Java

public static 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 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (x / y) + -2.0
	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 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(N[(2 + N[(N[(z * 2), $MachinePrecision] * N[(1 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(x / y), $MachinePrecision] + -2), $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))) < +inf.0

   1. Initial program 87.4%

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

   if +inf.0 < (+.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 87.4%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 53.8%

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

Alternative 3: 98.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \frac{\left(z + z\right) - -2}{t \cdot z} + \frac{x}{y}\\ t_2 := \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_2 \leq -199999999999999995497619646912068059136:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 200000000000:\\ \;\;\;\;\frac{x}{y} + 2 \cdot \frac{1 - t}{t}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (+ (/ (- (+ z z) -2) (* t z)) (/ x y)))
       (t_2 (+ (/ x y) (/ (+ 2 (* (* z 2) (- 1 t))) (* t z)))))
  (if (<= t_2 -199999999999999995497619646912068059136)
    t_1
    (if (<= t_2 200000000000)
      (+ (/ x y) (* 2 (/ (- 1 t) t)))
      (if (<= t_2 INFINITY) t_1 (+ (/ x y) -2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (((z + z) - -2.0) / (t * z)) + (x / y);
	double t_2 = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
	double tmp;
	if (t_2 <= -2e+38) {
		tmp = t_1;
	} else if (t_2 <= 200000000000.0) {
		tmp = (x / y) + (2.0 * ((1.0 - t) / t));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (((z + z) - -2.0) / (t * z)) + (x / y);
	double t_2 = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
	double tmp;
	if (t_2 <= -2e+38) {
		tmp = t_1;
	} else if (t_2 <= 200000000000.0) {
		tmp = (x / y) + (2.0 * ((1.0 - t) / t));
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (((z + z) - -2.0) / (t * z)) + (x / y)
	t_2 = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))
	tmp = 0
	if t_2 <= -2e+38:
		tmp = t_1
	elif t_2 <= 200000000000.0:
		tmp = (x / y) + (2.0 * ((1.0 - t) / t))
	elif t_2 <= math.inf:
		tmp = t_1
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(Float64(z + z) - -2.0) / Float64(t * z)) + Float64(x / y))
	t_2 = 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_2 <= -2e+38)
		tmp = t_1;
	elseif (t_2 <= 200000000000.0)
		tmp = Float64(Float64(x / y) + Float64(2.0 * Float64(Float64(1.0 - t) / t)));
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (((z + z) - -2.0) / (t * z)) + (x / y);
	t_2 = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
	tmp = 0.0;
	if (t_2 <= -2e+38)
		tmp = t_1;
	elseif (t_2 <= 200000000000.0)
		tmp = (x / y) + (2.0 * ((1.0 - t) / t));
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(z + z), $MachinePrecision] - -2), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + N[(N[(2 + N[(N[(z * 2), $MachinePrecision] * N[(1 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -199999999999999995497619646912068059136], t$95$1, If[LessEqual[t$95$2, 200000000000], N[(N[(x / y), $MachinePrecision] + N[(2 * N[(N[(1 - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$1, N[(N[(x / y), $MachinePrecision] + -2), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 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))) < -2e38 or 2e11 < (+.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))) < +inf.0

   1. Initial program 87.4%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 80.1%

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

   4. Applied rewrites 80.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 80.1%

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. add-flip N/A

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

      7. metadata-eval N/A

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

      8. lower--.f64 80.1%

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

      9. lift-*.f64 N/A

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

      10. count-2-rev N/A

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

      11. lower-+.f64 80.1%

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

   6. Applied rewrites 80.1%

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

   if -2e38 < (+.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))) < 2e11

   1. Initial program 87.4%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 71.3%

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

   4. Applied rewrites 71.3%

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

   if +inf.0 < (+.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 87.4%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 53.8%

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

Alternative 4: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \frac{\left(z + z\right) - -2}{t \cdot z} + \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -1000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5000000000:\\ \;\;\;\;\frac{2 \cdot \left(1 - t\right) + 2 \cdot \frac{1}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (+ (/ (- (+ z z) -2) (* t z)) (/ x y))))
  (if (<= (/ x y) -1000)
    t_1
    (if (<= (/ x y) 5000000000)
      (/ (+ (* 2 (- 1 t)) (* 2 (/ 1 z))) t)
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (((z + z) - -2.0) / (t * z)) + (x / y);
	double tmp;
	if ((x / y) <= -1000.0) {
		tmp = t_1;
	} else if ((x / y) <= 5000000000.0) {
		tmp = ((2.0 * (1.0 - t)) + (2.0 * (1.0 / z))) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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 = (((z + z) - (-2.0d0)) / (t * z)) + (x / y)
    if ((x / y) <= (-1000.0d0)) then
        tmp = t_1
    else if ((x / y) <= 5000000000.0d0) then
        tmp = ((2.0d0 * (1.0d0 - t)) + (2.0d0 * (1.0d0 / z))) / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (((z + z) - -2.0) / (t * z)) + (x / y);
	double tmp;
	if ((x / y) <= -1000.0) {
		tmp = t_1;
	} else if ((x / y) <= 5000000000.0) {
		tmp = ((2.0 * (1.0 - t)) + (2.0 * (1.0 / z))) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (((z + z) - -2.0) / (t * z)) + (x / y)
	tmp = 0
	if (x / y) <= -1000.0:
		tmp = t_1
	elif (x / y) <= 5000000000.0:
		tmp = ((2.0 * (1.0 - t)) + (2.0 * (1.0 / z))) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(Float64(z + z) - -2.0) / Float64(t * z)) + Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -1000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 5000000000.0)
		tmp = Float64(Float64(Float64(2.0 * Float64(1.0 - t)) + Float64(2.0 * Float64(1.0 / z))) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (((z + z) - -2.0) / (t * z)) + (x / y);
	tmp = 0.0;
	if ((x / y) <= -1000.0)
		tmp = t_1;
	elseif ((x / y) <= 5000000000.0)
		tmp = ((2.0 * (1.0 - t)) + (2.0 * (1.0 / z))) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(z + z), $MachinePrecision] - -2), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1000], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5000000000], N[(N[(N[(2 * N[(1 - t), $MachinePrecision]), $MachinePrecision] + N[(2 * N[(1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e3 or 5e9 < (/.f64 x y)

   1. Initial program 87.4%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 80.1%

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

   4. Applied rewrites 80.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 80.1%

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. add-flip N/A

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

      7. metadata-eval N/A

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

      8. lower--.f64 80.1%

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

      9. lift-*.f64 N/A

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

      10. count-2-rev N/A

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

      11. lower-+.f64 80.1%

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

   6. Applied rewrites 80.1%

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

   if -1e3 < (/.f64 x y) < 5e9

   1. Initial program 87.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/r* N/A

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

      7. lift-/.f64 N/A

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

      8. common-denominator N/A

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

      9. lower-/.f64 N/A

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

   3. Applied rewrites 74.9%

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

   4. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 66.5%

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

   6. Applied rewrites 66.5%

      \[\leadsto \color{blue}{\frac{2 \cdot \left(1 - t\right) + 2 \cdot \frac{1}{z}}{t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 92.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{y} + 2 \cdot \frac{1 - t}{t}\\ \mathbf{if}\;z \leq \frac{-8920298079412249}{89202980794122492566142873090593446023921664}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq \frac{4253529586511731}{170141183460469231731687303715884105728}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (+ (/ x y) (* 2 (/ (- 1 t) t)))))
  (if (<=
       z
       -8920298079412249/89202980794122492566142873090593446023921664)
    t_1
    (if (<=
         z
         4253529586511731/170141183460469231731687303715884105728)
      (+ (/ x y) (/ (/ 2 z) t))
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 * ((1.0 - t) / t));
	double tmp;
	if (z <= -1e-28) {
		tmp = t_1;
	} else if (z <= 2.5e-23) {
		tmp = (x / y) + ((2.0 / z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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 = (x / y) + (2.0d0 * ((1.0d0 - t) / t))
    if (z <= (-1d-28)) then
        tmp = t_1
    else if (z <= 2.5d-23) then
        tmp = (x / y) + ((2.0d0 / z) / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 * ((1.0 - t) / t));
	double tmp;
	if (z <= -1e-28) {
		tmp = t_1;
	} else if (z <= 2.5e-23) {
		tmp = (x / y) + ((2.0 / z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (2.0 * ((1.0 - t) / t))
	tmp = 0
	if z <= -1e-28:
		tmp = t_1
	elif z <= 2.5e-23:
		tmp = (x / y) + ((2.0 / z) / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(2.0 * Float64(Float64(1.0 - t) / t)))
	tmp = 0.0
	if (z <= -1e-28)
		tmp = t_1;
	elseif (z <= 2.5e-23)
		tmp = Float64(Float64(x / y) + 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 * ((1.0 - t) / t));
	tmp = 0.0;
	if (z <= -1e-28)
		tmp = t_1;
	elseif (z <= 2.5e-23)
		tmp = (x / y) + ((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] + N[(2 * N[(N[(1 - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8920298079412249/89202980794122492566142873090593446023921664], t$95$1, If[LessEqual[z, 4253529586511731/170141183460469231731687303715884105728], N[(N[(x / y), $MachinePrecision] + N[(N[(2 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999997e-29 or 2.5000000000000001e-23 < z

   1. Initial program 87.4%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 71.3%

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

   4. Applied rewrites 71.3%

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

   if -9.9999999999999997e-29 < z < 2.5000000000000001e-23

   1. Initial program 87.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lift-+.f64 N/A

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

      7. +-commutative N/A

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

      8. add-flip N/A

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

      9. lift-*.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-*l* N/A

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

      12. *-commutative N/A

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

      13. sub-to-fraction-rev N/A

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

      14. lower--.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. metadata-eval 99.1%

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

   3. Applied rewrites 99.1%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 62.8%

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

   6. Applied rewrites 62.8%

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

Alternative 6: 92.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{y} + 2 \cdot \frac{1 - t}{t}\\ \mathbf{if}\;z \leq \frac{-8920298079412249}{89202980794122492566142873090593446023921664}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq \frac{4253529586511731}{170141183460469231731687303715884105728}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (+ (/ x y) (* 2 (/ (- 1 t) t)))))
  (if (<=
       z
       -8920298079412249/89202980794122492566142873090593446023921664)
    t_1
    (if (<=
         z
         4253529586511731/170141183460469231731687303715884105728)
      (+ (/ x y) (/ 2 (* t z)))
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 * ((1.0 - t) / t));
	double tmp;
	if (z <= -1e-28) {
		tmp = t_1;
	} else if (z <= 2.5e-23) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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 = (x / y) + (2.0d0 * ((1.0d0 - t) / t))
    if (z <= (-1d-28)) then
        tmp = t_1
    else if (z <= 2.5d-23) then
        tmp = (x / y) + (2.0d0 / (t * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 * ((1.0 - t) / t));
	double tmp;
	if (z <= -1e-28) {
		tmp = t_1;
	} else if (z <= 2.5e-23) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (2.0 * ((1.0 - t) / t))
	tmp = 0
	if z <= -1e-28:
		tmp = t_1
	elif z <= 2.5e-23:
		tmp = (x / y) + (2.0 / (t * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(2.0 * Float64(Float64(1.0 - t) / t)))
	tmp = 0.0
	if (z <= -1e-28)
		tmp = t_1;
	elseif (z <= 2.5e-23)
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (2.0 * ((1.0 - t) / t));
	tmp = 0.0;
	if (z <= -1e-28)
		tmp = t_1;
	elseif (z <= 2.5e-23)
		tmp = (x / y) + (2.0 / (t * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(2 * N[(N[(1 - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8920298079412249/89202980794122492566142873090593446023921664], t$95$1, If[LessEqual[z, 4253529586511731/170141183460469231731687303715884105728], N[(N[(x / y), $MachinePrecision] + N[(2 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999997e-29 or 2.5000000000000001e-23 < z

   1. Initial program 87.4%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 71.3%

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

   4. Applied rewrites 71.3%

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

   if -9.9999999999999997e-29 < z < 2.5000000000000001e-23

   1. Initial program 87.4%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 62.8%

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

Alternative 7: 85.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{y} + -2\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_2 \leq -9999999999999999549291066784979473595300225087383524118479625982517885450291174622154390152298057300868772377386949310916067328:\\ \;\;\;\;\frac{2 + 2 \cdot \frac{1}{z}}{t}\\ \mathbf{elif}\;t\_2 \leq -200000:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;t\_2 \leq -2:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;\frac{2 + 2 \cdot \left(z \cdot \left(1 - t\right)\right)}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (+ (/ x y) -2))
       (t_2 (/ (+ 2 (* (* z 2) (- 1 t))) (* t z))))
  (if (<=
       t_2
       -9999999999999999549291066784979473595300225087383524118479625982517885450291174622154390152298057300868772377386949310916067328)
    (/ (+ 2 (* 2 (/ 1 z))) t)
    (if (<= t_2 -200000)
      (+ (/ x y) (/ 2 t))
      (if (<= t_2 -2)
        t_1
        (if (<= t_2 INFINITY)
          (/ (+ 2 (* 2 (* z (- 1 t)))) (* t z))
          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 tmp;
	if (t_2 <= -1e+127) {
		tmp = (2.0 + (2.0 * (1.0 / z))) / t;
	} else if (t_2 <= -200000.0) {
		tmp = (x / y) + (2.0 / t);
	} else if (t_2 <= -2.0) {
		tmp = t_1;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = (2.0 + (2.0 * (z * (1.0 - t)))) / (t * z);
	} 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 tmp;
	if (t_2 <= -1e+127) {
		tmp = (2.0 + (2.0 * (1.0 / z))) / t;
	} else if (t_2 <= -200000.0) {
		tmp = (x / y) + (2.0 / t);
	} else if (t_2 <= -2.0) {
		tmp = t_1;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = (2.0 + (2.0 * (z * (1.0 - t)))) / (t * z);
	} 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)
	tmp = 0
	if t_2 <= -1e+127:
		tmp = (2.0 + (2.0 * (1.0 / z))) / t
	elif t_2 <= -200000.0:
		tmp = (x / y) + (2.0 / t)
	elif t_2 <= -2.0:
		tmp = t_1
	elif t_2 <= math.inf:
		tmp = (2.0 + (2.0 * (z * (1.0 - t)))) / (t * z)
	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))
	tmp = 0.0
	if (t_2 <= -1e+127)
		tmp = Float64(Float64(2.0 + Float64(2.0 * Float64(1.0 / z))) / t);
	elseif (t_2 <= -200000.0)
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	elseif (t_2 <= -2.0)
		tmp = t_1;
	elseif (t_2 <= Inf)
		tmp = Float64(Float64(2.0 + Float64(2.0 * Float64(z * Float64(1.0 - t)))) / Float64(t * z));
	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);
	tmp = 0.0;
	if (t_2 <= -1e+127)
		tmp = (2.0 + (2.0 * (1.0 / z))) / t;
	elseif (t_2 <= -200000.0)
		tmp = (x / y) + (2.0 / t);
	elseif (t_2 <= -2.0)
		tmp = t_1;
	elseif (t_2 <= Inf)
		tmp = (2.0 + (2.0 * (z * (1.0 - t)))) / (t * z);
	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), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2 + N[(N[(z * 2), $MachinePrecision] * N[(1 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -9999999999999999549291066784979473595300225087383524118479625982517885450291174622154390152298057300868772377386949310916067328], N[(N[(2 + N[(2 * N[(1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$2, -200000], N[(N[(x / y), $MachinePrecision] + N[(2 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2], t$95$1, If[LessEqual[t$95$2, Infinity], N[(N[(2 + N[(2 * N[(z * N[(1 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $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)) < -9.9999999999999995e126

   1. Initial program 87.4%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 48.2%

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

   4. Applied rewrites 48.2%

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

   if -9.9999999999999995e126 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -2e5

   1. Initial program 87.4%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 71.3%

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

   4. Applied rewrites 71.3%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 52.8%

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

   7. Applied rewrites 52.8%

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

   if -2e5 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -2 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 87.4%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 53.8%

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

   if -2 < (/.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 87.4%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 53.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. add-to-fraction N/A

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

      5. lower-/.f64 N/A

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

      6. lower-+.f64 N/A

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

      7. lower-*.f64 53.8%

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

   6. Applied rewrites 53.8%

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

   7. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 60.6%

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

   9. Applied rewrites 60.6%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \left(z \cdot \left(1 - t\right)\right)}{t \cdot z}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 85.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{y} + -2\\ t_2 := \frac{2 + 2 \cdot \frac{1}{z}}{t}\\ t_3 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_3 \leq -9999999999999999549291066784979473595300225087383524118479625982517885450291174622154390152298057300868772377386949310916067328:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq -200000:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;t\_3 \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (+ (/ x y) -2))
       (t_2 (/ (+ 2 (* 2 (/ 1 z))) t))
       (t_3 (/ (+ 2 (* (* z 2) (- 1 t))) (* t z))))
  (if (<=
       t_3
       -9999999999999999549291066784979473595300225087383524118479625982517885450291174622154390152298057300868772377386949310916067328)
    t_2
    (if (<= t_3 -200000)
      (+ (/ x y) (/ 2 t))
      (if (<= t_3 -1) t_1 (if (<= t_3 INFINITY) t_2 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 + (2.0 * (1.0 / z))) / t;
	double t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_3 <= -1e+127) {
		tmp = t_2;
	} else if (t_3 <= -200000.0) {
		tmp = (x / y) + (2.0 / t);
	} else if (t_3 <= -1.0) {
		tmp = t_1;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} 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 + (2.0 * (1.0 / z))) / t;
	double t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_3 <= -1e+127) {
		tmp = t_2;
	} else if (t_3 <= -200000.0) {
		tmp = (x / y) + (2.0 / t);
	} else if (t_3 <= -1.0) {
		tmp = t_1;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	t_2 = (2.0 + (2.0 * (1.0 / z))) / t
	t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if t_3 <= -1e+127:
		tmp = t_2
	elif t_3 <= -200000.0:
		tmp = (x / y) + (2.0 / t)
	elif t_3 <= -1.0:
		tmp = t_1
	elif t_3 <= math.inf:
		tmp = t_2
	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(2.0 * Float64(1.0 / z))) / t)
	t_3 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if (t_3 <= -1e+127)
		tmp = t_2;
	elseif (t_3 <= -200000.0)
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	elseif (t_3 <= -1.0)
		tmp = t_1;
	elseif (t_3 <= Inf)
		tmp = t_2;
	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 + (2.0 * (1.0 / z))) / t;
	t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if (t_3 <= -1e+127)
		tmp = t_2;
	elseif (t_3 <= -200000.0)
		tmp = (x / y) + (2.0 / t);
	elseif (t_3 <= -1.0)
		tmp = t_1;
	elseif (t_3 <= Inf)
		tmp = t_2;
	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), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2 + N[(2 * N[(1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$3 = N[(N[(2 + N[(N[(z * 2), $MachinePrecision] * N[(1 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -9999999999999999549291066784979473595300225087383524118479625982517885450291174622154390152298057300868772377386949310916067328], t$95$2, If[LessEqual[t$95$3, -200000], N[(N[(x / y), $MachinePrecision] + N[(2 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -1], t$95$1, If[LessEqual[t$95$3, Infinity], t$95$2, 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)) < -9.9999999999999995e126 or -1 < (/.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 87.4%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 48.2%

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

   4. Applied rewrites 48.2%

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

   if -9.9999999999999995e126 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -2e5

   1. Initial program 87.4%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 71.3%

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

   4. Applied rewrites 71.3%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 52.8%

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

   7. Applied rewrites 52.8%

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

   if -2e5 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1 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 87.4%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 53.8%

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

Alternative 9: 70.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq \frac{-5404319552844595}{9007199254740992}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq \frac{7385903388887613}{18014398509481984}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (+ (/ x y) -2)))
  (if (<= t -5404319552844595/9007199254740992)
    t_1
    (if (<= t 7385903388887613/18014398509481984)
      (+ (/ x y) (/ 2 t))
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (t <= -0.6) {
		tmp = t_1;
	} else if (t <= 0.41) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
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 = (x / y) + (-2.0d0)
    if (t <= (-0.6d0)) then
        tmp = t_1
    else if (t <= 0.41d0) then
        tmp = (x / y) + (2.0d0 / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (t <= -0.6) {
		tmp = t_1;
	} else if (t <= 0.41) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	tmp = 0
	if t <= -0.6:
		tmp = t_1
	elif t <= 0.41:
		tmp = (x / y) + (2.0 / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t <= -0.6)
		tmp = t_1;
	elseif (t <= 0.41)
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	tmp = 0.0;
	if (t <= -0.6)
		tmp = t_1;
	elseif (t <= 0.41)
		tmp = (x / y) + (2.0 / 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), $MachinePrecision]}, If[LessEqual[t, -5404319552844595/9007199254740992], t$95$1, If[LessEqual[t, 7385903388887613/18014398509481984], N[(N[(x / y), $MachinePrecision] + N[(2 / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -0.59999999999999998 or 0.40999999999999998 < t

   1. Initial program 87.4%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 53.8%

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

   if -0.59999999999999998 < t < 0.40999999999999998

   1. Initial program 87.4%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 71.3%

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

   4. Applied rewrites 71.3%

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

   5. Taylor expanded in t around 0

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

      1. lower-/.f64 52.8%

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

   7. Applied rewrites 52.8%

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

Alternative 10: 53.8% accurate, 3.1× speedup

Math

\[\frac{x}{y} + -2 \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (+ (/ x y) -2))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + -2), $MachinePrecision]

Derivation

1. Initial program 87.4%

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

2. Taylor expanded in t around inf

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

4. Applied rewrites 53.8%

   \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64
  (+ (/ x y) (/ (+ 2 (* (* z 2) (- 1 t))) (* t z))))