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

Percentage Accurate: 86.2% → 99.6%

Time: 15.2s

Precision: binary64

Cost: 1988

• 23.2% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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));
}

↓

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

Python

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

↓

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

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

↓

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

MATLAB

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

↓

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

↓

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

Target

Original	86.2%
Target	99.3%
Herbie	99.6%

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.9%

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

   2. Simplified 99.9%

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

      [Start] 99.9%	\[ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
      sub-neg [=>] 99.9%	\[ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \color{blue}{\left(1 + \left(-t\right)\right)}}{t \cdot z} \]
      distribute-rgt-in [=>] 99.9%	\[ \frac{x}{y} + \frac{2 + \color{blue}{\left(1 \cdot \left(z \cdot 2\right) + \left(-t\right) \cdot \left(z \cdot 2\right)\right)}}{t \cdot z} \]
      *-lft-identity [=>] 99.9%	\[ \frac{x}{y} + \frac{2 + \left(\color{blue}{z \cdot 2} + \left(-t\right) \cdot \left(z \cdot 2\right)\right)}{t \cdot z} \]
      associate-+r+ [=>] 99.9%	\[ \frac{x}{y} + \frac{\color{blue}{\left(2 + z \cdot 2\right) + \left(-t\right) \cdot \left(z \cdot 2\right)}}{t \cdot z} \]
      cancel-sign-sub-inv [<=] 99.9%	\[ \frac{x}{y} + \frac{\color{blue}{\left(2 + z \cdot 2\right) - t \cdot \left(z \cdot 2\right)}}{t \cdot z} \]
      div-sub [=>] 87.0%	\[ \frac{x}{y} + \color{blue}{\left(\frac{2 + z \cdot 2}{t \cdot z} - \frac{t \cdot \left(z \cdot 2\right)}{t \cdot z}\right)} \]
      associate-*r* [=>] 87.0%	\[ \frac{x}{y} + \left(\frac{2 + z \cdot 2}{t \cdot z} - \frac{\color{blue}{\left(t \cdot z\right) \cdot 2}}{t \cdot z}\right) \]
      associate-*l/ [<=] 87.0%	\[ \frac{x}{y} + \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{t \cdot z}{t \cdot z} \cdot 2}\right) \]
      *-inverses [=>] 99.9%	\[ \frac{x}{y} + \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{1} \cdot 2\right) \]
      metadata-eval [=>] 99.9%	\[ \frac{x}{y} + \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{2}\right) \]
      sub-neg [=>] 99.9%	\[ \frac{x}{y} + \color{blue}{\left(\frac{2 + z \cdot 2}{t \cdot z} + \left(-2\right)\right)} \]
      metadata-eval [=>] 99.9%	\[ \frac{x}{y} + \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{-2}\right) \]
      metadata-eval [<=] 99.9%	\[ \frac{x}{y} + \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{2 \cdot -1}\right) \]
      +-commutative [<=] 99.9%	\[ \frac{x}{y} + \color{blue}{\left(2 \cdot -1 + \frac{2 + z \cdot 2}{t \cdot z}\right)} \]
      metadata-eval [=>] 99.9%	\[ \frac{x}{y} + \left(\color{blue}{-2} + \frac{2 + z \cdot 2}{t \cdot z}\right) \]
      associate-/l/ [<=] 99.9%	\[ \frac{x}{y} + \left(-2 + \color{blue}{\frac{\frac{2 + z \cdot 2}{z}}{t}}\right) \]

   if +inf.0 < (+.f64 (/.f64 x y) (/.f64 (+.f64 2 (*.f64 (*.f64 z 2) (-.f64 1 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. Simplified 84.6%

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

      [Start] 0.0%	\[ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
      sub-neg [=>] 0.0%	\[ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \color{blue}{\left(1 + \left(-t\right)\right)}}{t \cdot z} \]
      distribute-rgt-in [=>] 0.0%	\[ \frac{x}{y} + \frac{2 + \color{blue}{\left(1 \cdot \left(z \cdot 2\right) + \left(-t\right) \cdot \left(z \cdot 2\right)\right)}}{t \cdot z} \]
      *-lft-identity [=>] 0.0%	\[ \frac{x}{y} + \frac{2 + \left(\color{blue}{z \cdot 2} + \left(-t\right) \cdot \left(z \cdot 2\right)\right)}{t \cdot z} \]
      associate-+r+ [=>] 0.0%	\[ \frac{x}{y} + \frac{\color{blue}{\left(2 + z \cdot 2\right) + \left(-t\right) \cdot \left(z \cdot 2\right)}}{t \cdot z} \]
      cancel-sign-sub-inv [<=] 0.0%	\[ \frac{x}{y} + \frac{\color{blue}{\left(2 + z \cdot 2\right) - t \cdot \left(z \cdot 2\right)}}{t \cdot z} \]
      div-sub [=>] 0.0%	\[ \frac{x}{y} + \color{blue}{\left(\frac{2 + z \cdot 2}{t \cdot z} - \frac{t \cdot \left(z \cdot 2\right)}{t \cdot z}\right)} \]
      associate-*r* [=>] 0.0%	\[ \frac{x}{y} + \left(\frac{2 + z \cdot 2}{t \cdot z} - \frac{\color{blue}{\left(t \cdot z\right) \cdot 2}}{t \cdot z}\right) \]
      associate-*l/ [<=] 0.0%	\[ \frac{x}{y} + \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{\frac{t \cdot z}{t \cdot z} \cdot 2}\right) \]
      *-inverses [=>] 84.6%	\[ \frac{x}{y} + \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{1} \cdot 2\right) \]
      metadata-eval [=>] 84.6%	\[ \frac{x}{y} + \left(\frac{2 + z \cdot 2}{t \cdot z} - \color{blue}{2}\right) \]
      sub-neg [=>] 84.6%	\[ \frac{x}{y} + \color{blue}{\left(\frac{2 + z \cdot 2}{t \cdot z} + \left(-2\right)\right)} \]
      metadata-eval [=>] 84.6%	\[ \frac{x}{y} + \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{-2}\right) \]
      metadata-eval [<=] 84.6%	\[ \frac{x}{y} + \left(\frac{2 + z \cdot 2}{t \cdot z} + \color{blue}{2 \cdot -1}\right) \]
      +-commutative [<=] 84.6%	\[ \frac{x}{y} + \color{blue}{\left(2 \cdot -1 + \frac{2 + z \cdot 2}{t \cdot z}\right)} \]
      metadata-eval [=>] 84.6%	\[ \frac{x}{y} + \left(\color{blue}{-2} + \frac{2 + z \cdot 2}{t \cdot z}\right) \]
      associate-/l/ [<=] 84.6%	\[ \frac{x}{y} + \left(-2 + \color{blue}{\frac{\frac{2 + z \cdot 2}{z}}{t}}\right) \]

   3. Taylor expanded in t around inf 97.4%

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

4. Final simplification 99.5%

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

Alternatives

Alternative 1
Accuracy	99.6%
Cost	1988

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

Alternative 2
Accuracy	88.4%
Cost	1225

\[\begin{array}{l} t_1 := \frac{2}{t} - 2\\ \mathbf{if}\;\frac{x}{y} \leq -2.15 \cdot 10^{+98} \lor \neg \left(\frac{x}{y} \leq 2.9 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{x}{y} + t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{2}{z \cdot t}\\ \end{array} \]

Alternative 3
Accuracy	61.8%
Cost	1114

\[\begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -6 \cdot 10^{+204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+43}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-113} \lor \neg \left(z \leq 6.2 \cdot 10^{-169}\right) \land \left(z \leq 2.15 \cdot 10^{-92} \lor \neg \left(z \leq 1.6 \cdot 10^{-9}\right)\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \]

Alternative 4
Accuracy	61.7%
Cost	1113

\[\begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{+43}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-169}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-91} \lor \neg \left(z \leq 6.8 \cdot 10^{-9}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \]

Alternative 5
Accuracy	80.5%
Cost	1105

\[\begin{array}{l} t_1 := \frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-169}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-93} \lor \neg \left(z \leq 6.8 \cdot 10^{-9}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 6
Accuracy	79.6%
Cost	976

\[\begin{array}{l} t_1 := \frac{2 + \frac{2}{z}}{t}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -68000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Accuracy	51.4%
Cost	972

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.1 \cdot 10^{+89}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2.7 \cdot 10^{-30}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.35 \cdot 10^{-14}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 8
Accuracy	85.0%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-111} \lor \neg \left(z \leq 5.4 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} - 2\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{\frac{1}{t}}{z} - 2\\ \end{array} \]

Alternative 9
Accuracy	64.1%
Cost	840

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.4 \cdot 10^{+89}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.6 \cdot 10^{+27}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 10
Accuracy	64.3%
Cost	840

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.6 \cdot 10^{+89}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 450:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 11
Accuracy	37.5%
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -0.0075:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 12
Accuracy	20.1%
Cost	64

\[-2 \]

Reproduce

herbie shell --seed 2023263 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :herbie-target
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

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