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

Percentage Accurate: 86.4% → 99.4%

Time: 4.1s

Alternatives: 13

Speedup: 1.1×

• 23.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.4% 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. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{2 + \left(-2 \cdot \left(t \cdot z\right) + 2 \cdot z\right)}}{t \cdot z} \]
   4. 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 99.8

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

   5. Applied rewrites 99.8%

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

   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. Add Preprocessing

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 96.8%

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

Alternative 2: 67.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_2 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+268}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+35}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+229}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -2e+268)
     (/ (/ 2.0 z) t)
     (if (<= t_1 -1e+35)
       (- (/ 2.0 t) 2.0)
       (if (<= t_1 2e+70)
         t_2
         (if (<= t_1 4e+229)
           (/ 2.0 t)
           (if (<= t_1 INFINITY) (/ (/ 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 <= -2e+268) {
		tmp = (2.0 / z) / t;
	} else if (t_1 <= -1e+35) {
		tmp = (2.0 / t) - 2.0;
	} else if (t_1 <= 2e+70) {
		tmp = t_2;
	} else if (t_1 <= 4e+229) {
		tmp = 2.0 / t;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_2 = (x / y) + -2.0;
	double tmp;
	if (t_1 <= -2e+268) {
		tmp = (2.0 / z) / t;
	} else if (t_1 <= -1e+35) {
		tmp = (2.0 / t) - 2.0;
	} else if (t_1 <= 2e+70) {
		tmp = t_2;
	} else if (t_1 <= 4e+229) {
		tmp = 2.0 / t;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	t_2 = (x / y) + -2.0
	tmp = 0
	if t_1 <= -2e+268:
		tmp = (2.0 / z) / t
	elif t_1 <= -1e+35:
		tmp = (2.0 / t) - 2.0
	elif t_1 <= 2e+70:
		tmp = t_2
	elif t_1 <= 4e+229:
		tmp = 2.0 / t
	elif t_1 <= math.inf:
		tmp = (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 <= -2e+268)
		tmp = Float64(Float64(2.0 / z) / t);
	elseif (t_1 <= -1e+35)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	elseif (t_1 <= 2e+70)
		tmp = t_2;
	elseif (t_1 <= 4e+229)
		tmp = Float64(2.0 / t);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(2.0 / t) / z);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	t_2 = (x / y) + -2.0;
	tmp = 0.0;
	if (t_1 <= -2e+268)
		tmp = (2.0 / z) / t;
	elseif (t_1 <= -1e+35)
		tmp = (2.0 / t) - 2.0;
	elseif (t_1 <= 2e+70)
		tmp = t_2;
	elseif (t_1 <= 4e+229)
		tmp = 2.0 / t;
	elseif (t_1 <= Inf)
		tmp = (2.0 / t) / z;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+268], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, -1e+35], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+70], t$95$2, If[LessEqual[t$95$1, 4e+229], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.9999999999999999e268

   1. Initial program 95.2%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

   5. Applied rewrites 97.2%

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

   6. Taylor expanded in z around 0

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

      1. lift-/.f64 77.5

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

   8. Applied rewrites 77.5%

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

   if -1.9999999999999999e268 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -9.9999999999999997e34

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 69.3

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

   5. Applied rewrites 69.3%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 34.5

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

   8. Applied rewrites 34.5%

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

   9. Taylor expanded in t around inf

      \[\leadsto 2 \cdot \frac{1}{t} - 2 \]
   10. 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. lift-/.f64 34.5

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

   11. Applied rewrites 34.5%

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

   if -9.9999999999999997e34 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2.00000000000000015e70 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 72.4%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 88.1%

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

   if 2.00000000000000015e70 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4e229

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

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

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 70.9

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

   5. Applied rewrites 70.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 34.8%

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

   if 4e229 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 96.6%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lift-*.f64 71.0

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

   5. Applied rewrites 71.0%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r* N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. lower-/.f64 N/A

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

      7. associate-*r/ N/A

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

      8. metadata-eval N/A

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

      9. lower-/.f64 71.0

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

   7. Applied rewrites 71.0%

      \[\leadsto \color{blue}{\frac{\frac{2}{t}}{z}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 3: 67.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_2 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+268}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+35}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+229}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -2e+268)
     (/ (/ 2.0 z) t)
     (if (<= t_1 -1e+35)
       (- (/ 2.0 t) 2.0)
       (if (<= t_1 2e+70)
         t_2
         (if (<= t_1 4e+229)
           (/ 2.0 t)
           (if (<= t_1 INFINITY) (/ 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 <= -2e+268) {
		tmp = (2.0 / z) / t;
	} else if (t_1 <= -1e+35) {
		tmp = (2.0 / t) - 2.0;
	} else if (t_1 <= 2e+70) {
		tmp = t_2;
	} else if (t_1 <= 4e+229) {
		tmp = 2.0 / t;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_2 = (x / y) + -2.0;
	double tmp;
	if (t_1 <= -2e+268) {
		tmp = (2.0 / z) / t;
	} else if (t_1 <= -1e+35) {
		tmp = (2.0 / t) - 2.0;
	} else if (t_1 <= 2e+70) {
		tmp = t_2;
	} else if (t_1 <= 4e+229) {
		tmp = 2.0 / t;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	t_2 = (x / y) + -2.0
	tmp = 0
	if t_1 <= -2e+268:
		tmp = (2.0 / z) / t
	elif t_1 <= -1e+35:
		tmp = (2.0 / t) - 2.0
	elif t_1 <= 2e+70:
		tmp = t_2
	elif t_1 <= 4e+229:
		tmp = 2.0 / t
	elif t_1 <= math.inf:
		tmp = 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 <= -2e+268)
		tmp = Float64(Float64(2.0 / z) / t);
	elseif (t_1 <= -1e+35)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	elseif (t_1 <= 2e+70)
		tmp = t_2;
	elseif (t_1 <= 4e+229)
		tmp = Float64(2.0 / t);
	elseif (t_1 <= Inf)
		tmp = Float64(2.0 / Float64(t * z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	t_2 = (x / y) + -2.0;
	tmp = 0.0;
	if (t_1 <= -2e+268)
		tmp = (2.0 / z) / t;
	elseif (t_1 <= -1e+35)
		tmp = (2.0 / t) - 2.0;
	elseif (t_1 <= 2e+70)
		tmp = t_2;
	elseif (t_1 <= 4e+229)
		tmp = 2.0 / t;
	elseif (t_1 <= Inf)
		tmp = 2.0 / (t * z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+268], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, -1e+35], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[t$95$1, 2e+70], t$95$2, If[LessEqual[t$95$1, 4e+229], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.9999999999999999e268

   1. Initial program 95.2%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

   5. Applied rewrites 97.2%

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

   6. Taylor expanded in z around 0

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

      1. lift-/.f64 77.5

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

   8. Applied rewrites 77.5%

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

   if -1.9999999999999999e268 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -9.9999999999999997e34

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 69.3

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

   5. Applied rewrites 69.3%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 34.5

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

   8. Applied rewrites 34.5%

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

   9. Taylor expanded in t around inf

      \[\leadsto 2 \cdot \frac{1}{t} - 2 \]
   10. 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. lift-/.f64 34.5

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

   11. Applied rewrites 34.5%

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

   if -9.9999999999999997e34 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2.00000000000000015e70 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 72.4%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 88.1%

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

   if 2.00000000000000015e70 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4e229

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

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

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 70.9

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

   5. Applied rewrites 70.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 34.8%

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

   if 4e229 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 96.6%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lift-*.f64 71.0

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

   5. Applied rewrites 71.0%

      \[\leadsto \color{blue}{\frac{2}{t \cdot z}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 4: 67.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_3 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+268}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+35}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+70}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+229}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z)))
        (t_2 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))
        (t_3 (+ (/ x y) -2.0)))
   (if (<= t_2 -2e+268)
     t_1
     (if (<= t_2 -1e+35)
       (- (/ 2.0 t) 2.0)
       (if (<= t_2 2e+70)
         t_3
         (if (<= t_2 4e+229) (/ 2.0 t) (if (<= t_2 INFINITY) t_1 t_3)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_3 = (x / y) + -2.0;
	double tmp;
	if (t_2 <= -2e+268) {
		tmp = t_1;
	} else if (t_2 <= -1e+35) {
		tmp = (2.0 / t) - 2.0;
	} else if (t_2 <= 2e+70) {
		tmp = t_3;
	} else if (t_2 <= 4e+229) {
		tmp = 2.0 / t;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_3 = (x / y) + -2.0;
	double tmp;
	if (t_2 <= -2e+268) {
		tmp = t_1;
	} else if (t_2 <= -1e+35) {
		tmp = (2.0 / t) - 2.0;
	} else if (t_2 <= 2e+70) {
		tmp = t_3;
	} else if (t_2 <= 4e+229) {
		tmp = 2.0 / t;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	t_3 = (x / y) + -2.0
	tmp = 0
	if t_2 <= -2e+268:
		tmp = t_1
	elif t_2 <= -1e+35:
		tmp = (2.0 / t) - 2.0
	elif t_2 <= 2e+70:
		tmp = t_3
	elif t_2 <= 4e+229:
		tmp = 2.0 / t
	elif t_2 <= math.inf:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	t_3 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t_2 <= -2e+268)
		tmp = t_1;
	elseif (t_2 <= -1e+35)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	elseif (t_2 <= 2e+70)
		tmp = t_3;
	elseif (t_2 <= 4e+229)
		tmp = Float64(2.0 / t);
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	t_3 = (x / y) + -2.0;
	tmp = 0.0;
	if (t_2 <= -2e+268)
		tmp = t_1;
	elseif (t_2 <= -1e+35)
		tmp = (2.0 / t) - 2.0;
	elseif (t_2 <= 2e+70)
		tmp = t_3;
	elseif (t_2 <= 4e+229)
		tmp = 2.0 / t;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+268], t$95$1, If[LessEqual[t$95$2, -1e+35], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[t$95$2, 2e+70], t$95$3, If[LessEqual[t$95$2, 4e+229], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1.9999999999999999e268 or 4e229 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 96.0%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lift-*.f64 73.8

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

   5. Applied rewrites 73.8%

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

   if -1.9999999999999999e268 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -9.9999999999999997e34

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 69.3

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

   5. Applied rewrites 69.3%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 34.5

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

   8. Applied rewrites 34.5%

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

   9. Taylor expanded in t around inf

      \[\leadsto 2 \cdot \frac{1}{t} - 2 \]
   10. 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. lift-/.f64 34.5

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

   11. Applied rewrites 34.5%

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

   if -9.9999999999999997e34 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2.00000000000000015e70 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 72.4%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 88.1%

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

   if 2.00000000000000015e70 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4e229

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

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

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 70.9

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

   5. Applied rewrites 70.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 34.8%

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

Alternative 5: 83.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_2 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+35}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+33}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{2}{t} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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+35)
     (/ (- (/ 2.0 z) -2.0) t)
     (if (<= t_1 5e+33)
       t_2
       (if (<= t_1 INFINITY) (+ (/ 2.0 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+35) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else if (t_1 <= 5e+33) {
		tmp = t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (2.0 / t) + (2.0 / (t * z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_2 = (x / y) + -2.0;
	double tmp;
	if (t_1 <= -1e+35) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else if (t_1 <= 5e+33) {
		tmp = t_2;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (2.0 / t) + (2.0 / (t * z));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	t_2 = (x / y) + -2.0
	tmp = 0
	if t_1 <= -1e+35:
		tmp = ((2.0 / z) - -2.0) / t
	elif t_1 <= 5e+33:
		tmp = t_2
	elif t_1 <= math.inf:
		tmp = (2.0 / 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+35)
		tmp = Float64(Float64(Float64(2.0 / z) - -2.0) / t);
	elseif (t_1 <= 5e+33)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(2.0 / t) + Float64(2.0 / Float64(t * z)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	t_2 = (x / y) + -2.0;
	tmp = 0.0;
	if (t_1 <= -1e+35)
		tmp = ((2.0 / z) - -2.0) / t;
	elseif (t_1 <= 5e+33)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = (2.0 / t) + (2.0 / (t * z));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+35], N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 5e+33], t$95$2, If[LessEqual[t$95$1, Infinity], N[(N[(2.0 / t), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $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)) < -9.9999999999999997e34

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      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 76.9

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

   5. Applied rewrites 76.9%

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

   if -9.9999999999999997e34 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4.99999999999999973e33 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 70.5%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 91.5%

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

   if 4.99999999999999973e33 < (/.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 98.4%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      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 79.2

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

   5. Applied rewrites 79.2%

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

   6. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. metadata-eval N/A

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

      3. lower-+.f64 N/A

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

      4. associate-*r/ N/A

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

      5. metadata-eval N/A

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

      6. lower-/.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. lift-*.f64 79.2

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

   8. Applied rewrites 79.2%

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

Alternative 6: 83.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{z} - -2}{t}\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_3 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+35}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+33}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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+35)
     t_1
     (if (<= t_2 5e+33) 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+35) {
		tmp = t_1;
	} else if (t_2 <= 5e+33) {
		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+35) {
		tmp = t_1;
	} else if (t_2 <= 5e+33) {
		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+35:
		tmp = t_1
	elif t_2 <= 5e+33:
		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+35)
		tmp = t_1;
	elseif (t_2 <= 5e+33)
		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+35)
		tmp = t_1;
	elseif (t_2 <= 5e+33)
		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+35], t$95$1, If[LessEqual[t$95$2, 5e+33], 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)) < -9.9999999999999997e34 or 4.99999999999999973e33 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      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 78.1

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

   5. Applied rewrites 78.1%

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

   if -9.9999999999999997e34 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4.99999999999999973e33 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 70.5%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 91.5%

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

Alternative 7: 98.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z}\\ \mathbf{if}\;\frac{x}{y} \leq -30500000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;\mathsf{fma}\left(\frac{1 - t}{t}, 2, \frac{2}{t \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ (fma z 2.0 2.0) (* t z)))))
   (if (<= (/ x y) -30500000.0)
     t_1
     (if (<= (/ x y) 2.0) (fma (/ (- 1.0 t) t) 2.0 (/ 2.0 (* t z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (fma(z, 2.0, 2.0) / (t * z));
	double tmp;
	if ((x / y) <= -30500000.0) {
		tmp = t_1;
	} else if ((x / y) <= 2.0) {
		tmp = fma(((1.0 - t) / t), 2.0, (2.0 / (t * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(fma(z, 2.0, 2.0) / Float64(t * z)))
	tmp = 0.0
	if (Float64(x / y) <= -30500000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 2.0)
		tmp = fma(Float64(Float64(1.0 - t) / t), 2.0, 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[(x / y), $MachinePrecision] + N[(N[(z * 2.0 + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -30500000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2.0], N[(N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision] * 2.0 + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3.05e7 or 2 < (/.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. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 97.5

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

   5. Applied rewrites 97.5%

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

   if -3.05e7 < (/.f64 x y) < 2

   1. Initial program 87.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 98.9

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

   5. Applied rewrites 98.9%

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

Alternative 8: 93.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{x}{y} + t\_1\\ \mathbf{if}\;\frac{x}{y} \leq -1050000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+14}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1 - t}{t}, 2, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z))) (t_2 (+ (/ x y) t_1)))
   (if (<= (/ x y) -1050000000.0)
     t_2
     (if (<= (/ x y) 2e+14) (fma (/ (- 1.0 t) t) 2.0 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) + t_1;
	double tmp;
	if ((x / y) <= -1050000000.0) {
		tmp = t_2;
	} else if ((x / y) <= 2e+14) {
		tmp = fma(((1.0 - t) / t), 2.0, 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) + t_1)
	tmp = 0.0
	if (Float64(x / y) <= -1050000000.0)
		tmp = t_2;
	elseif (Float64(x / y) <= 2e+14)
		tmp = fma(Float64(Float64(1.0 - t) / t), 2.0, t_1);
	else
		tmp = t_2;
	end
	return 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] + t$95$1), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1050000000.0], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 2e+14], N[(N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision] * 2.0 + t$95$1), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.05e9 or 2e14 < (/.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. Add Preprocessing

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 88.4%

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

   if -1.05e9 < (/.f64 x y) < 2e14

   1. Initial program 87.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 97.9

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

   5. Applied rewrites 97.9%

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

Alternative 9: 65.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;\frac{x}{y} \leq -6.5 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0106:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)))
   (if (<= (/ x y) -6.5e-17)
     t_1
     (if (<= (/ x y) 0.0106) (- (/ 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 ((x / y) <= -6.5e-17) {
		tmp = t_1;
	} else if ((x / y) <= 0.0106) {
		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 ((x / y) <= (-6.5d-17)) then
        tmp = t_1
    else if ((x / y) <= 0.0106d0) 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 ((x / y) <= -6.5e-17) {
		tmp = t_1;
	} else if ((x / y) <= 0.0106) {
		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 (x / y) <= -6.5e-17:
		tmp = t_1
	elif (x / y) <= 0.0106:
		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 (Float64(x / y) <= -6.5e-17)
		tmp = t_1;
	elseif (Float64(x / y) <= 0.0106)
		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 ((x / y) <= -6.5e-17)
		tmp = t_1;
	elseif ((x / y) <= 0.0106)
		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[N[(x / y), $MachinePrecision], -6.5e-17], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 0.0106], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -6.4999999999999996e-17 or 0.0106 < (/.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. Add Preprocessing

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 68.3%

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

   if -6.4999999999999996e-17 < (/.f64 x y) < 0.0106

   1. Initial program 87.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 99.7

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 62.2

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

   8. Applied rewrites 62.2%

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

   9. Taylor expanded in t around inf

      \[\leadsto 2 \cdot \frac{1}{t} - 2 \]
   10. 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. lift-/.f64 62.2

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

   11. Applied rewrites 62.2%

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

Alternative 10: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6800000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+14}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -6800000.0)
   (/ x y)
   (if (<= (/ x y) 2e+14) (- (/ 2.0 t) 2.0) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -6800000.0) {
		tmp = x / y;
	} else if ((x / y) <= 2e+14) {
		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) <= (-6800000.0d0)) then
        tmp = x / y
    else if ((x / y) <= 2d+14) 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) <= -6800000.0) {
		tmp = x / y;
	} else if ((x / y) <= 2e+14) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -6800000.0:
		tmp = x / y
	elif (x / y) <= 2e+14:
		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) <= -6800000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 2e+14)
		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) <= -6800000.0)
		tmp = x / y;
	elseif ((x / y) <= 2e+14)
		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], -6800000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e+14], 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) < -6.8e6 or 2e14 < (/.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. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lift-/.f64 70.1

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

   5. Applied rewrites 70.1%

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

   if -6.8e6 < (/.f64 x y) < 2e14

   1. Initial program 87.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 98.0

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

   5. Applied rewrites 98.0%

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

   6. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 60.7

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

   8. Applied rewrites 60.7%

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

   9. Taylor expanded in t around inf

      \[\leadsto 2 \cdot \frac{1}{t} - 2 \]
   10. 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. lift-/.f64 60.7

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

   11. Applied rewrites 60.7%

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

Alternative 11: 52.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -98000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -98000.0) (/ x y) (if (<= (/ x y) 2.0) -2.0 (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -98000.0) {
		tmp = x / y;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-98000.0d0)) then
        tmp = x / y
    else if ((x / y) <= 2.0d0) then
        tmp = -2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -98000.0) {
		tmp = x / y;
	} else if ((x / y) <= 2.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -98000.0:
		tmp = x / y
	elif (x / y) <= 2.0:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -98000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -98000.0)
		tmp = x / y;
	elseif ((x / y) <= 2.0)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -98000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.0], -2.0, N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -98000 or 2 < (/.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. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. lift-/.f64 68.8

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

   5. Applied rewrites 68.8%

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

   if -98000 < (/.f64 x y) < 2

   1. Initial program 87.0%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 99.0

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

   5. Applied rewrites 99.0%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 37.7%

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

Alternative 12: 91.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{1 - t}{t}, 2, \frac{x}{y}\right)\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (/ (- 1.0 t) t) 2.0 (/ x y))))
   (if (<= z -4.3e-10)
     t_1
     (if (<= z 7.1e-56) (+ (/ 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 <= -4.3e-10) {
		tmp = t_1;
	} else if (z <= 7.1e-56) {
		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 <= -4.3e-10)
		tmp = t_1;
	elseif (z <= 7.1e-56)
		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, -4.3e-10], t$95$1, If[LessEqual[z, 7.1e-56], 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 < -4.30000000000000014e-10 or 7.1e-56 < z

   1. Initial program 76.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 95.1

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

   5. Applied rewrites 95.1%

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

   if -4.30000000000000014e-10 < z < 7.1e-56

   1. Initial program 98.1%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 86.1%

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

Alternative 13: 20.5% 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. Add Preprocessing

3. Taylor expanded in x around 0

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

   1. *-commutative N/A

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

   2. lower-fma.f64 N/A

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

   3. lower-/.f64 N/A

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

   4. lift--.f64 N/A

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

   5. associate-*r/ N/A

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

   6. metadata-eval N/A

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

   7. lower-/.f64 N/A

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

   8. lift-*.f64 67.2

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

5. Applied rewrites 67.2%

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

6. Taylor expanded in t around inf

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

8. Applied rewrites 20.5%

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

Developer Target 1: 99.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2025088 
(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))))