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

Percentage Accurate: 86.0% → 99.4%

Time: 3.3s

Alternatives: 12

Speedup: 1.2×

• 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
  :pre TRUE
  (+ (/ 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

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]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	(x / y) + (((2) + ((z * (2)) * ((1) - t))) / (t * z))
END code

Initial Program: 86.0% 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
  :pre TRUE
  (+ (/ 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

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]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	(x / y) + (((2) + ((z * (2)) * ((1) - t))) / (t * z))
END code

Alternative 1: 99.4% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (fma (fma -2.0 (- t 1.0) (/ 2.0 z)) (/ 1.0 t) (/ x y)))

C

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

Julia

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

Wolfram

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

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	((((-2) * (t - (1))) + ((2) / z)) * ((1) / t)) + (x / y)
END code

Derivation

1. Initial program 86.0%

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

3. Applied rewrites 99.3%

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

Alternative 2: 99.3% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (fma x (/ 1.0 y) (/ (fma -2.0 (- t 1.0) (/ 2.0 z)) t)))

C

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

Julia

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

Wolfram

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

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	(x * ((1) / y)) + ((((-2) * (t - (1))) + ((2) / z)) / t)
END code

Derivation

1. Initial program 86.0%

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

3. Applied rewrites 99.4%

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

Alternative 3: 98.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{y} + \frac{2 + 2 \cdot z}{t \cdot z}\\ \mathbf{if}\;\frac{x}{y} \leq -50:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0.1:\\ \;\;\;\;\frac{\mathsf{fma}\left(t - 1, -2, \frac{2}{z}\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* t z)))))
  (if (<= (/ x y) -50.0)
    t_1
    (if (<= (/ x y) 0.1) (/ (fma (- t 1.0) -2.0 (/ 2.0 z)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((2.0 + (2.0 * z)) / (t * z));
	double tmp;
	if ((x / y) <= -50.0) {
		tmp = t_1;
	} else if ((x / y) <= 0.1) {
		tmp = fma((t - 1.0), -2.0, (2.0 / z)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 * z)) / Float64(t * z)))
	tmp = 0.0
	if (Float64(x / y) <= -50.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 0.1)
		tmp = Float64(fma(Float64(t - 1.0), -2.0, Float64(2.0 / z)) / t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 * z), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -50.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 0.1], N[(N[(N[(t - 1.0), $MachinePrecision] * -2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((x / y) + (((2) + ((2) * z)) / (t * z))) IN
		LET tmp_1 = IF ((x / y) <= (1000000000000000055511151231257827021181583404541015625e-55)) THEN ((((t - (1)) * (-2)) + ((2) / z)) / t) ELSE t_1 ENDIF IN
		LET tmp = IF ((x / y) <= (-50)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -50 or 0.10000000000000001 < (/.f64 x y)

   1. Initial program 86.0%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 79.9%

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

   if -50 < (/.f64 x y) < 0.10000000000000001

   1. Initial program 86.0%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 66.4%

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

   6. Applied rewrites 66.3%

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

Alternative 4: 91.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+133}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t - 1, -2, \frac{2}{z}\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (+ (/ x y) (/ (/ 2.0 t) z))))
  (if (<= (/ x y) -5e+56)
    t_1
    (if (<= (/ x y) 5e+133)
      (/ (fma (- t 1.0) -2.0 (/ 2.0 z)) t)
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((2.0 / t) / z);
	double tmp;
	if ((x / y) <= -5e+56) {
		tmp = t_1;
	} else if ((x / y) <= 5e+133) {
		tmp = fma((t - 1.0), -2.0, (2.0 / z)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z))
	tmp = 0.0
	if (Float64(x / y) <= -5e+56)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e+133)
		tmp = Float64(fma(Float64(t - 1.0), -2.0, Float64(2.0 / z)) / t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e+56], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e+133], N[(N[(N[(t - 1.0), $MachinePrecision] * -2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((x / y) + (((2) / t) / z)) IN
		LET tmp_1 = IF ((x / y) <= (49999999999999996074101824835349657503774913686486230752187555524924150803830162236428630807572544714024682228918922745266209965473792)) THEN ((((t - (1)) * (-2)) + ((2) / z)) / t) ELSE t_1 ENDIF IN
		LET tmp = IF ((x / y) <= (-500000000000000024173346057776829528764197422945257127936)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.0000000000000002e56 or 4.9999999999999996e133 < (/.f64 x y)

   1. Initial program 86.0%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 62.1%

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

   6. Applied rewrites 62.1%

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

   if -5.0000000000000002e56 < (/.f64 x y) < 4.9999999999999996e133

   1. Initial program 86.0%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 66.4%

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

   6. Applied rewrites 66.3%

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

Alternative 5: 91.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := \left(\frac{2}{t} + -2\right) + \frac{x}{y}\\ \mathbf{if}\;z \leq -1.1527263176328143 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2804222428380006 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (+ (+ (/ 2.0 t) -2.0) (/ x y))))
  (if (<= z -1.1527263176328143e-32)
    t_1
    (if (<= z 2.2804222428380006e-48)
      (+ (/ x y) (/ (/ 2.0 t) z))
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / t) + -2.0) + (x / y);
	double tmp;
	if (z <= -1.1527263176328143e-32) {
		tmp = t_1;
	} else if (z <= 2.2804222428380006e-48) {
		tmp = (x / y) + ((2.0 / t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 = ((2.0d0 / t) + (-2.0d0)) + (x / y)
    if (z <= (-1.1527263176328143d-32)) then
        tmp = t_1
    else if (z <= 2.2804222428380006d-48) 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 = ((2.0 / t) + -2.0) + (x / y);
	double tmp;
	if (z <= -1.1527263176328143e-32) {
		tmp = t_1;
	} else if (z <= 2.2804222428380006e-48) {
		tmp = (x / y) + ((2.0 / t) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((2.0 / t) + -2.0) + (x / y)
	tmp = 0
	if z <= -1.1527263176328143e-32:
		tmp = t_1
	elif z <= 2.2804222428380006e-48:
		tmp = (x / y) + ((2.0 / t) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(2.0 / t) + -2.0) + Float64(x / y))
	tmp = 0.0
	if (z <= -1.1527263176328143e-32)
		tmp = t_1;
	elseif (z <= 2.2804222428380006e-48)
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((2.0 / t) + -2.0) + (x / y);
	tmp = 0.0;
	if (z <= -1.1527263176328143e-32)
		tmp = t_1;
	elseif (z <= 2.2804222428380006e-48)
		tmp = (x / y) + ((2.0 / t) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1527263176328143e-32], t$95$1, If[LessEqual[z, 2.2804222428380006e-48], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((((2) / t) + (-2)) + (x / y)) IN
		LET tmp_1 = IF (z <= (228042224283800059809609376234241336538274904084958403300396680134643890249126720821505716309192713695574511552482672820107989508642276632599532604217529296875e-206)) THEN ((x / y) + (((2) / t) / z)) ELSE t_1 ENDIF IN
		LET tmp = IF (z <= (-11527263176328143227424342740422383978830461433611629481166701467372269894677480809685836404820946654581348411738872528076171875e-159)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -1.1527263176328143e-32 or 2.2804222428380006e-48 < z

   1. Initial program 86.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 72.2%

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

   6. Applied rewrites 72.0%

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

   8. Applied rewrites 72.2%

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

   if -1.1527263176328143e-32 < z < 2.2804222428380006e-48

   1. Initial program 86.0%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 62.1%

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

   6. Applied rewrites 62.1%

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

Alternative 6: 89.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := \left(\frac{2}{t} + -2\right) + \frac{x}{y}\\ \mathbf{if}\;z \leq -1.1527263176328143 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.2804222428380006 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (+ (+ (/ 2.0 t) -2.0) (/ x y))))
  (if (<= z -1.1527263176328143e-32)
    t_1
    (if (<= z 2.2804222428380006e-48)
      (+ (/ x y) (/ 2.0 (* t z)))
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / t) + -2.0) + (x / y);
	double tmp;
	if (z <= -1.1527263176328143e-32) {
		tmp = t_1;
	} else if (z <= 2.2804222428380006e-48) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 = ((2.0d0 / t) + (-2.0d0)) + (x / y)
    if (z <= (-1.1527263176328143d-32)) then
        tmp = t_1
    else if (z <= 2.2804222428380006d-48) 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 = ((2.0 / t) + -2.0) + (x / y);
	double tmp;
	if (z <= -1.1527263176328143e-32) {
		tmp = t_1;
	} else if (z <= 2.2804222428380006e-48) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((2.0 / t) + -2.0) + (x / y)
	tmp = 0
	if z <= -1.1527263176328143e-32:
		tmp = t_1
	elif z <= 2.2804222428380006e-48:
		tmp = (x / y) + (2.0 / (t * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(2.0 / t) + -2.0) + Float64(x / y))
	tmp = 0.0
	if (z <= -1.1527263176328143e-32)
		tmp = t_1;
	elseif (z <= 2.2804222428380006e-48)
		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 = ((2.0 / t) + -2.0) + (x / y);
	tmp = 0.0;
	if (z <= -1.1527263176328143e-32)
		tmp = t_1;
	elseif (z <= 2.2804222428380006e-48)
		tmp = (x / y) + (2.0 / (t * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1527263176328143e-32], t$95$1, If[LessEqual[z, 2.2804222428380006e-48], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((((2) / t) + (-2)) + (x / y)) IN
		LET tmp_1 = IF (z <= (228042224283800059809609376234241336538274904084958403300396680134643890249126720821505716309192713695574511552482672820107989508642276632599532604217529296875e-206)) THEN ((x / y) + ((2) / (t * z))) ELSE t_1 ENDIF IN
		LET tmp = IF (z <= (-11527263176328143227424342740422383978830461433611629481166701467372269894677480809685836404820946654581348411738872528076171875e-159)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -1.1527263176328143e-32 or 2.2804222428380006e-48 < z

   1. Initial program 86.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 72.2%

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

   6. Applied rewrites 72.0%

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

   8. Applied rewrites 72.2%

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

   if -1.1527263176328143e-32 < z < 2.2804222428380006e-48

   1. Initial program 86.0%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 62.1%

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

Alternative 7: 86.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z}\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+233}:\\ \;\;\;\;\left(\frac{2}{t} + -2\right) + \frac{x}{y}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (fma z 2.0 2.0) (* t z)))
       (t_2 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
  (if (<= t_2 -2e+192)
    t_1
    (if (<= t_2 2e+233)
      (+ (+ (/ 2.0 t) -2.0) (/ x y))
      (if (<= t_2 INFINITY) t_1 (+ (/ x y) -2.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(z, 2.0, 2.0) / (t * z);
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_2 <= -2e+192) {
		tmp = t_1;
	} else if (t_2 <= 2e+233) {
		tmp = ((2.0 / t) + -2.0) + (x / y);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(z, 2.0, 2.0) / Float64(t * z))
	t_2 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if (t_2 <= -2e+192)
		tmp = t_1;
	elseif (t_2 <= 2e+233)
		tmp = Float64(Float64(Float64(2.0 / t) + -2.0) + Float64(x / y));
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * 2.0 + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+192], t$95$1, If[LessEqual[t$95$2, 2e+233], N[(N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision] + N[(x / y), $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)) < -2.0000000000000001e192 or 1.9999999999999999e233 < (/.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 86.0%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 66.4%

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

   6. Applied rewrites 60.0%

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

   7. Taylor expanded in t around 0

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

   9. Applied rewrites 47.8%

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

   11. Applied rewrites 47.8%

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

   if -2.0000000000000001e192 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 1.9999999999999999e233

   1. Initial program 86.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 72.2%

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

   6. Applied rewrites 72.0%

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

   8. Applied rewrites 72.2%

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

   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 86.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 54.1%

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

Alternative 8: 80.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq -206451349775.9092:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.4938250291154155 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (+ (/ x y) -2.0)))
  (if (<= t -206451349775.9092)
    t_1
    (if (<= t 2.4938250291154155e-30) (/ (- (/ 2.0 z) -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 <= -206451349775.9092) {
		tmp = t_1;
	} else if (t <= 2.4938250291154155e-30) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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 <= (-206451349775.9092d0)) then
        tmp = t_1
    else if (t <= 2.4938250291154155d-30) then
        tmp = ((2.0d0 / z) - (-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 <= -206451349775.9092) {
		tmp = t_1;
	} else if (t <= 2.4938250291154155e-30) {
		tmp = ((2.0 / z) - -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 <= -206451349775.9092:
		tmp = t_1
	elif t <= 2.4938250291154155e-30:
		tmp = ((2.0 / z) - -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 <= -206451349775.9092)
		tmp = t_1;
	elseif (t <= 2.4938250291154155e-30)
		tmp = Float64(Float64(Float64(2.0 / z) - -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 <= -206451349775.9092)
		tmp = t_1;
	elseif (t <= 2.4938250291154155e-30)
		tmp = ((2.0 / z) - -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, -206451349775.9092], t$95$1, If[LessEqual[t, 2.4938250291154155e-30], N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((x / y) + (-2)) IN
		LET tmp_1 = IF (t <= (249382502911541550355192637886397054984156366211968544873980887146575280560191999190688960652551031671464443206787109375e-149)) THEN ((((2) / z) - (-2)) / t) ELSE t_1 ENDIF IN
		LET tmp = IF (t <= (-206451349775909210205078125e-15)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if t < -206451349775.90921 or 2.4938250291154155e-30 < t

   1. Initial program 86.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 54.1%

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

   if -206451349775.90921 < t < 2.4938250291154155e-30

   1. Initial program 86.0%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 47.9%

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

   6. Applied rewrites 47.9%

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

Alternative 9: 64.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;\frac{x}{y} \leq -83.87016083948713:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq -5.422130002277487 \cdot 10^{-40}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{y} \leq 4.341024126774362 \cdot 10^{+78}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (+ (/ x y) -2.0)))
  (if (<= (/ x y) -83.87016083948713)
    t_1
    (if (<= (/ x y) -5.422130002277487e-40)
      (/ 2.0 (* t z))
      (if (<= (/ x y) 4.341024126774362e+78)
        (+ (/ 2.0 t) -2.0)
        t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if ((x / y) <= -83.87016083948713) {
		tmp = t_1;
	} else if ((x / y) <= -5.422130002277487e-40) {
		tmp = 2.0 / (t * z);
	} else if ((x / y) <= 4.341024126774362e+78) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

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) <= (-83.87016083948713d0)) then
        tmp = t_1
    else if ((x / y) <= (-5.422130002277487d-40)) then
        tmp = 2.0d0 / (t * z)
    else if ((x / y) <= 4.341024126774362d+78) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if ((x / y) <= -83.87016083948713) {
		tmp = t_1;
	} else if ((x / y) <= -5.422130002277487e-40) {
		tmp = 2.0 / (t * z);
	} else if ((x / y) <= 4.341024126774362e+78) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	tmp = 0
	if (x / y) <= -83.87016083948713:
		tmp = t_1
	elif (x / y) <= -5.422130002277487e-40:
		tmp = 2.0 / (t * z)
	elif (x / y) <= 4.341024126774362e+78:
		tmp = (2.0 / t) + -2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (Float64(x / y) <= -83.87016083948713)
		tmp = t_1;
	elseif (Float64(x / y) <= -5.422130002277487e-40)
		tmp = Float64(2.0 / Float64(t * z));
	elseif (Float64(x / y) <= 4.341024126774362e+78)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	tmp = 0.0;
	if ((x / y) <= -83.87016083948713)
		tmp = t_1;
	elseif ((x / y) <= -5.422130002277487e-40)
		tmp = 2.0 / (t * z);
	elseif ((x / y) <= 4.341024126774362e+78)
		tmp = (2.0 / t) + -2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -83.87016083948713], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -5.422130002277487e-40], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4.341024126774362e+78], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], t$95$1]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((x / y) + (-2)) IN
		LET tmp_2 = IF ((x / y) <= (4341024126774361912387758395932053365125021319042548456651306295327418256195584)) THEN (((2) / t) + (-2)) ELSE t_1 ENDIF IN
		LET tmp_1 = IF ((x / y) <= (-542213000227748740623245459074508043051958398136356926030504625131376132386926413115796477702148487118512243387868920763139612972736358642578125e-183)) THEN ((2) / (t * z)) ELSE tmp_2 ENDIF IN
		LET tmp = IF ((x / y) <= (-838701608394871271912052179686725139617919921875e-46)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -83.870160839487127 or 4.3410241267743619e78 < (/.f64 x y)

   1. Initial program 86.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 54.1%

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

   if -83.870160839487127 < (/.f64 x y) < -5.4221300022774874e-40

   1. Initial program 86.0%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 66.4%

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

   6. Applied rewrites 60.0%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 30.2%

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

   if -5.4221300022774874e-40 < (/.f64 x y) < 4.3410241267743619e78

   1. Initial program 86.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 72.2%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 38.2%

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

   9. Applied rewrites 38.2%

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

Alternative 10: 64.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;\frac{x}{y} \leq -6.699564148421449 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4.341024126774362 \cdot 10^{+78}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (+ (/ x y) -2.0)))
  (if (<= (/ x y) -6.699564148421449e+56)
    t_1
    (if (<= (/ x y) 4.341024126774362e+78) (+ (/ 2.0 t) -2.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if ((x / y) <= -6.699564148421449e+56) {
		tmp = t_1;
	} else if ((x / y) <= 4.341024126774362e+78) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (-2.0d0)
    if ((x / y) <= (-6.699564148421449d+56)) then
        tmp = t_1
    else if ((x / y) <= 4.341024126774362d+78) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if ((x / y) <= -6.699564148421449e+56) {
		tmp = t_1;
	} else if ((x / y) <= 4.341024126774362e+78) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	tmp = 0
	if (x / y) <= -6.699564148421449e+56:
		tmp = t_1
	elif (x / y) <= 4.341024126774362e+78:
		tmp = (2.0 / t) + -2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (Float64(x / y) <= -6.699564148421449e+56)
		tmp = t_1;
	elseif (Float64(x / y) <= 4.341024126774362e+78)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	tmp = 0.0;
	if ((x / y) <= -6.699564148421449e+56)
		tmp = t_1;
	elseif ((x / y) <= 4.341024126774362e+78)
		tmp = (2.0 / t) + -2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -6.699564148421449e+56], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 4.341024126774362e+78], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((x / y) + (-2)) IN
		LET tmp_1 = IF ((x / y) <= (4341024126774361912387758395932053365125021319042548456651306295327418256195584)) THEN (((2) / t) + (-2)) ELSE t_1 ENDIF IN
		LET tmp = IF ((x / y) <= (-669956414842144940630113263268846291481863438817984249856)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -6.6995641484214494e56 or 4.3410241267743619e78 < (/.f64 x y)

   1. Initial program 86.0%

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

   2. Taylor expanded in t around inf

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

   4. Applied rewrites 54.1%

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

   if -6.6995641484214494e56 < (/.f64 x y) < 4.3410241267743619e78

   1. Initial program 86.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 72.2%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 38.2%

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

   9. Applied rewrites 38.2%

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

Alternative 11: 38.2% accurate, 3.4× speedup

Math

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

FPCore

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

C

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

Fortran

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) + (-2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	((2) / t) + (-2)
END code

Derivation

1. Initial program 86.0%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 72.2%

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

5. Taylor expanded in x around 0

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

7. Applied rewrites 38.2%

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

9. Applied rewrites 38.2%

   \[\leadsto \frac{2}{t} + -2 \]
10. Add Preprocessing

Alternative 12: 20.3% accurate, 25.4× speedup

Math

\[-2 \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	-2
END code

Derivation

1. Initial program 86.0%

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

2. Taylor expanded in x around 0

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

4. Applied rewrites 66.4%

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

5. Taylor expanded in t around inf

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

7. Applied rewrites 20.3%

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

Reproduce

herbie shell --seed 2026092 
(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))))