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

Percentage Accurate: 87.0% → 99.5%

Time: 4.8s

Alternatives: 16

Speedup: 1.2×

• 24.5% 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: 87.0% 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: 99.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+26}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1 - t}{t}, 2, \frac{x}{y}\right)\\ \mathbf{elif}\;z \leq 4100000000:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{\mathsf{fma}\left(z + z, 1 - t, 2\right)}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{y} - \frac{-2}{t}\right) - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5e+26)
   (fma (/ (- 1.0 t) t) 2.0 (/ x y))
   (if (<= z 4100000000.0)
     (+ (/ x y) (/ (/ (fma (+ z z) (- 1.0 t) 2.0) t) z))
     (- (- (/ x y) (/ -2.0 t)) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e+26) {
		tmp = fma(((1.0 - t) / t), 2.0, (x / y));
	} else if (z <= 4100000000.0) {
		tmp = (x / y) + ((fma((z + z), (1.0 - t), 2.0) / t) / z);
	} else {
		tmp = ((x / y) - (-2.0 / t)) - 2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5e+26)
		tmp = fma(Float64(Float64(1.0 - t) / t), 2.0, Float64(x / y));
	elseif (z <= 4100000000.0)
		tmp = Float64(Float64(x / y) + Float64(Float64(fma(Float64(z + z), Float64(1.0 - t), 2.0) / t) / z));
	else
		tmp = Float64(Float64(Float64(x / y) - Float64(-2.0 / t)) - 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5e+26], N[(N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision] * 2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4100000000.0], N[(N[(x / y), $MachinePrecision] + N[(N[(N[(N[(z + z), $MachinePrecision] * N[(1.0 - t), $MachinePrecision] + 2.0), $MachinePrecision] / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.0000000000000001e26

   1. Initial program 71.6%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 100.0

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

   4. Applied rewrites 100.0%

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

   if -5.0000000000000001e26 < z < 4.1e9

   1. Initial program 98.6%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-+.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. associate-/r* N/A

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

      8. lower-/.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. +-commutative N/A

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

      11. *-commutative N/A

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

      12. lower-fma.f64 N/A

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

      13. count-2-rev N/A

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

      14. lower-+.f64 N/A

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

      15. lift--.f64 98.5

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

   3. Applied rewrites 98.5%

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

   if 4.1e9 < z

   1. Initial program 75.1%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 99.9

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

   7. Applied rewrites 99.9%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower--.f64 N/A

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

      9. lift-/.f64 N/A

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

      10. distribute-lft-neg-out N/A

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

      11. associate-*r/ N/A

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

      12. metadata-eval N/A

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

      13. distribute-frac-neg N/A

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

      14. metadata-eval N/A

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

      15. lower-/.f64 99.9

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

   9. Applied rewrites 99.9%

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

Alternative 2: 99.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z}\\ \mathbf{if}\;\frac{x}{y} \leq -200000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-7}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1 - t}{t}, 2, \frac{2}{t \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ (fma z 2.0 2.0) (* t z)))))
   (if (<= (/ x y) -200000000.0)
     t_1
     (if (<= (/ x y) 2e-7) (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) <= -200000000.0) {
		tmp = t_1;
	} else if ((x / y) <= 2e-7) {
		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) <= -200000000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e-7)
		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], -200000000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e-7], 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) < -2e8 or 1.9999999999999999e-7 < (/.f64 x y)

   1. Initial program 86.9%

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

   2. Taylor expanded in t around 0

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{2 + 2 \cdot z}}{t \cdot z} \]
   3. 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 97.8

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

   4. Applied rewrites 97.8%

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

   if -2e8 < (/.f64 x y) < 1.9999999999999999e-7

   1. Initial program 87.1%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 99.0

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

   4. Applied rewrites 99.0%

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

Alternative 3: 98.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. lift-/.f64 97.5

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

   4. Applied rewrites 97.5%

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

Alternative 4: 93.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{x}{y} + t\_1\\ \mathbf{if}\;\frac{x}{y} \leq -3 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;\frac{x}{y} \leq 0.0066:\\ \;\;\;\;\mathsf{fma}\left(\frac{1 - t}{t}, 2, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z))) (t_2 (+ (/ x y) t_1)))
   (if (<= (/ x y) -3e+30)
     t_2
     (if (<= (/ x y) 0.0066) (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) <= -3e+30) {
		tmp = t_2;
	} else if ((x / y) <= 0.0066) {
		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) <= -3e+30)
		tmp = t_2;
	elseif (Float64(x / y) <= 0.0066)
		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], -3e+30], t$95$2, If[LessEqual[N[(x / y), $MachinePrecision], 0.0066], 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) < -2.99999999999999978e30 or 0.0066 < (/.f64 x y)

   1. Initial program 86.9%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 88.4%

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

   if -2.99999999999999978e30 < (/.f64 x y) < 0.0066

   1. Initial program 87.1%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 97.9

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

   4. 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 5: 90.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-13}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1 - t}{t}, 2, \frac{x}{y}\right)\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{y} - \frac{-2}{t}\right) - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.3e-13)
   (fma (/ (- 1.0 t) t) 2.0 (/ x y))
   (if (<= z 3.8e-92)
     (+ (/ x y) (/ 2.0 (* t z)))
     (- (- (/ x y) (/ -2.0 t)) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.3e-13) {
		tmp = fma(((1.0 - t) / t), 2.0, (x / y));
	} else if (z <= 3.8e-92) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = ((x / y) - (-2.0 / t)) - 2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.3e-13)
		tmp = fma(Float64(Float64(1.0 - t) / t), 2.0, Float64(x / y));
	elseif (z <= 3.8e-92)
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	else
		tmp = Float64(Float64(Float64(x / y) - Float64(-2.0 / t)) - 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.3e-13], N[(N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision] * 2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e-92], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.29999999999999979e-13

   1. Initial program 74.8%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 97.7

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

   4. Applied rewrites 97.7%

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

   if -2.29999999999999979e-13 < z < 3.8000000000000001e-92

   1. Initial program 98.5%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 86.6%

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

   if 3.8000000000000001e-92 < z

   1. Initial program 81.5%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 89.8

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

   4. Applied rewrites 89.8%

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

   5. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 89.8

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

   7. Applied rewrites 89.8%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower--.f64 N/A

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

      9. lift-/.f64 N/A

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

      10. distribute-lft-neg-out N/A

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

      11. associate-*r/ N/A

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

      12. metadata-eval N/A

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

      13. distribute-frac-neg N/A

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

      14. metadata-eval N/A

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

      15. lower-/.f64 89.8

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

   9. Applied rewrites 89.8%

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

Alternative 6: 90.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{x}{y} - \frac{-2}{t}\right) - 2\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (- (/ x y) (/ -2.0 t)) 2.0)))
   (if (<= z -2.3e-13)
     t_1
     (if (<= z 3.8e-92) (+ (/ x y) (/ 2.0 (* t z))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) - (-2.0 / t)) - 2.0;
	double tmp;
	if (z <= -2.3e-13) {
		tmp = t_1;
	} else if (z <= 3.8e-92) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x / y) - ((-2.0d0) / t)) - 2.0d0
    if (z <= (-2.3d-13)) then
        tmp = t_1
    else if (z <= 3.8d-92) then
        tmp = (x / y) + (2.0d0 / (t * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) - (-2.0 / t)) - 2.0;
	double tmp;
	if (z <= -2.3e-13) {
		tmp = t_1;
	} else if (z <= 3.8e-92) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x / y) - (-2.0 / t)) - 2.0
	tmp = 0
	if z <= -2.3e-13:
		tmp = t_1
	elif z <= 3.8e-92:
		tmp = (x / y) + (2.0 / (t * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x / y) - Float64(-2.0 / t)) - 2.0)
	tmp = 0.0
	if (z <= -2.3e-13)
		tmp = t_1;
	elseif (z <= 3.8e-92)
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x / y) - (-2.0 / t)) - 2.0;
	tmp = 0.0;
	if (z <= -2.3e-13)
		tmp = t_1;
	elseif (z <= 3.8e-92)
		tmp = (x / y) + (2.0 / (t * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[z, -2.3e-13], t$95$1, If[LessEqual[z, 3.8e-92], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.29999999999999979e-13 or 3.8000000000000001e-92 < z

   1. Initial program 78.5%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 93.3

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

   4. Applied rewrites 93.3%

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

   5. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 93.3

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

   7. Applied rewrites 93.3%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower--.f64 N/A

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

      9. lift-/.f64 N/A

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

      10. distribute-lft-neg-out N/A

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

      11. associate-*r/ N/A

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

      12. metadata-eval N/A

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

      13. distribute-frac-neg N/A

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

      14. metadata-eval N/A

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

      15. lower-/.f64 93.3

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

   9. Applied rewrites 93.3%

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

   if -2.29999999999999979e-13 < z < 3.8000000000000001e-92

   1. Initial program 98.5%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 86.6%

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

Alternative 7: 86.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+81}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+156}:\\ \;\;\;\;\left(\frac{x}{y} - \frac{-2}{t}\right) - 2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{2}{t} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (<= t_1 -5e+81)
     (/ (- (/ 2.0 z) -2.0) t)
     (if (<= t_1 2e+156)
       (- (- (/ x y) (/ -2.0 t)) 2.0)
       (if (<= t_1 INFINITY) (+ (/ 2.0 t) (/ 2.0 (* t z))) (- (/ x y) 2.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_1 <= -5e+81) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else if (t_1 <= 2e+156) {
		tmp = ((x / y) - (-2.0 / t)) - 2.0;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (2.0 / t) + (2.0 / (t * z));
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_1 <= -5e+81) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else if (t_1 <= 2e+156) {
		tmp = ((x / y) - (-2.0 / t)) - 2.0;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (2.0 / t) + (2.0 / (t * z));
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if t_1 <= -5e+81:
		tmp = ((2.0 / z) - -2.0) / t
	elif t_1 <= 2e+156:
		tmp = ((x / y) - (-2.0 / t)) - 2.0
	elif t_1 <= math.inf:
		tmp = (2.0 / t) + (2.0 / (t * z))
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if (t_1 <= -5e+81)
		tmp = Float64(Float64(Float64(2.0 / z) - -2.0) / t);
	elseif (t_1 <= 2e+156)
		tmp = Float64(Float64(Float64(x / y) - Float64(-2.0 / t)) - 2.0);
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(2.0 / t) + Float64(2.0 / Float64(t * z)));
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if (t_1 <= -5e+81)
		tmp = ((2.0 / z) - -2.0) / t;
	elseif (t_1 <= 2e+156)
		tmp = ((x / y) - (-2.0 / t)) - 2.0;
	elseif (t_1 <= Inf)
		tmp = (2.0 / t) + (2.0 / (t * z));
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+81], N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 2e+156], N[(N[(N[(x / y), $MachinePrecision] - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(2.0 / t), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]]]

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)) < -4.9999999999999998e81

   1. Initial program 98.0%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

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

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 81.4

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

   4. Applied rewrites 81.4%

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

   if -4.9999999999999998e81 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2e156

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 86.6

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

   4. Applied rewrites 86.6%

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

   5. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 86.6

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

   7. Applied rewrites 86.6%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower--.f64 N/A

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

      9. lift-/.f64 N/A

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

      10. distribute-lft-neg-out N/A

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

      11. associate-*r/ N/A

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

      12. metadata-eval N/A

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

      13. distribute-frac-neg N/A

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

      14. metadata-eval N/A

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

      15. lower-/.f64 86.6

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

   9. Applied rewrites 86.6%

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

   if 2e156 < (/.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 98.7%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

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

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 84.9

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

   4. Applied rewrites 84.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-+.f64 N/A

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

      2. associate-*r/ N/A

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

      3. metadata-eval N/A

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

      4. lift-/.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lower-*.f64 84.9

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

   7. Applied rewrites 84.9%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. lift-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

Alternative 8: 86.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{z} - -2}{t}\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+156}:\\ \;\;\;\;\left(\frac{x}{y} - \frac{-2}{t}\right) - 2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- (/ 2.0 z) -2.0) t))
        (t_2 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (<= t_2 -5e+81)
     t_1
     (if (<= t_2 2e+156)
       (- (- (/ x y) (/ -2.0 t)) 2.0)
       (if (<= t_2 INFINITY) t_1 (- (/ x y) 2.0))))))

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 tmp;
	if (t_2 <= -5e+81) {
		tmp = t_1;
	} else if (t_2 <= 2e+156) {
		tmp = ((x / y) - (-2.0 / t)) - 2.0;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / z) - -2.0) / t;
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_2 <= -5e+81) {
		tmp = t_1;
	} else if (t_2 <= 2e+156) {
		tmp = ((x / y) - (-2.0 / t)) - 2.0;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((2.0 / z) - -2.0) / t
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if t_2 <= -5e+81:
		tmp = t_1
	elif t_2 <= 2e+156:
		tmp = ((x / y) - (-2.0 / t)) - 2.0
	elif t_2 <= math.inf:
		tmp = t_1
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(2.0 / z) - -2.0) / t)
	t_2 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if (t_2 <= -5e+81)
		tmp = t_1;
	elseif (t_2 <= 2e+156)
		tmp = Float64(Float64(Float64(x / y) - Float64(-2.0 / t)) - 2.0);
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((2.0 / z) - -2.0) / t;
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if (t_2 <= -5e+81)
		tmp = t_1;
	elseif (t_2 <= 2e+156)
		tmp = ((x / y) - (-2.0 / t)) - 2.0;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(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]}, If[LessEqual[t$95$2, -5e+81], t$95$1, If[LessEqual[t$95$2, 2e+156], N[(N[(N[(x / y), $MachinePrecision] - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$1, N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -4.9999999999999998e81 or 2e156 < (/.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. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

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

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 82.9

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

   4. Applied rewrites 82.9%

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

   if -4.9999999999999998e81 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2e156

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 86.6

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

   4. Applied rewrites 86.6%

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

   5. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 86.6

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

   7. Applied rewrites 86.6%

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

      1. lift-+.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. +-commutative N/A

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

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

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

      8. lower--.f64 N/A

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

      9. lift-/.f64 N/A

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

      10. distribute-lft-neg-out N/A

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

      11. associate-*r/ N/A

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

      12. metadata-eval N/A

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

      13. distribute-frac-neg N/A

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

      14. metadata-eval N/A

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

      15. lower-/.f64 86.6

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

   9. Applied rewrites 86.6%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. lift-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

Alternative 9: 84.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{z} - -2}{t}\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_3 := \frac{x}{y} - 2\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+156}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{t}, 2, \frac{x}{y}\right)\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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+61)
     t_1
     (if (<= t_2 -1.0)
       t_3
       (if (<= t_2 2e+156)
         (fma (/ 1.0 t) 2.0 (/ x y))
         (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+61) {
		tmp = t_1;
	} else if (t_2 <= -1.0) {
		tmp = t_3;
	} else if (t_2 <= 2e+156) {
		tmp = fma((1.0 / t), 2.0, (x / y));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(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+61)
		tmp = t_1;
	elseif (t_2 <= -1.0)
		tmp = t_3;
	elseif (t_2 <= 2e+156)
		tmp = fma(Float64(1.0 / t), 2.0, Float64(x / y));
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(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+61], t$95$1, If[LessEqual[t$95$2, -1.0], t$95$3, If[LessEqual[t$95$2, 2e+156], N[(N[(1.0 / t), $MachinePrecision] * 2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -9.99999999999999949e60 or 2e156 < (/.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. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

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

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 81.9

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

   4. Applied rewrites 81.9%

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

   if -9.99999999999999949e60 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 71.2%

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

   2. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. lift-/.f64 93.3

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

   4. Applied rewrites 93.3%

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

   if -1 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2e156

   1. Initial program 99.7%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 67.3

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

   4. Applied rewrites 67.3%

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

   5. Taylor expanded in t around 0

      \[\leadsto \mathsf{fma}\left(\frac{1}{t}, 2, \frac{x}{y}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 66.5%

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

Alternative 10: 83.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{z} - -2}{t}\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_3 := \frac{x}{y} - 2\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 4 \cdot 10^{+55}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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+61)
     t_1
     (if (<= t_2 4e+55) 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+61) {
		tmp = t_1;
	} else if (t_2 <= 4e+55) {
		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+61) {
		tmp = t_1;
	} else if (t_2 <= 4e+55) {
		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+61:
		tmp = t_1
	elif t_2 <= 4e+55:
		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+61)
		tmp = t_1;
	elseif (t_2 <= 4e+55)
		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+61)
		tmp = t_1;
	elseif (t_2 <= 4e+55)
		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+61], t$95$1, If[LessEqual[t$95$2, 4e+55], 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)) < -9.99999999999999949e60 or 4.00000000000000004e55 < (/.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 98.6%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

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

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 78.9

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

   4. Applied rewrites 78.9%

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

   if -9.99999999999999949e60 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4.00000000000000004e55 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 73.9%

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

   2. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. lift-/.f64 88.6

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

   4. Applied rewrites 88.6%

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

Alternative 11: 69.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+243}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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 -1e+133)
     (/ (/ 2.0 z) t)
     (if (<= t_1 4e+55)
       t_2
       (if (<= t_1 1e+243)
         (/ 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 <= -1e+133) {
		tmp = (2.0 / z) / t;
	} else if (t_1 <= 4e+55) {
		tmp = t_2;
	} else if (t_1 <= 1e+243) {
		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 <= -1e+133) {
		tmp = (2.0 / z) / t;
	} else if (t_1 <= 4e+55) {
		tmp = t_2;
	} else if (t_1 <= 1e+243) {
		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 <= -1e+133:
		tmp = (2.0 / z) / t
	elif t_1 <= 4e+55:
		tmp = t_2
	elif t_1 <= 1e+243:
		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 <= -1e+133)
		tmp = Float64(Float64(2.0 / z) / t);
	elseif (t_1 <= 4e+55)
		tmp = t_2;
	elseif (t_1 <= 1e+243)
		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 <= -1e+133)
		tmp = (2.0 / z) / t;
	elseif (t_1 <= 4e+55)
		tmp = t_2;
	elseif (t_1 <= 1e+243)
		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, -1e+133], N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 4e+55], t$95$2, If[LessEqual[t$95$1, 1e+243], 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 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)) < -1e133

   1. Initial program 97.7%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

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

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 84.8

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

   4. Applied rewrites 84.8%

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

   5. Taylor expanded in z around 0

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

      1. lift-/.f64 59.2

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

   7. Applied rewrites 59.2%

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

   if -1e133 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4.00000000000000004e55 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 76.8%

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

   2. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. lift-/.f64 83.2

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

   4. Applied rewrites 83.2%

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

   if 4.00000000000000004e55 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.0000000000000001e243

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

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

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 68.6

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

   4. Applied rewrites 68.6%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 34.2%

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

   if 1.0000000000000001e243 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 98.1%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lift-*.f64 72.0

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

   4. Applied rewrites 72.0%

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

Alternative 12: 69.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{x}{y} - 2\\ t_3 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{+133}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 4 \cdot 10^{+55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 10^{+243}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z)))
        (t_2 (- (/ x y) 2.0))
        (t_3 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (<= t_3 -1e+133)
     t_1
     (if (<= t_3 4e+55)
       t_2
       (if (<= t_3 1e+243) (/ 2.0 t) (if (<= t_3 INFINITY) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) - 2.0;
	double t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_3 <= -1e+133) {
		tmp = t_1;
	} else if (t_3 <= 4e+55) {
		tmp = t_2;
	} else if (t_3 <= 1e+243) {
		tmp = 2.0 / t;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) - 2.0;
	double t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_3 <= -1e+133) {
		tmp = t_1;
	} else if (t_3 <= 4e+55) {
		tmp = t_2;
	} else if (t_3 <= 1e+243) {
		tmp = 2.0 / t;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (x / y) - 2.0
	t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if t_3 <= -1e+133:
		tmp = t_1
	elif t_3 <= 4e+55:
		tmp = t_2
	elif t_3 <= 1e+243:
		tmp = 2.0 / t
	elif t_3 <= math.inf:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(x / y) - 2.0)
	t_3 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if (t_3 <= -1e+133)
		tmp = t_1;
	elseif (t_3 <= 4e+55)
		tmp = t_2;
	elseif (t_3 <= 1e+243)
		tmp = Float64(2.0 / t);
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = (x / y) - 2.0;
	t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if (t_3 <= -1e+133)
		tmp = t_1;
	elseif (t_3 <= 4e+55)
		tmp = t_2;
	elseif (t_3 <= 1e+243)
		tmp = 2.0 / t;
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+133], t$95$1, If[LessEqual[t$95$3, 4e+55], t$95$2, If[LessEqual[t$95$3, 1e+243], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -1e133 or 1.0000000000000001e243 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 97.8%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lift-*.f64 63.8

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

   4. Applied rewrites 63.8%

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

   if -1e133 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4.00000000000000004e55 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 76.8%

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

   2. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. lift-/.f64 83.2

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

   4. Applied rewrites 83.2%

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

   if 4.00000000000000004e55 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.0000000000000001e243

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

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

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

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

      7. lower--.f64 N/A

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

      8. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. lower-/.f64 68.6

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

   4. Applied rewrites 68.6%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 34.2%

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

Alternative 13: 65.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.9 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 28000000000:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -3.9e+28)
   (/ x y)
   (if (<= (/ x y) 28000000000.0) (- (/ 2.0 t) 2.0) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -3.9e+28) {
		tmp = x / y;
	} else if ((x / y) <= 28000000000.0) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-3.9d+28)) then
        tmp = x / y
    else if ((x / y) <= 28000000000.0d0) then
        tmp = (2.0d0 / t) - 2.0d0
    else
        tmp = (x / y) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -3.9e+28) {
		tmp = x / y;
	} else if ((x / y) <= 28000000000.0) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -3.9e+28:
		tmp = x / y
	elif (x / y) <= 28000000000.0:
		tmp = (2.0 / t) - 2.0
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -3.9e+28)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 28000000000.0)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -3.9e+28)
		tmp = x / y;
	elseif ((x / y) <= 28000000000.0)
		tmp = (2.0 / t) - 2.0;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -3.9e+28], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 28000000000.0], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -3.8999999999999999e28

   1. Initial program 88.3%

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

   2. Taylor expanded in x around inf

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

      1. lift-/.f64 72.4

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

   4. Applied rewrites 72.4%

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

   if -3.8999999999999999e28 < (/.f64 x y) < 2.8e10

   1. Initial program 87.1%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 62.0

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

   4. Applied rewrites 62.0%

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

   5. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 62.0

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

   7. Applied rewrites 62.0%

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

   8. Taylor expanded in x around 0

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

      1. lift-/.f64 59.5

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

   10. Applied rewrites 59.5%

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

   if 2.8e10 < (/.f64 x y)

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. lift-/.f64 70.0

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

   4. Applied rewrites 70.0%

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

Alternative 14: 65.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.9 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 28000000000:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -3.9e+28)
   (/ x y)
   (if (<= (/ x y) 28000000000.0) (- (/ 2.0 t) 2.0) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -3.9e+28) {
		tmp = x / y;
	} else if ((x / y) <= 28000000000.0) {
		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) <= (-3.9d+28)) then
        tmp = x / y
    else if ((x / y) <= 28000000000.0d0) 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) <= -3.9e+28) {
		tmp = x / y;
	} else if ((x / y) <= 28000000000.0) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -3.9e+28:
		tmp = x / y
	elif (x / y) <= 28000000000.0:
		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) <= -3.9e+28)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 28000000000.0)
		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) <= -3.9e+28)
		tmp = x / y;
	elseif ((x / y) <= 28000000000.0)
		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], -3.9e+28], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 28000000000.0], 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) < -3.8999999999999999e28 or 2.8e10 < (/.f64 x y)

   1. Initial program 86.9%

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

   2. Taylor expanded in x around inf

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

      1. lift-/.f64 71.1

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

   4. Applied rewrites 71.1%

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

   if -3.8999999999999999e28 < (/.f64 x y) < 2.8e10

   1. Initial program 87.1%

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

   2. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 62.0

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

   4. Applied rewrites 62.0%

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

   5. Taylor expanded in t around inf

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 62.0

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

   7. Applied rewrites 62.0%

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

   8. Taylor expanded in x around 0

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

      1. lift-/.f64 59.5

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

   10. Applied rewrites 59.5%

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

Alternative 15: 53.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.7 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2.7e+19) (/ 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) <= -2.7e+19) {
		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) <= (-2.7d+19)) 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) <= -2.7e+19) {
		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) <= -2.7e+19:
		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) <= -2.7e+19)
		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) <= -2.7e+19)
		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], -2.7e+19], 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) < -2.7e19 or 2 < (/.f64 x y)

   1. Initial program 87.0%

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

   2. Taylor expanded in x around inf

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

      1. lift-/.f64 69.9

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

   4. Applied rewrites 69.9%

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

   if -2.7e19 < (/.f64 x y) < 2

   1. Initial program 87.1%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. lower-/.f64 N/A

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

      8. lift-*.f64 98.2

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

   4. Applied rewrites 98.2%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 37.0%

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

Alternative 16: 20.1% accurate, 24.7× 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 87.0%

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

2. Taylor expanded in x around 0

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

   1. *-commutative N/A

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

   2. lower-fma.f64 N/A

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

   3. lower-/.f64 N/A

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

   4. lift--.f64 N/A

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

   5. associate-*r/ N/A

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

   6. metadata-eval N/A

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

   7. lower-/.f64 N/A

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

   8. lift-*.f64 66.0

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

4. Applied rewrites 66.0%

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

5. Taylor expanded in t around inf

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

7. Applied rewrites 20.1%

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

Reproduce

herbie shell --seed 2025114 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64
  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))