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

Percentage Accurate: 86.4% → 99.4%

Time: 4.0s

Alternatives: 14

Speedup: 1.1×

• 22.9% 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: 86.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))) INFINITY)
   (+ (/ x y) (/ (fma z (fma -2.0 t 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) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))) <= ((double) INFINITY)) {
		tmp = (x / y) + (fma(z, fma(-2.0, t, 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(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))) <= Inf)
		tmp = Float64(Float64(x / y) + Float64(fma(z, fma(-2.0, t, 2.0), 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[(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], Infinity], N[(N[(x / y), $MachinePrecision] + N[(N[(z * N[(-2.0 * t + 2.0), $MachinePrecision] + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $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 99.8%

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

   2. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. distribute-rgt-out N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-fma.f64 99.7

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

   4. Applied rewrites 99.7%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 97.2%

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

Alternative 2: 69.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{x}{y} + -2\\ t_3 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{+270}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z)))
        (t_2 (+ (/ x y) -2.0))
        (t_3 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (<= t_3 -1e+88)
     t_1
     (if (<= t_3 5e+53)
       t_2
       (if (<= t_3 4e+270) (/ 2.0 t) (if (<= t_3 INFINITY) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) + -2.0;
	double t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_3 <= -1e+88) {
		tmp = t_1;
	} else if (t_3 <= 5e+53) {
		tmp = t_2;
	} else if (t_3 <= 4e+270) {
		tmp = 2.0 / t;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) + -2.0;
	double t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_3 <= -1e+88) {
		tmp = t_1;
	} else if (t_3 <= 5e+53) {
		tmp = t_2;
	} else if (t_3 <= 4e+270) {
		tmp = 2.0 / t;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (x / y) + -2.0
	t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if t_3 <= -1e+88:
		tmp = t_1
	elif t_3 <= 5e+53:
		tmp = t_2
	elif t_3 <= 4e+270:
		tmp = 2.0 / t
	elif t_3 <= math.inf:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(x / y) + -2.0)
	t_3 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if (t_3 <= -1e+88)
		tmp = t_1;
	elseif (t_3 <= 5e+53)
		tmp = t_2;
	elseif (t_3 <= 4e+270)
		tmp = Float64(2.0 / t);
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = (x / y) + -2.0;
	t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if (t_3 <= -1e+88)
		tmp = t_1;
	elseif (t_3 <= 5e+53)
		tmp = t_2;
	elseif (t_3 <= 4e+270)
		tmp = 2.0 / t;
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+88], t$95$1, If[LessEqual[t$95$3, 5e+53], t$95$2, If[LessEqual[t$95$3, 4e+270], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -9.99999999999999959e87 or 4.0000000000000002e270 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 97.7%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lift-*.f64 61.2

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

   4. Applied rewrites 61.2%

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

   if -9.99999999999999959e87 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 5.0000000000000004e53 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 74.4%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 86.4%

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

   if 5.0000000000000004e53 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4.0000000000000002e270

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   3. 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 71.6

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

   4. Applied rewrites 71.6%

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

   5. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \color{blue}{\frac{1 - t}{t}} \]
   6. 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 34.6

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

   7. Applied rewrites 34.6%

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

   8. Taylor expanded in t around 0

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

      1. lower-/.f64 34.9

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

   10. Applied rewrites 34.9%

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

Alternative 3: 83.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_2 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+88}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{elif}\;t\_1 \leq 10:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(z + z, 1 - t, 2\right)}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))
        (t_2 (+ (/ x y) -2.0)))
   (if (<= t_1 -1e+88)
     (/ (- (/ 2.0 z) -2.0) t)
     (if (<= t_1 10.0)
       t_2
       (if (<= t_1 INFINITY) (/ (fma (+ z z) (- 1.0 t) 2.0) (* t z)) t_2)))))

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 t_2 = (x / y) + -2.0;
	double tmp;
	if (t_1 <= -1e+88) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else if (t_1 <= 10.0) {
		tmp = t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = fma((z + z), (1.0 - t), 2.0) / (t * z);
	} else {
		tmp = t_2;
	}
	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))
	t_2 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t_1 <= -1e+88)
		tmp = Float64(Float64(Float64(2.0 / z) - -2.0) / t);
	elseif (t_1 <= 10.0)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = Float64(fma(Float64(z + z), Float64(1.0 - t), 2.0) / Float64(t * z));
	else
		tmp = t_2;
	end
	return 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]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+88], N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 10.0], t$95$2, If[LessEqual[t$95$1, Infinity], N[(N[(N[(z + z), $MachinePrecision] * N[(1.0 - t), $MachinePrecision] + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -9.99999999999999959e87

   1. Initial program 98.2%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-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 81.5

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

   4. Applied rewrites 81.5%

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

   if -9.99999999999999959e87 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 10 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 71.8%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 90.5%

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

   if 10 < (/.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. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   3. 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 75.1

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

   4. Applied rewrites 75.1%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. metadata-eval N/A

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

      4. associate-*r/ N/A

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

      5. div-add-rev N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. associate-/r* N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift--.f64 N/A

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

      16. lift-*.f64 74.9

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

   7. Applied rewrites 74.9%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. count-2-rev N/A

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

      4. lower-+.f64 74.9

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

   9. Applied rewrites 74.9%

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

Alternative 4: 83.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{z} - -2}{t}\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_3 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 20000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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 -1e+88)
     t_1
     (if (<= t_2 20000000000.0) t_3 (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 <= -1e+88) {
		tmp = t_1;
	} else if (t_2 <= 20000000000.0) {
		tmp = t_3;
	} 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 <= -1e+88) {
		tmp = t_1;
	} else if (t_2 <= 20000000000.0) {
		tmp = t_3;
	} 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 <= -1e+88:
		tmp = t_1
	elif t_2 <= 20000000000.0:
		tmp = t_3
	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 <= -1e+88)
		tmp = t_1;
	elseif (t_2 <= 20000000000.0)
		tmp = t_3;
	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 <= -1e+88)
		tmp = t_1;
	elseif (t_2 <= 20000000000.0)
		tmp = t_3;
	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, -1e+88], t$95$1, If[LessEqual[t$95$2, 20000000000.0], t$95$3, If[LessEqual[t$95$2, Infinity], t$95$1, t$95$3]]]]]]

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)) < -9.99999999999999959e87 or 2e10 < (/.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 98.5%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-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 78.2

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

   4. Applied rewrites 78.2%

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

   if -9.99999999999999959e87 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2e10 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 72.3%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 89.9%

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

Alternative 5: 83.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z}\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_3 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 20000000000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (fma z 2.0 2.0) (* t z)))
        (t_2 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))
        (t_3 (+ (/ x y) -2.0)))
   (if (<= t_2 -1e+88)
     t_1
     (if (<= t_2 20000000000.0) t_3 (if (<= t_2 INFINITY) t_1 t_3)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(z, 2.0, 2.0) / (t * z);
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_3 = (x / y) + -2.0;
	double tmp;
	if (t_2 <= -1e+88) {
		tmp = t_1;
	} else if (t_2 <= 20000000000.0) {
		tmp = t_3;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(z, 2.0, 2.0) / Float64(t * z))
	t_2 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	t_3 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t_2 <= -1e+88)
		tmp = t_1;
	elseif (t_2 <= 20000000000.0)
		tmp = t_3;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * 2.0 + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+88], t$95$1, If[LessEqual[t$95$2, 20000000000.0], t$95$3, If[LessEqual[t$95$2, Infinity], t$95$1, t$95$3]]]]]]

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)) < -9.99999999999999959e87 or 2e10 < (/.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 98.5%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   3. 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 78.3

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

   4. Applied rewrites 78.3%

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

   5. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. associate-*r/ N/A

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

      3. metadata-eval N/A

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

      4. associate-*r/ N/A

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

      5. div-add-rev N/A

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

      6. associate-*r* N/A

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

      7. *-commutative N/A

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

      8. associate-/r* N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-*.f64 N/A

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

      15. lift--.f64 N/A

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

      16. lift-*.f64 78.2

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

   7. Applied rewrites 78.2%

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

   8. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 78.1

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

   10. Applied rewrites 78.1%

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

   if -9.99999999999999959e87 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2e10 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 72.3%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 89.9%

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

Alternative 6: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \left(z - -1\right) \cdot \frac{2}{t \cdot z}\\ \mathbf{if}\;\frac{x}{y} \leq -50:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-12}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (* (- z -1.0) (/ 2.0 (* t z))))))
   (if (<= (/ x y) -50.0)
     t_1
     (if (<= (/ x y) 1e-12) (- (/ (- (/ 2.0 z) -2.0) t) 2.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((z - -1.0) * (2.0 / (t * z)));
	double tmp;
	if ((x / y) <= -50.0) {
		tmp = t_1;
	} else if ((x / y) <= 1e-12) {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + ((z - (-1.0d0)) * (2.0d0 / (t * z)))
    if ((x / y) <= (-50.0d0)) then
        tmp = t_1
    else if ((x / y) <= 1d-12) then
        tmp = (((2.0d0 / z) - (-2.0d0)) / t) - 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((z - -1.0) * (2.0 / (t * z)));
	double tmp;
	if ((x / y) <= -50.0) {
		tmp = t_1;
	} else if ((x / y) <= 1e-12) {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + ((z - -1.0) * (2.0 / (t * z)))
	tmp = 0
	if (x / y) <= -50.0:
		tmp = t_1
	elif (x / y) <= 1e-12:
		tmp = (((2.0 / z) - -2.0) / t) - 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(Float64(z - -1.0) * Float64(2.0 / Float64(t * z))))
	tmp = 0.0
	if (Float64(x / y) <= -50.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e-12)
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + ((z - -1.0) * (2.0 / (t * z)));
	tmp = 0.0;
	if ((x / y) <= -50.0)
		tmp = t_1;
	elseif ((x / y) <= 1e-12)
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(N[(z - -1.0), $MachinePrecision] * N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -50.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e-12], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -50 or 9.9999999999999998e-13 < (/.f64 x y)

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{2 + 2 \cdot z}{t \cdot z}} \]
   3. 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 85.8

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

   4. Applied rewrites 85.8%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-fma.f64 N/A

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

      4. associate-/l/ N/A

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

      5. distribute-lft1-in N/A

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

      6. associate-/l* N/A

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

      7. lower-*.f64 N/A

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

      8. metadata-eval N/A

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

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

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lower-*.f64 96.9

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

   6. Applied rewrites 96.9%

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

   if -50 < (/.f64 x y) < 9.9999999999999998e-13

   1. Initial program 87.2%

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

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{2 + 2 \cdot z}{t \cdot z}} \]
   3. 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 51.2

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

   4. Applied rewrites 51.2%

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

   5. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. div-sub N/A

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

      5. *-inverses N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate--l+ N/A

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

      9. +-commutative N/A

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

      10. lower--.f64 N/A

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

   7. Applied rewrites 99.4%

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

Alternative 7: 52.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.1 \cdot 10^{-128}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 6.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2.0)
   (/ x y)
   (if (<= (/ x y) 1.1e-128)
     -2.0
     (if (<= (/ x y) 6.6e+15) (/ 2.0 t) (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2.0) {
		tmp = x / y;
	} else if ((x / y) <= 1.1e-128) {
		tmp = -2.0;
	} else if ((x / y) <= 6.6e+15) {
		tmp = 2.0 / t;
	} 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) <= (-2.0d0)) then
        tmp = x / y
    else if ((x / y) <= 1.1d-128) then
        tmp = -2.0d0
    else if ((x / y) <= 6.6d+15) then
        tmp = 2.0d0 / t
    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) <= -2.0) {
		tmp = x / y;
	} else if ((x / y) <= 1.1e-128) {
		tmp = -2.0;
	} else if ((x / y) <= 6.6e+15) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2.0:
		tmp = x / y
	elif (x / y) <= 1.1e-128:
		tmp = -2.0
	elif (x / y) <= 6.6e+15:
		tmp = 2.0 / t
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 1.1e-128)
		tmp = -2.0;
	elseif (Float64(x / y) <= 6.6e+15)
		tmp = Float64(2.0 / t);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2.0)
		tmp = x / y;
	elseif ((x / y) <= 1.1e-128)
		tmp = -2.0;
	elseif ((x / y) <= 6.6e+15)
		tmp = 2.0 / t;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.1e-128], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 6.6e+15], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2 or 6.6e15 < (/.f64 x y)

   1. Initial program 85.8%

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

   2. Taylor expanded in x around inf

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

      1. lift-/.f64 69.9

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

   4. Applied rewrites 69.9%

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

   if -2 < (/.f64 x y) < 1.10000000000000005e-128

   1. Initial program 87.1%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   3. 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 99.4

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

   4. Applied rewrites 99.4%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 39.1%

      \[\leadsto -2 \]

   if 1.10000000000000005e-128 < (/.f64 x y) < 6.6e15

   1. Initial program 86.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   3. 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 93.3

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

   4. Applied rewrites 93.3%

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

   5. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \color{blue}{\frac{1 - t}{t}} \]
   6. 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 57.3

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

   7. Applied rewrites 57.3%

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

   8. Taylor expanded in t around 0

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

      1. lower-/.f64 25.3

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

   10. Applied rewrites 25.3%

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

Alternative 8: 89.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -9.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{y} \leq 4.5 \cdot 10^{+100}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -9.8e+39)
   (+ (/ x y) (/ 2.0 (* t z)))
   (if (<= (/ x y) 4.5e+100)
     (- (/ (- (/ 2.0 z) -2.0) t) 2.0)
     (+ (/ x y) (/ 2.0 t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -9.8e+39) {
		tmp = (x / y) + (2.0 / (t * z));
	} else if ((x / y) <= 4.5e+100) {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	} else {
		tmp = (x / y) + (2.0 / t);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-9.8d+39)) then
        tmp = (x / y) + (2.0d0 / (t * z))
    else if ((x / y) <= 4.5d+100) then
        tmp = (((2.0d0 / z) - (-2.0d0)) / t) - 2.0d0
    else
        tmp = (x / y) + (2.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -9.8e+39) {
		tmp = (x / y) + (2.0 / (t * z));
	} else if ((x / y) <= 4.5e+100) {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	} else {
		tmp = (x / y) + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -9.8e+39:
		tmp = (x / y) + (2.0 / (t * z))
	elif (x / y) <= 4.5e+100:
		tmp = (((2.0 / z) - -2.0) / t) - 2.0
	else:
		tmp = (x / y) + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -9.8e+39)
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	elseif (Float64(x / y) <= 4.5e+100)
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -9.8e+39)
		tmp = (x / y) + (2.0 / (t * z));
	elseif ((x / y) <= 4.5e+100)
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	else
		tmp = (x / y) + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -9.8e+39], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4.5e+100], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -9.79999999999999974e39

   1. Initial program 86.0%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 90.0%

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

   if -9.79999999999999974e39 < (/.f64 x y) < 4.50000000000000036e100

   1. Initial program 86.9%

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

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{2 + 2 \cdot z}{t \cdot z}} \]
   3. 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 56.6

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

   4. Applied rewrites 56.6%

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

   5. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. div-sub N/A

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

      5. *-inverses N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate--l+ N/A

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

      9. +-commutative N/A

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

      10. lower--.f64 N/A

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

   7. Applied rewrites 91.2%

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

   if 4.50000000000000036e100 < (/.f64 x y)

   1. Initial program 85.1%

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

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{2 + 2 \cdot z}{t \cdot z}} \]
   3. 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 87.6

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

   4. Applied rewrites 87.6%

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

   5. Taylor expanded in z around inf

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

      1. lift-/.f64 84.2

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

   7. Applied rewrites 84.2%

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

Alternative 9: 87.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2}{t}\\ \mathbf{if}\;\frac{x}{y} \leq -1.5 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4.5 \cdot 10^{+100}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ 2.0 t))))
   (if (<= (/ x y) -1.5e+95)
     t_1
     (if (<= (/ x y) 4.5e+100) (- (/ (- (/ 2.0 z) -2.0) t) 2.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / t);
	double tmp;
	if ((x / y) <= -1.5e+95) {
		tmp = t_1;
	} else if ((x / y) <= 4.5e+100) {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (2.0d0 / t)
    if ((x / y) <= (-1.5d+95)) then
        tmp = t_1
    else if ((x / y) <= 4.5d+100) then
        tmp = (((2.0d0 / z) - (-2.0d0)) / t) - 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / t);
	double tmp;
	if ((x / y) <= -1.5e+95) {
		tmp = t_1;
	} else if ((x / y) <= 4.5e+100) {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (2.0 / t)
	tmp = 0
	if (x / y) <= -1.5e+95:
		tmp = t_1
	elif (x / y) <= 4.5e+100:
		tmp = (((2.0 / z) - -2.0) / t) - 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(2.0 / t))
	tmp = 0.0
	if (Float64(x / y) <= -1.5e+95)
		tmp = t_1;
	elseif (Float64(x / y) <= 4.5e+100)
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (2.0 / t);
	tmp = 0.0;
	if ((x / y) <= -1.5e+95)
		tmp = t_1;
	elseif ((x / y) <= 4.5e+100)
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1.5e+95], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4.5e+100], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.49999999999999996e95 or 4.50000000000000036e100 < (/.f64 x y)

   1. Initial program 85.2%

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

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{2 + 2 \cdot z}{t \cdot z}} \]
   3. 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 87.8

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

   4. Applied rewrites 87.8%

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

   5. Taylor expanded in z around inf

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

      1. lift-/.f64 85.2

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

   7. Applied rewrites 85.2%

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

   if -1.49999999999999996e95 < (/.f64 x y) < 4.50000000000000036e100

   1. Initial program 87.0%

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

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{2 + 2 \cdot z}{t \cdot z}} \]
   3. 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 58.5

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

   4. Applied rewrites 58.5%

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

   5. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. div-sub N/A

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

      5. *-inverses N/A

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

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

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

      7. metadata-eval N/A

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

      8. associate--l+ N/A

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

      9. +-commutative N/A

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

      10. lower--.f64 N/A

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

   7. Applied rewrites 89.0%

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

Alternative 10: 65.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.05 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 6.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.05e+18)
   (/ x y)
   (if (<= (/ x y) 6.6e+15) (- (/ 2.0 t) 2.0) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.05e+18) {
		tmp = x / y;
	} else if ((x / y) <= 6.6e+15) {
		tmp = (2.0 / t) - 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) <= (-1.05d+18)) then
        tmp = x / y
    else if ((x / y) <= 6.6d+15) then
        tmp = (2.0d0 / t) - 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) <= -1.05e+18) {
		tmp = x / y;
	} else if ((x / y) <= 6.6e+15) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.05e+18:
		tmp = x / y
	elif (x / y) <= 6.6e+15:
		tmp = (2.0 / t) - 2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.05e+18)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 6.6e+15)
		tmp = Float64(Float64(2.0 / t) - 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) <= -1.05e+18)
		tmp = x / y;
	elseif ((x / y) <= 6.6e+15)
		tmp = (2.0 / t) - 2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.05e+18], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 6.6e+15], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.05e18 or 6.6e15 < (/.f64 x y)

   1. Initial program 85.7%

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

   2. Taylor expanded in x around inf

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

      1. lift-/.f64 71.5

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

   4. Applied rewrites 71.5%

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

   if -1.05e18 < (/.f64 x y) < 6.6e15

   1. Initial program 87.0%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   3. 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 97.0

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

   4. Applied rewrites 97.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \color{blue}{\frac{1 - t}{t}} \]
   6. 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 60.1

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

   7. Applied rewrites 60.1%

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

   8. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. associate-*r/ N/A

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

      3. metadata-eval N/A

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

      4. lower-/.f64 60.1

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

   10. Applied rewrites 60.1%

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

Alternative 11: 91.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{1 - t}{t}, 2, \frac{x}{y}\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (/ (- 1.0 t) t) 2.0 (/ x y))))
   (if (<= z -2.7e-5)
     t_1
     (if (<= z 1.05e-7) (+ (/ x y) (/ 2.0 (* t z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(((1.0 - t) / t), 2.0, (x / y));
	double tmp;
	if (z <= -2.7e-5) {
		tmp = t_1;
	} else if (z <= 1.05e-7) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(Float64(1.0 - t) / t), 2.0, Float64(x / y))
	tmp = 0.0
	if (z <= -2.7e-5)
		tmp = t_1;
	elseif (z <= 1.05e-7)
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision] * 2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e-5], t$95$1, If[LessEqual[z, 1.05e-7], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6999999999999999e-5 or 1.05e-7 < z

   1. Initial program 74.6%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + \frac{x}{y}} \]
   3. 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 98.5

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

   4. Applied rewrites 98.5%

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

   if -2.6999999999999999e-5 < z < 1.05e-7

   1. Initial program 98.6%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 84.7%

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

Alternative 12: 61.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{-102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-7}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)))
   (if (<= t -5.2e-102) t_1 (if (<= t 1.95e-7) (- (/ 2.0 t) 2.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (t <= -5.2e-102) {
		tmp = t_1;
	} else if (t <= 1.95e-7) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (-2.0d0)
    if (t <= (-5.2d-102)) then
        tmp = t_1
    else if (t <= 1.95d-7) then
        tmp = (2.0d0 / t) - 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (t <= -5.2e-102) {
		tmp = t_1;
	} else if (t <= 1.95e-7) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	tmp = 0
	if t <= -5.2e-102:
		tmp = t_1
	elif t <= 1.95e-7:
		tmp = (2.0 / t) - 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t <= -5.2e-102)
		tmp = t_1;
	elseif (t <= 1.95e-7)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	tmp = 0.0;
	if (t <= -5.2e-102)
		tmp = t_1;
	elseif (t <= 1.95e-7)
		tmp = (2.0 / t) - 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t, -5.2e-102], t$95$1, If[LessEqual[t, 1.95e-7], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.19999999999999973e-102 or 1.95000000000000012e-7 < t

   1. Initial program 78.5%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 76.5%

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

   if -5.19999999999999973e-102 < t < 1.95000000000000012e-7

   1. Initial program 98.2%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   3. 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 81.3

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

   4. Applied rewrites 81.3%

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

   5. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \color{blue}{\frac{1 - t}{t}} \]
   6. 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 38.1

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

   7. Applied rewrites 38.1%

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

   8. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. associate-*r/ N/A

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

      3. metadata-eval N/A

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

      4. lower-/.f64 38.1

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

   10. Applied rewrites 38.1%

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

Alternative 13: 36.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2050000000:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{+34}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2050000000.0) -2.0 (if (<= t 7.4e+34) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2050000000.0) {
		tmp = -2.0;
	} else if (t <= 7.4e+34) {
		tmp = 2.0 / t;
	} else {
		tmp = -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 (t <= (-2050000000.0d0)) then
        tmp = -2.0d0
    else if (t <= 7.4d+34) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2050000000.0) {
		tmp = -2.0;
	} else if (t <= 7.4e+34) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2050000000.0:
		tmp = -2.0
	elif t <= 7.4e+34:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2050000000.0)
		tmp = -2.0;
	elseif (t <= 7.4e+34)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2050000000.0)
		tmp = -2.0;
	elseif (t <= 7.4e+34)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2050000000.0], -2.0, If[LessEqual[t, 7.4e+34], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -2.05e9 or 7.40000000000000017e34 < t

   1. Initial program 73.2%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   3. 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 53.8

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

   4. Applied rewrites 53.8%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 39.7%

      \[\leadsto -2 \]

   if -2.05e9 < t < 7.40000000000000017e34

   1. Initial program 98.4%

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

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   3. 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 77.5

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

   4. Applied rewrites 77.5%

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

   5. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \color{blue}{\frac{1 - t}{t}} \]
   6. 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 35.6

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

   7. Applied rewrites 35.6%

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

   8. Taylor expanded in t around 0

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

      1. lower-/.f64 33.4

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

   10. Applied rewrites 33.4%

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

Alternative 14: 20.9% 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 86.4%

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

2. Taylor expanded in x around 0

   \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
3. 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 66.3

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

4. Applied rewrites 66.3%

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

5. Taylor expanded in t around inf

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

7. Applied rewrites 20.9%

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

Developer Target 1: 99.3% 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 2025093 
(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))))