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

Percentage Accurate: 86.1% → 99.3%

Time: 4.7s

Alternatives: 14

Speedup: 1.1×

• 24.0% 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: 86.1% 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: 99.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision] * 2.0 + N[(x / y), $MachinePrecision]), $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 99.9%

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

   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 0.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 100.0

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

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1 - t}{t}, 2, \frac{x}{y}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 83.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{z} - -2}{t}\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_3 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1.999999999:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+208}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- (/ 2.0 z) -2.0) t))
        (t_2 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))
        (t_3 (+ (/ x y) -2.0)))
   (if (<= t_2 -5e+73)
     t_1
     (if (<= t_2 -1.999999999)
       t_3
       (if (<= t_2 2e+208)
         (+ (/ x y) (/ 2.0 (* t z)))
         (if (<= t_2 INFINITY) t_1 t_3))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / z) - -2.0) / t;
	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 <= -5e+73) {
		tmp = t_1;
	} else if (t_2 <= -1.999999999) {
		tmp = t_3;
	} else if (t_2 <= 2e+208) {
		tmp = (x / y) + (2.0 / (t * z));
	} 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 / z) - -2.0) / t;
	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 <= -5e+73) {
		tmp = t_1;
	} else if (t_2 <= -1.999999999) {
		tmp = t_3;
	} else if (t_2 <= 2e+208) {
		tmp = (x / y) + (2.0 / (t * z));
	} 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 / z) - -2.0) / t
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	t_3 = (x / y) + -2.0
	tmp = 0
	if t_2 <= -5e+73:
		tmp = t_1
	elif t_2 <= -1.999999999:
		tmp = t_3
	elif t_2 <= 2e+208:
		tmp = (x / y) + (2.0 / (t * z))
	elif t_2 <= math.inf:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(2.0 / z) - -2.0) / t)
	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 <= -5e+73)
		tmp = t_1;
	elseif (t_2 <= -1.999999999)
		tmp = t_3;
	elseif (t_2 <= 2e+208)
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	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 / z) - -2.0) / t;
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	t_3 = (x / y) + -2.0;
	tmp = 0.0;
	if (t_2 <= -5e+73)
		tmp = t_1;
	elseif (t_2 <= -1.999999999)
		tmp = t_3;
	elseif (t_2 <= 2e+208)
		tmp = (x / y) + (2.0 / (t * z));
	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[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $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, -5e+73], t$95$1, If[LessEqual[t$95$2, -1.999999999], t$95$3, If[LessEqual[t$95$2, 2e+208], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $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)) < -4.99999999999999976e73 or 2e208 < (/.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 98.8%

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

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

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

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 86.3

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

   5. Applied rewrites 86.3%

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

   if -4.99999999999999976e73 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.9999999989999999 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 68.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 96.3%

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

   if -1.9999999989999999 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2e208

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 86.0%

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

Alternative 3: 83.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+73} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+90} \lor \neg \left(t\_1 \leq \infty\right)\right):\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (or (<= t_1 -5e+73) (not (or (<= t_1 2e+90) (not (<= t_1 INFINITY)))))
     (/ (- (/ 2.0 z) -2.0) t)
     (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if ((t_1 <= -5e+73) || !((t_1 <= 2e+90) || !(t_1 <= ((double) INFINITY)))) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if ((t_1 <= -5e+73) || !((t_1 <= 2e+90) || !(t_1 <= Double.POSITIVE_INFINITY))) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if (t_1 <= -5e+73) or not ((t_1 <= 2e+90) or not (t_1 <= math.inf)):
		tmp = ((2.0 / z) - -2.0) / t
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if ((t_1 <= -5e+73) || !((t_1 <= 2e+90) || !(t_1 <= Inf)))
		tmp = Float64(Float64(Float64(2.0 / z) - -2.0) / t);
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if ((t_1 <= -5e+73) || ~(((t_1 <= 2e+90) || ~((t_1 <= Inf)))))
		tmp = ((2.0 / z) - -2.0) / t;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+73], N[Not[Or[LessEqual[t$95$1, 2e+90], 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)) < -4.99999999999999976e73 or 1.99999999999999993e90 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 99.0%

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

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

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

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 80.3

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

   5. Applied rewrites 80.3%

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

   if -4.99999999999999976e73 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.99999999999999993e90 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 73.8%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 90.0%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -5 \cdot 10^{+73} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq 2 \cdot 10^{+90} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq \infty\right)\right):\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+96}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+208} \lor \neg \left(t\_1 \leq \infty\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (<= t_1 -2e+96)
     (/ 2.0 (* t z))
     (if (or (<= t_1 2e+208) (not (<= t_1 INFINITY)))
       (+ (/ x y) -2.0)
       (/ (/ 2.0 z) t)))))

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+96) {
		tmp = 2.0 / (t * z);
	} else if ((t_1 <= 2e+208) || !(t_1 <= ((double) INFINITY))) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (2.0 / z) / t;
	}
	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+96) {
		tmp = 2.0 / (t * z);
	} else if ((t_1 <= 2e+208) || !(t_1 <= Double.POSITIVE_INFINITY)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (2.0 / z) / t;
	}
	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+96:
		tmp = 2.0 / (t * z)
	elif (t_1 <= 2e+208) or not (t_1 <= math.inf):
		tmp = (x / y) + -2.0
	else:
		tmp = (2.0 / z) / t
	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+96)
		tmp = Float64(2.0 / Float64(t * z));
	elseif ((t_1 <= 2e+208) || !(t_1 <= Inf))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(Float64(2.0 / z) / t);
	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+96)
		tmp = 2.0 / (t * z);
	elseif ((t_1 <= 2e+208) || ~((t_1 <= Inf)))
		tmp = (x / y) + -2.0;
	else
		tmp = (2.0 / z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+96], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$1, 2e+208], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]]]]

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)) < -2.0000000000000001e96

   1. Initial program 98.3%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lift-*.f64 52.1

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

   5. Applied rewrites 52.1%

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

   if -2.0000000000000001e96 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2e208 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 78.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 81.2%

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

   if 2e208 < (/.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 99.8%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lift-*.f64 71.4

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

   5. Applied rewrites 71.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 71.4

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

   7. Applied rewrites 71.4%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r* N/A

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

      4. *-commutative N/A

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

      5. associate-/r* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. lower-/.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. lower-/.f64 71.4

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

   9. Applied rewrites 71.4%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -2 \cdot 10^{+96}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq 2 \cdot 10^{+208} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq \infty\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+96} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+208} \lor \neg \left(t\_1 \leq \infty\right)\right):\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

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+96) (not (or (<= t_1 2e+208) (not (<= t_1 INFINITY)))))
     (/ 2.0 (* t z))
     (+ (/ 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+96) || !((t_1 <= 2e+208) || !(t_1 <= ((double) INFINITY)))) {
		tmp = 2.0 / (t * z);
	} 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+96) || !((t_1 <= 2e+208) || !(t_1 <= Double.POSITIVE_INFINITY))) {
		tmp = 2.0 / (t * z);
	} 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+96) or not ((t_1 <= 2e+208) or not (t_1 <= math.inf)):
		tmp = 2.0 / (t * z)
	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+96) || !((t_1 <= 2e+208) || !(t_1 <= Inf)))
		tmp = Float64(2.0 / Float64(t * z));
	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+96) || ~(((t_1 <= 2e+208) || ~((t_1 <= Inf)))))
		tmp = 2.0 / (t * z);
	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+96], N[Not[Or[LessEqual[t$95$1, 2e+208], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]]], $MachinePrecision]], N[(2.0 / N[(t * z), $MachinePrecision]), $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)) < -2.0000000000000001e96 or 2e208 < (/.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 98.8%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lift-*.f64 58.6

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

   5. Applied rewrites 58.6%

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

   if -2.0000000000000001e96 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2e208 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 78.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 81.2%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -2 \cdot 10^{+96} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq 2 \cdot 10^{+208} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq \infty\right)\right):\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ \mathbf{if}\;\frac{x}{y} \leq -1.08 \cdot 10^{+15} \lor \neg \left(\frac{x}{y} \leq 430\right):\\ \;\;\;\;\frac{x}{y} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1 - t}{t}, 2, t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z))))
   (if (or (<= (/ x y) -1.08e+15) (not (<= (/ x y) 430.0)))
     (+ (/ x y) t_1)
     (fma (/ (- 1.0 t) t) 2.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double tmp;
	if (((x / y) <= -1.08e+15) || !((x / y) <= 430.0)) {
		tmp = (x / y) + t_1;
	} else {
		tmp = fma(((1.0 - t) / t), 2.0, t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	tmp = 0.0
	if ((Float64(x / y) <= -1.08e+15) || !(Float64(x / y) <= 430.0))
		tmp = Float64(Float64(x / y) + t_1);
	else
		tmp = fma(Float64(Float64(1.0 - t) / t), 2.0, t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(x / y), $MachinePrecision], -1.08e+15], N[Not[LessEqual[N[(x / y), $MachinePrecision], 430.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision] * 2.0 + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.08e15 or 430 < (/.f64 x y)

   1. Initial program 89.4%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 91.2%

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

   if -1.08e15 < (/.f64 x y) < 430

   1. Initial program 83.6%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 98.9

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

   5. Applied rewrites 98.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1 - t}{t}, 2, \frac{2}{t \cdot z}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.08 \cdot 10^{+15} \lor \neg \left(\frac{x}{y} \leq 430\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1 - t}{t}, 2, \frac{2}{t \cdot z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.08 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -3.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.08e+15)
   (/ x y)
   (if (<= (/ x y) -3.8e-22) (/ 2.0 t) (if (<= (/ x y) 2.0) -2.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.08e+15) {
		tmp = x / y;
	} else if ((x / y) <= -3.8e-22) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-1.08d+15)) then
        tmp = x / y
    else if ((x / y) <= (-3.8d-22)) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 2.0d0) then
        tmp = -2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.08e+15) {
		tmp = x / y;
	} else if ((x / y) <= -3.8e-22) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.08e+15:
		tmp = x / y
	elif (x / y) <= -3.8e-22:
		tmp = 2.0 / t
	elif (x / y) <= 2.0:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.08e+15)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -3.8e-22)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1.08e+15)
		tmp = x / y;
	elseif ((x / y) <= -3.8e-22)
		tmp = 2.0 / t;
	elseif ((x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.08e+15], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -3.8e-22], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.0], -2.0, N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.08e15 or 2 < (/.f64 x y)

   1. Initial program 89.4%

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

   3. Taylor expanded in x around inf

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

      1. lift-/.f64 71.0

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

   5. Applied rewrites 71.0%

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

   if -1.08e15 < (/.f64 x y) < -3.80000000000000023e-22

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 95.6

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

   5. Applied rewrites 95.6%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 53.4

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

   8. Applied rewrites 53.4%

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

   9. Taylor expanded in t around 0

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

       1. lift-/.f64 49.3

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

   11. Applied rewrites 49.3%

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

   if -3.80000000000000023e-22 < (/.f64 x y) < 2

   1. Initial program 82.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 99.2

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

   5. Applied rewrites 99.2%

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

   6. Taylor expanded in t around inf

      \[\leadsto -2 \]
   7. Step-by-step derivation

   8. Applied rewrites 41.2%

      \[\leadsto -2 \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.08 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -3.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5.5 \cdot 10^{+91}:\\ \;\;\;\;\mathsf{fma}\left(-1, 2, \frac{2}{t \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -6.5e+19)
   (/ x y)
   (if (<= (/ x y) 5.5e+91) (fma -1.0 2.0 (/ 2.0 (* t z))) (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -6.5e+19) {
		tmp = x / y;
	} else if ((x / y) <= 5.5e+91) {
		tmp = fma(-1.0, 2.0, (2.0 / (t * z)));
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -6.5e+19)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 5.5e+91)
		tmp = fma(-1.0, 2.0, Float64(2.0 / Float64(t * z)));
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -6.5e+19], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5.5e+91], N[(-1.0 * 2.0 + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -6.5e19

   1. Initial program 90.7%

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

   3. Taylor expanded in x around inf

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

      1. lift-/.f64 70.5

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

   5. Applied rewrites 70.5%

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

   if -6.5e19 < (/.f64 x y) < 5.4999999999999998e91

   1. Initial program 83.3%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 94.8

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

   5. Applied rewrites 94.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 73.0%

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

   if 5.4999999999999998e91 < (/.f64 x y)

   1. Initial program 90.2%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 86.2%

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

Alternative 9: 92.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0185 \lor \neg \left(z \leq 820000\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{1 - t}{t}, 2, \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{\mathsf{fma}\left(z, 2, 2\right)}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.0185) (not (<= z 820000.0)))
   (fma (/ (- 1.0 t) t) 2.0 (/ x y))
   (+ (/ x y) (/ (/ (fma z 2.0 2.0) t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.0185) || !(z <= 820000.0)) {
		tmp = fma(((1.0 - t) / t), 2.0, (x / y));
	} else {
		tmp = (x / y) + ((fma(z, 2.0, 2.0) / t) / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.0185) || !(z <= 820000.0))
		tmp = fma(Float64(Float64(1.0 - t) / t), 2.0, Float64(x / y));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(fma(z, 2.0, 2.0) / t) / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.0185], N[Not[LessEqual[z, 820000.0]], $MachinePrecision]], N[(N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision] * 2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(N[(z * 2.0 + 2.0), $MachinePrecision] / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0184999999999999991 or 8.2e5 < z

   1. Initial program 73.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 99.7

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

   5. Applied rewrites 99.7%

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

   if -0.0184999999999999991 < z < 8.2e5

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0

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

      1. associate-/r* N/A

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

      2. div-add N/A

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

      3. metadata-eval N/A

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

      4. associate-*r/ N/A

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

      5. associate-*r/ N/A

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

      6. +-commutative N/A

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

      7. lower-/.f64 N/A

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

      8. +-commutative N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r/ N/A

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

      12. div-add N/A

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

      13. lower-/.f64 N/A

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

      14. +-commutative N/A

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

      15. *-commutative N/A

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

      16. lower-fma.f64 91.0

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

   5. Applied rewrites 91.0%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0185 \lor \neg \left(z \leq 820000\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{1 - t}{t}, 2, \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{\mathsf{fma}\left(z, 2, 2\right)}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.08 \cdot 10^{+15} \lor \neg \left(\frac{x}{y} \leq 465\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1.08e+15) (not (<= (/ x y) 465.0)))
   (/ x y)
   (- (/ 2.0 t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.08e+15) || !((x / y) <= 465.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1.08d+15)) .or. (.not. ((x / y) <= 465.0d0))) then
        tmp = x / y
    else
        tmp = (2.0d0 / t) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.08e+15) || !((x / y) <= 465.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1.08e+15) or not ((x / y) <= 465.0):
		tmp = x / y
	else:
		tmp = (2.0 / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1.08e+15) || !(Float64(x / y) <= 465.0))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(2.0 / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1.08e+15) || ~(((x / y) <= 465.0)))
		tmp = x / y;
	else
		tmp = (2.0 / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1.08e+15], N[Not[LessEqual[N[(x / y), $MachinePrecision], 465.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.08e15 or 465 < (/.f64 x y)

   1. Initial program 89.4%

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

   3. Taylor expanded in x around inf

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

      1. lift-/.f64 71.0

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

   5. Applied rewrites 71.0%

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

   if -1.08e15 < (/.f64 x y) < 465

   1. Initial program 83.6%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 98.9

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

   5. Applied rewrites 98.9%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 61.4

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

   8. Applied rewrites 61.4%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r/ N/A

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

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

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

      7. metadata-eval N/A

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

      8. metadata-eval N/A

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

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

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

      10. div-add N/A

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

      11. metadata-eval N/A

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

      12. associate-*r/ N/A

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

      13. associate-/l* N/A

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

      14. metadata-eval N/A

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

      15. *-inverses N/A

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

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

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

      17. metadata-eval N/A

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

      18. lower--.f64 N/A

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

      19. associate-*r/ N/A

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

      20. metadata-eval N/A

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

      21. lift-/.f64 61.4

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

   10. Applied rewrites 61.4%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.08 \cdot 10^{+15} \lor \neg \left(\frac{x}{y} \leq 465\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.08 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.75 \cdot 10^{-14}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.08e+15)
   (/ x y)
   (if (<= (/ x y) 2.75e-14) (- (/ 2.0 t) 2.0) (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.08e+15) {
		tmp = x / y;
	} else if ((x / y) <= 2.75e-14) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-1.08d+15)) then
        tmp = x / y
    else if ((x / y) <= 2.75d-14) then
        tmp = (2.0d0 / t) - 2.0d0
    else
        tmp = (x / y) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.08e+15) {
		tmp = x / y;
	} else if ((x / y) <= 2.75e-14) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.08e+15:
		tmp = x / y
	elif (x / y) <= 2.75e-14:
		tmp = (2.0 / t) - 2.0
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.08e+15)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 2.75e-14)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1.08e+15)
		tmp = x / y;
	elseif ((x / y) <= 2.75e-14)
		tmp = (2.0 / t) - 2.0;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.08e+15], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.75e-14], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.08e15

   1. Initial program 90.7%

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

   3. Taylor expanded in x around inf

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

      1. lift-/.f64 70.5

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

   5. Applied rewrites 70.5%

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

   if -1.08e15 < (/.f64 x y) < 2.74999999999999996e-14

   1. Initial program 84.1%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 99.6

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

   5. Applied rewrites 99.6%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 61.5

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

   8. Applied rewrites 61.5%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*r/ N/A

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

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

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

      7. metadata-eval N/A

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

      8. metadata-eval N/A

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

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

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

      10. div-add N/A

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

      11. metadata-eval N/A

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

      12. associate-*r/ N/A

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

      13. associate-/l* N/A

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

      14. metadata-eval N/A

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

      15. *-inverses N/A

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

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

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

      17. metadata-eval N/A

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

      18. lower--.f64 N/A

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

      19. associate-*r/ N/A

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

      20. metadata-eval N/A

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

      21. lift-/.f64 61.5

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

   10. Applied rewrites 61.5%

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

   if 2.74999999999999996e-14 < (/.f64 x y)

   1. Initial program 86.4%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 74.0%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.08 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.75 \cdot 10^{-14}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 91.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-35} \lor \neg \left(z \leq 0.085\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{1 - t}{t}, 2, \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.2e-35) (not (<= z 0.085)))
   (fma (/ (- 1.0 t) t) 2.0 (/ x y))
   (+ (/ x y) (/ 2.0 (* t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e-35) || !(z <= 0.085)) {
		tmp = fma(((1.0 - t) / t), 2.0, (x / y));
	} else {
		tmp = (x / y) + (2.0 / (t * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.2e-35) || !(z <= 0.085))
		tmp = fma(Float64(Float64(1.0 - t) / t), 2.0, Float64(x / y));
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.2e-35], N[Not[LessEqual[z, 0.085]], $MachinePrecision]], N[(N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision] * 2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.20000000000000009e-35 or 0.0850000000000000061 < z

   1. Initial program 74.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 98.9

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

   5. Applied rewrites 98.9%

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

   if -5.20000000000000009e-35 < z < 0.0850000000000000061

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 90.5%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-35} \lor \neg \left(z \leq 0.085\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{1 - t}{t}, 2, \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1800 \lor \neg \left(t \leq 1\right):\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1800.0) (not (<= t 1.0))) -2.0 (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1800.0) || !(t <= 1.0)) {
		tmp = -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 <= (-1800.0d0)) .or. (.not. (t <= 1.0d0))) then
        tmp = -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 <= -1800.0) || !(t <= 1.0)) {
		tmp = -2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1800.0) or not (t <= 1.0):
		tmp = -2.0
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1800.0) || !(t <= 1.0))
		tmp = -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 <= -1800.0) || ~((t <= 1.0)))
		tmp = -2.0;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1800.0], N[Not[LessEqual[t, 1.0]], $MachinePrecision]], -2.0, N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1800 or 1 < t

   1. Initial program 73.6%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 51.1

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

   5. Applied rewrites 51.1%

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

   6. Taylor expanded in t around inf

      \[\leadsto -2 \]
   7. Step-by-step derivation

   8. Applied rewrites 37.7%

      \[\leadsto -2 \]

   if -1800 < t < 1

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 76.2

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

   5. Applied rewrites 76.2%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 31.6

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

   8. Applied rewrites 31.6%

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

   9. Taylor expanded in t around 0

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

       1. lift-/.f64 31.6

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

   11. Applied rewrites 31.6%

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

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1800 \lor \neg \left(t \leq 1\right):\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 20.3% accurate, 47.0× speedup

Math

\[\begin{array}{l} \\ -2 \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return -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 = -2.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := -2.0

Derivation

1. Initial program 86.6%

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

3. Taylor expanded in x around 0

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

   1. *-commutative N/A

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

   2. lower-fma.f64 N/A

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

   3. lower-/.f64 N/A

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

   4. lift--.f64 N/A

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

   5. associate-*r/ N/A

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

   6. metadata-eval N/A

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

   7. lower-/.f64 N/A

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

   8. lift-*.f64 63.9

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

5. Applied rewrites 63.9%

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

6. Taylor expanded in t around inf

   \[\leadsto -2 \]
7. Step-by-step derivation

8. Applied rewrites 19.7%

   \[\leadsto -2 \]

9. Final simplification 19.7%

   \[\leadsto -2 \]
10. Add Preprocessing

Developer Target 1: 99.0% 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 2025051 
(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))))