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

Percentage Accurate: 86.6% → 99.5%

Time: 11.2s

Alternatives: 15

Speedup: 0.7×

• 23.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    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: 86.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 99.8

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

   4. Applied rewrites 99.8%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 100.0%

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

4. Final simplification 99.9%

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

Alternative 2: 69.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z}\\ t_2 := -2 + \frac{x}{y}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+306}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{+118}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;t\_1 \leq 10^{+126}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (* (- 1.0 t) (* z 2.0)) 2.0) (* t z)))
        (t_2 (+ -2.0 (/ x y))))
   (if (<= t_1 -5e+306)
     (/ (/ 2.0 t) z)
     (if (<= t_1 -1e+118)
       (- (/ 2.0 t) 2.0)
       (if (<= t_1 1e+126) t_2 (if (<= t_1 INFINITY) (/ (/ 2.0 z) t) t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double t_2 = -2.0 + (x / y);
	double tmp;
	if (t_1 <= -5e+306) {
		tmp = (2.0 / t) / z;
	} else if (t_1 <= -1e+118) {
		tmp = (2.0 / t) - 2.0;
	} else if (t_1 <= 1e+126) {
		tmp = t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (2.0 / z) / t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double t_2 = -2.0 + (x / y);
	double tmp;
	if (t_1 <= -5e+306) {
		tmp = (2.0 / t) / z;
	} else if (t_1 <= -1e+118) {
		tmp = (2.0 / t) - 2.0;
	} else if (t_1 <= 1e+126) {
		tmp = t_2;
	} else if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = (2.0 / z) / t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z)
	t_2 = -2.0 + (x / y)
	tmp = 0
	if t_1 <= -5e+306:
		tmp = (2.0 / t) / z
	elif t_1 <= -1e+118:
		tmp = (2.0 / t) - 2.0
	elif t_1 <= 1e+126:
		tmp = t_2
	elif t_1 <= math.inf:
		tmp = (2.0 / z) / t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(Float64(1.0 - t) * Float64(z * 2.0)) + 2.0) / Float64(t * z))
	t_2 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (t_1 <= -5e+306)
		tmp = Float64(Float64(2.0 / t) / z);
	elseif (t_1 <= -1e+118)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	elseif (t_1 <= 1e+126)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(2.0 / z) / t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	t_2 = -2.0 + (x / y);
	tmp = 0.0;
	if (t_1 <= -5e+306)
		tmp = (2.0 / t) / z;
	elseif (t_1 <= -1e+118)
		tmp = (2.0 / t) - 2.0;
	elseif (t_1 <= 1e+126)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = (2.0 / z) / t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(1.0 - t), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+306], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, -1e+118], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[t$95$1, 1e+126], t$95$2, If[LessEqual[t$95$1, Infinity], N[(N[(2.0 / z), $MachinePrecision] / t), $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)) < -4.99999999999999993e306

   1. Initial program 95.1%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 96.1

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

   5. Applied rewrites 96.1%

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

   7. Applied rewrites 96.1%

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

   if -4.99999999999999993e306 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -9.99999999999999967e117

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 78.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 38.9%

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

   if -9.99999999999999967e117 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 9.99999999999999925e125 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 77.9%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 79.3%

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

   if 9.99999999999999925e125 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 98.0%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 56.4

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

   5. Applied rewrites 56.4%

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

   7. Applied rewrites 56.5%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq -5 \cdot 10^{+306}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq -1 \cdot 10^{+118}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq 10^{+126}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq \infty:\\ \;\;\;\;\frac{\frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Developer Target 1: 99.2% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024230 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y))))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))