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

Percentage Accurate: 86.7% → 99.3%

Time: 4.5s

Alternatives: 11

Speedup: 1.0×

• 76.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (+ (/ x y) (/ (+ 2.0 (* (* 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 86.7%

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

   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 86.7%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 54.0%

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

Alternative 2: 98.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{\left(z + z\right) - -2}{t \cdot z} + \frac{x}{y}\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_2 \leq -4000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 50:\\ \;\;\;\;\frac{x}{y} + 2 \cdot \frac{1 - t}{t}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (+ (/ (- (+ z z) -2.0) (* t z)) (/ x y)))
       (t_2 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
  (if (<= t_2 -4000000.0)
    t_1
    (if (<= t_2 50.0)
      (+ (/ x y) (* 2.0 (/ (- 1.0 t) t)))
      (if (<= t_2 INFINITY) t_1 (+ (/ x y) -2.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (((z + z) - -2.0) / (t * z)) + (x / y);
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_2 <= -4000000.0) {
		tmp = t_1;
	} else if (t_2 <= 50.0) {
		tmp = (x / y) + (2.0 * ((1.0 - t) / t));
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (((z + z) - -2.0) / (t * z)) + (x / y);
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_2 <= -4000000.0) {
		tmp = t_1;
	} else if (t_2 <= 50.0) {
		tmp = (x / y) + (2.0 * ((1.0 - t) / t));
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (((z + z) - -2.0) / (t * z)) + (x / y)
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if t_2 <= -4000000.0:
		tmp = t_1
	elif t_2 <= 50.0:
		tmp = (x / y) + (2.0 * ((1.0 - t) / t))
	elif t_2 <= math.inf:
		tmp = t_1
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(Float64(z + z) - -2.0) / Float64(t * z)) + Float64(x / y))
	t_2 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if (t_2 <= -4000000.0)
		tmp = t_1;
	elseif (t_2 <= 50.0)
		tmp = Float64(Float64(x / y) + Float64(2.0 * Float64(Float64(1.0 - t) / t)));
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (((z + z) - -2.0) / (t * z)) + (x / y);
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if (t_2 <= -4000000.0)
		tmp = t_1;
	elseif (t_2 <= 50.0)
		tmp = (x / y) + (2.0 * ((1.0 - t) / t));
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(z + z), $MachinePrecision] - -2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4000000.0], t$95$1, If[LessEqual[t$95$2, 50.0], N[(N[(x / y), $MachinePrecision] + N[(2.0 * N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $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)) < -4e6 or 50 < (/.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 86.7%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 80.5%

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

   4. Applied rewrites 80.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 80.5%

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. add-flip N/A

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

      7. metadata-eval N/A

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

      8. lower--.f64 80.5%

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

      9. lift-*.f64 N/A

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

      10. count-2-rev N/A

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

      11. lower-+.f64 80.5%

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

   6. Applied rewrites 80.5%

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

   if -4e6 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 50

   1. Initial program 86.7%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 71.9%

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

   4. Applied rewrites 71.9%

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

   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 86.7%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 54.0%

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

Alternative 3: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \frac{\left(z + z\right) - -2}{t \cdot z} + \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -5000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-24}:\\ \;\;\;\;2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (+ (/ (- (+ z z) -2.0) (* t z)) (/ x y))))
  (if (<= (/ x y) -5000.0)
    t_1
    (if (<= (/ x y) 1e-24)
      (+ (* 2.0 (/ (- 1.0 t) t)) (* 2.0 (/ 1.0 (* t z))))
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (((z + z) - -2.0) / (t * z)) + (x / y);
	double tmp;
	if ((x / y) <= -5000.0) {
		tmp = t_1;
	} else if ((x / y) <= 1e-24) {
		tmp = (2.0 * ((1.0 - t) / t)) + (2.0 * (1.0 / (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 = (((z + z) - (-2.0d0)) / (t * z)) + (x / y)
    if ((x / y) <= (-5000.0d0)) then
        tmp = t_1
    else if ((x / y) <= 1d-24) then
        tmp = (2.0d0 * ((1.0d0 - t) / t)) + (2.0d0 * (1.0d0 / (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 = (((z + z) - -2.0) / (t * z)) + (x / y);
	double tmp;
	if ((x / y) <= -5000.0) {
		tmp = t_1;
	} else if ((x / y) <= 1e-24) {
		tmp = (2.0 * ((1.0 - t) / t)) + (2.0 * (1.0 / (t * z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (((z + z) - -2.0) / (t * z)) + (x / y)
	tmp = 0
	if (x / y) <= -5000.0:
		tmp = t_1
	elif (x / y) <= 1e-24:
		tmp = (2.0 * ((1.0 - t) / t)) + (2.0 * (1.0 / (t * z)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(Float64(z + z) - -2.0) / Float64(t * z)) + Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -5000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e-24)
		tmp = Float64(Float64(2.0 * Float64(Float64(1.0 - t) / t)) + Float64(2.0 * Float64(1.0 / Float64(t * z))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (((z + z) - -2.0) / (t * z)) + (x / y);
	tmp = 0.0;
	if ((x / y) <= -5000.0)
		tmp = t_1;
	elseif ((x / y) <= 1e-24)
		tmp = (2.0 * ((1.0 - t) / t)) + (2.0 * (1.0 / (t * z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(z + z), $MachinePrecision] - -2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e-24], N[(N[(2.0 * N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + N[(2.0 * N[(1.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5e3 or 9.9999999999999992e-25 < (/.f64 x y)

   1. Initial program 86.7%

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

   2. Taylor expanded in t around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 80.5%

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

   4. Applied rewrites 80.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 80.5%

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

      4. lift-+.f64 N/A

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

      5. +-commutative N/A

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

      6. add-flip N/A

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

      7. metadata-eval N/A

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

      8. lower--.f64 80.5%

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

      9. lift-*.f64 N/A

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

      10. count-2-rev N/A

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

      11. lower-+.f64 80.5%

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

   6. Applied rewrites 80.5%

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

   if -5e3 < (/.f64 x y) < 9.9999999999999992e-25

   1. Initial program 86.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 65.8%

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

   4. Applied rewrites 65.8%

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

Alternative 4: 90.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{y} + 2 \cdot \frac{1 - t}{t}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-119}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (+ (/ x y) (* 2.0 (/ (- 1.0 t) t)))))
  (if (<= z -1.65e-23)
    t_1
    (if (<= z 8.8e-119) (+ (/ 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 * ((1.0 - t) / t));
	double tmp;
	if (z <= -1.65e-23) {
		tmp = t_1;
	} else if (z <= 8.8e-119) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (2.0d0 * ((1.0d0 - t) / t))
    if (z <= (-1.65d-23)) then
        tmp = t_1
    else if (z <= 8.8d-119) then
        tmp = (x / y) + (2.0d0 / (t * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 * ((1.0 - t) / t));
	double tmp;
	if (z <= -1.65e-23) {
		tmp = t_1;
	} else if (z <= 8.8e-119) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (2.0 * ((1.0 - t) / t))
	tmp = 0
	if z <= -1.65e-23:
		tmp = t_1
	elif z <= 8.8e-119:
		tmp = (x / y) + (2.0 / (t * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(2.0 * Float64(Float64(1.0 - t) / t)))
	tmp = 0.0
	if (z <= -1.65e-23)
		tmp = t_1;
	elseif (z <= 8.8e-119)
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (2.0 * ((1.0 - t) / t));
	tmp = 0.0;
	if (z <= -1.65e-23)
		tmp = t_1;
	elseif (z <= 8.8e-119)
		tmp = (x / y) + (2.0 / (t * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(2.0 * N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e-23], t$95$1, If[LessEqual[z, 8.8e-119], 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 < -1.6500000000000001e-23 or 8.8000000000000002e-119 < z

   1. Initial program 86.7%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 71.9%

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

   4. Applied rewrites 71.9%

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

   if -1.6500000000000001e-23 < z < 8.8000000000000002e-119

   1. Initial program 86.7%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 62.6%

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

Alternative 5: 84.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_2 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+43}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{1 + z}{t \cdot z} \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

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 -5e+43)
    (/ (- (/ 2.0 z) -2.0) t)
    (if (<= t_1 1e+51)
      t_2
      (if (<= t_1 INFINITY) (* (/ (+ 1.0 z) (* t z)) 2.0) 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 <= -5e+43) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else if (t_1 <= 1e+51) {
		tmp = t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = ((1.0 + z) / (t * z)) * 2.0;
	} 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 <= -5e+43) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else if (t_1 <= 1e+51) {
		tmp = t_2;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = ((1.0 + z) / (t * z)) * 2.0;
	} 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 <= -5e+43:
		tmp = ((2.0 / z) - -2.0) / t
	elif t_1 <= 1e+51:
		tmp = t_2
	elif t_1 <= math.inf:
		tmp = ((1.0 + z) / (t * z)) * 2.0
	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 <= -5e+43)
		tmp = Float64(Float64(Float64(2.0 / z) - -2.0) / t);
	elseif (t_1 <= 1e+51)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(Float64(1.0 + z) / Float64(t * z)) * 2.0);
	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 <= -5e+43)
		tmp = ((2.0 / z) - -2.0) / t;
	elseif (t_1 <= 1e+51)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = ((1.0 + z) / (t * z)) * 2.0;
	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, -5e+43], N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 1e+51], t$95$2, If[LessEqual[t$95$1, Infinity], N[(N[(N[(1.0 + z), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -5.0000000000000004e43

   1. Initial program 86.7%

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

   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. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 47.9%

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

   4. Applied rewrites 47.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. add-flip N/A

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

      4. metadata-eval N/A

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

      5. lower--.f64 47.9%

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

      6. lift-*.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. mult-flip-rev N/A

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

      9. lower-/.f64 47.9%

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

   6. Applied rewrites 47.9%

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

   if -5.0000000000000004e43 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 9.9999999999999999e50 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 86.7%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 54.0%

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

   if 9.9999999999999999e50 < (/.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 86.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 65.8%

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

   4. Applied rewrites 65.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. distribute-lft-out N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. frac-add N/A

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

      12. lift-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. mult-flip N/A

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

      15. *-inverses N/A

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

      16. lower-+.f64 N/A

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

      17. lower-*.f64 59.9%

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

   6. Applied rewrites 59.9%

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

   7. Taylor expanded in t around 0

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

      1. lower-+.f64 47.9%

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

   9. Applied rewrites 47.9%

      \[\leadsto \frac{1 + z}{t \cdot z} \cdot 2 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 84.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{1 + z}{t \cdot z} \cdot 2\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_3 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+51}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (* (/ (+ 1.0 z) (* t z)) 2.0))
       (t_2 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))
       (t_3 (+ (/ x y) -2.0)))
  (if (<= t_2 -5e+43)
    t_1
    (if (<= t_2 1e+51) t_3 (if (<= t_2 INFINITY) t_1 t_3)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((1.0 + z) / (t * z)) * 2.0;
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_3 = (x / y) + -2.0;
	double tmp;
	if (t_2 <= -5e+43) {
		tmp = t_1;
	} else if (t_2 <= 1e+51) {
		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 = ((1.0 + z) / (t * z)) * 2.0;
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double t_3 = (x / y) + -2.0;
	double tmp;
	if (t_2 <= -5e+43) {
		tmp = t_1;
	} else if (t_2 <= 1e+51) {
		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 = ((1.0 + z) / (t * z)) * 2.0
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	t_3 = (x / y) + -2.0
	tmp = 0
	if t_2 <= -5e+43:
		tmp = t_1
	elif t_2 <= 1e+51:
		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(1.0 + z) / Float64(t * z)) * 2.0)
	t_2 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	t_3 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t_2 <= -5e+43)
		tmp = t_1;
	elseif (t_2 <= 1e+51)
		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 = ((1.0 + z) / (t * z)) * 2.0;
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	t_3 = (x / y) + -2.0;
	tmp = 0.0;
	if (t_2 <= -5e+43)
		tmp = t_1;
	elseif (t_2 <= 1e+51)
		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[(1.0 + z), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision] * 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+43], t$95$1, If[LessEqual[t$95$2, 1e+51], 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)) < -5.0000000000000004e43 or 9.9999999999999999e50 < (/.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 86.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 65.8%

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

   4. Applied rewrites 65.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. distribute-lft-out N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. frac-add N/A

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

      12. lift-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. mult-flip N/A

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

      15. *-inverses N/A

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

      16. lower-+.f64 N/A

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

      17. lower-*.f64 59.9%

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

   6. Applied rewrites 59.9%

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

   7. Taylor expanded in t around 0

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

      1. lower-+.f64 47.9%

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

   9. Applied rewrites 47.9%

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

   if -5.0000000000000004e43 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 9.9999999999999999e50 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 86.7%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 54.0%

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

Alternative 7: 69.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_2 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+234}:\\ \;\;\;\;\left(-1 + -1\right) - \frac{-2}{t \cdot z}\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{+43}:\\ \;\;\;\;\frac{1 - t}{t} \cdot 2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+89}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{1}{t \cdot z} \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

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+234)
    (- (+ -1.0 -1.0) (/ -2.0 (* t z)))
    (if (<= t_1 -5e+43)
      (* (/ (- 1.0 t) t) 2.0)
      (if (<= t_1 5e+89)
        t_2
        (if (<= t_1 INFINITY) (* (/ 1.0 (* t z)) 2.0) 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+234) {
		tmp = (-1.0 + -1.0) - (-2.0 / (t * z));
	} else if (t_1 <= -5e+43) {
		tmp = ((1.0 - t) / t) * 2.0;
	} else if (t_1 <= 5e+89) {
		tmp = t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (1.0 / (t * z)) * 2.0;
	} 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+234) {
		tmp = (-1.0 + -1.0) - (-2.0 / (t * z));
	} else if (t_1 <= -5e+43) {
		tmp = ((1.0 - t) / t) * 2.0;
	} else if (t_1 <= 5e+89) {
		tmp = t_2;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (1.0 / (t * z)) * 2.0;
	} 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+234:
		tmp = (-1.0 + -1.0) - (-2.0 / (t * z))
	elif t_1 <= -5e+43:
		tmp = ((1.0 - t) / t) * 2.0
	elif t_1 <= 5e+89:
		tmp = t_2
	elif t_1 <= math.inf:
		tmp = (1.0 / (t * z)) * 2.0
	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+234)
		tmp = Float64(Float64(-1.0 + -1.0) - Float64(-2.0 / Float64(t * z)));
	elseif (t_1 <= -5e+43)
		tmp = Float64(Float64(Float64(1.0 - t) / t) * 2.0);
	elseif (t_1 <= 5e+89)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(1.0 / Float64(t * z)) * 2.0);
	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+234)
		tmp = (-1.0 + -1.0) - (-2.0 / (t * z));
	elseif (t_1 <= -5e+43)
		tmp = ((1.0 - t) / t) * 2.0;
	elseif (t_1 <= 5e+89)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = (1.0 / (t * z)) * 2.0;
	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+234], N[(N[(-1.0 + -1.0), $MachinePrecision] - N[(-2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+43], N[(N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[t$95$1, 5e+89], t$95$2, If[LessEqual[t$95$1, Infinity], N[(N[(1.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] * 2.0), $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)) < -1e234

   1. Initial program 86.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 65.8%

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

   4. Applied rewrites 65.8%

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

   5. Taylor expanded in t around inf

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

   7. Applied rewrites 47.7%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. count-2-rev N/A

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

      6. lower-+.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. mult-flip-rev N/A

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

      10. distribute-neg-frac N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 47.7%

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

   9. Applied rewrites 47.7%

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

   if -1e234 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -5.0000000000000004e43

   1. Initial program 86.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 65.8%

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

   4. Applied rewrites 65.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. distribute-lft-out N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. frac-add N/A

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

      12. lift-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. mult-flip N/A

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

      15. *-inverses N/A

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

      16. lower-+.f64 N/A

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

      17. lower-*.f64 59.9%

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

   6. Applied rewrites 59.9%

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

   7. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 37.4%

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

   9. Applied rewrites 37.4%

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

   if -5.0000000000000004e43 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4.9999999999999998e89 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 86.7%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 54.0%

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

   if 4.9999999999999998e89 < (/.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 86.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 65.8%

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

   4. Applied rewrites 65.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. distribute-lft-out N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. frac-add N/A

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

      12. lift-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. mult-flip N/A

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

      15. *-inverses N/A

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

      16. lower-+.f64 N/A

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

      17. lower-*.f64 59.9%

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

   6. Applied rewrites 59.9%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 30.1%

      \[\leadsto \frac{1}{t \cdot z} \cdot 2 \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 8: 69.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{1}{t \cdot z} \cdot 2\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ t_3 := \frac{x}{y} + -2\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+234}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+43}:\\ \;\;\;\;\frac{1 - t}{t} \cdot 2\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+89}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (* (/ 1.0 (* t z)) 2.0))
       (t_2 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))
       (t_3 (+ (/ x y) -2.0)))
  (if (<= t_2 -1e+234)
    t_1
    (if (<= t_2 -5e+43)
      (* (/ (- 1.0 t) t) 2.0)
      (if (<= t_2 5e+89) t_3 (if (<= t_2 INFINITY) t_1 t_3))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (1.0 / (t * z)) * 2.0;
	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+234) {
		tmp = t_1;
	} else if (t_2 <= -5e+43) {
		tmp = ((1.0 - t) / t) * 2.0;
	} else if (t_2 <= 5e+89) {
		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 = (1.0 / (t * z)) * 2.0;
	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+234) {
		tmp = t_1;
	} else if (t_2 <= -5e+43) {
		tmp = ((1.0 - t) / t) * 2.0;
	} else if (t_2 <= 5e+89) {
		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 = (1.0 / (t * z)) * 2.0
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	t_3 = (x / y) + -2.0
	tmp = 0
	if t_2 <= -1e+234:
		tmp = t_1
	elif t_2 <= -5e+43:
		tmp = ((1.0 - t) / t) * 2.0
	elif t_2 <= 5e+89:
		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(1.0 / Float64(t * z)) * 2.0)
	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+234)
		tmp = t_1;
	elseif (t_2 <= -5e+43)
		tmp = Float64(Float64(Float64(1.0 - t) / t) * 2.0);
	elseif (t_2 <= 5e+89)
		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 = (1.0 / (t * z)) * 2.0;
	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+234)
		tmp = t_1;
	elseif (t_2 <= -5e+43)
		tmp = ((1.0 - t) / t) * 2.0;
	elseif (t_2 <= 5e+89)
		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[(1.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] * 2.0), $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+234], t$95$1, If[LessEqual[t$95$2, -5e+43], N[(N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[t$95$2, 5e+89], t$95$3, 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)) < -1e234 or 4.9999999999999998e89 < (/.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 86.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 65.8%

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

   4. Applied rewrites 65.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. distribute-lft-out N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. frac-add N/A

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

      12. lift-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. mult-flip N/A

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

      15. *-inverses N/A

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

      16. lower-+.f64 N/A

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

      17. lower-*.f64 59.9%

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

   6. Applied rewrites 59.9%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 30.1%

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

   if -1e234 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -5.0000000000000004e43

   1. Initial program 86.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 65.8%

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

   4. Applied rewrites 65.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. distribute-lft-out N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. frac-add N/A

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

      12. lift-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. mult-flip N/A

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

      15. *-inverses N/A

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

      16. lower-+.f64 N/A

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

      17. lower-*.f64 59.9%

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

   6. Applied rewrites 59.9%

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

   7. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 37.4%

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

   9. Applied rewrites 37.4%

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

   if -5.0000000000000004e43 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4.9999999999999998e89 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 86.7%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 54.0%

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

Alternative 9: 65.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;\frac{x}{y} \leq -4.4 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-25}:\\ \;\;\;\;\frac{1 - t}{t} \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (+ (/ x y) -2.0)))
  (if (<= (/ x y) -4.4e+15)
    t_1
    (if (<= (/ x y) 5e-25) (* (/ (- 1.0 t) t) 2.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if ((x / y) <= -4.4e+15) {
		tmp = t_1;
	} else if ((x / y) <= 5e-25) {
		tmp = ((1.0 - t) / t) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (-2.0d0)
    if ((x / y) <= (-4.4d+15)) then
        tmp = t_1
    else if ((x / y) <= 5d-25) then
        tmp = ((1.0d0 - t) / t) * 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if ((x / y) <= -4.4e+15) {
		tmp = t_1;
	} else if ((x / y) <= 5e-25) {
		tmp = ((1.0 - t) / t) * 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	tmp = 0
	if (x / y) <= -4.4e+15:
		tmp = t_1
	elif (x / y) <= 5e-25:
		tmp = ((1.0 - t) / t) * 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (Float64(x / y) <= -4.4e+15)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-25)
		tmp = Float64(Float64(Float64(1.0 - t) / t) * 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	tmp = 0.0;
	if ((x / y) <= -4.4e+15)
		tmp = t_1;
	elseif ((x / y) <= 5e-25)
		tmp = ((1.0 - t) / t) * 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -4.4e+15], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-25], N[(N[(N[(1.0 - t), $MachinePrecision] / t), $MachinePrecision] * 2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.4e15 or 4.9999999999999996e-25 < (/.f64 x y)

   1. Initial program 86.7%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 54.0%

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

   if -4.4e15 < (/.f64 x y) < 4.9999999999999996e-25

   1. Initial program 86.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-+.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 65.8%

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

   4. Applied rewrites 65.8%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. distribute-lft-out N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. lift-/.f64 N/A

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

      9. lift-*.f64 N/A

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

      10. associate-/r* N/A

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

      11. frac-add N/A

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

      12. lift-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. mult-flip N/A

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

      15. *-inverses N/A

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

      16. lower-+.f64 N/A

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

      17. lower-*.f64 59.9%

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

   6. Applied rewrites 59.9%

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

   7. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 37.4%

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

   9. Applied rewrites 37.4%

      \[\leadsto \frac{1 - t}{t} \cdot 2 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 61.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq -4.4 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-74}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (+ (/ x y) -2.0)))
  (if (<= t -4.4e-72) t_1 (if (<= t 5.4e-74) (/ 2.0 t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (t <= -4.4e-72) {
		tmp = t_1;
	} else if (t <= 5.4e-74) {
		tmp = 2.0 / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (-2.0d0)
    if (t <= (-4.4d-72)) then
        tmp = t_1
    else if (t <= 5.4d-74) then
        tmp = 2.0d0 / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (t <= -4.4e-72) {
		tmp = t_1;
	} else if (t <= 5.4e-74) {
		tmp = 2.0 / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	tmp = 0
	if t <= -4.4e-72:
		tmp = t_1
	elif t <= 5.4e-74:
		tmp = 2.0 / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t <= -4.4e-72)
		tmp = t_1;
	elseif (t <= 5.4e-74)
		tmp = Float64(2.0 / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	tmp = 0.0;
	if (t <= -4.4e-72)
		tmp = t_1;
	elseif (t <= 5.4e-74)
		tmp = 2.0 / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t, -4.4e-72], t$95$1, If[LessEqual[t, 5.4e-74], N[(2.0 / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4e-72 or 5.4000000000000004e-74 < t

   1. Initial program 86.7%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 54.0%

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

   if -4.4e-72 < t < 5.4000000000000004e-74

   1. Initial program 86.7%

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

   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. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 47.9%

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

   4. Applied rewrites 47.9%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 20.0%

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

   7. Applied rewrites 20.0%

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

Alternative 11: 20.0% accurate, 3.9× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(2.0 / t), $MachinePrecision]

Derivation

1. Initial program 86.7%

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

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. lower-+.f64 N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 47.9%

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

4. Applied rewrites 47.9%

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

5. Taylor expanded in z around inf

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

   1. lower-/.f64 20.0%

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

7. Applied rewrites 20.0%

   \[\leadsto \frac{2}{\color{blue}{t}} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025258 
(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))))