Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Average Error: 12.2 → 0.3

Time: 6.6s

Precision: binary64

Cost: 2512

Math

\[\frac{x \cdot \left(y + z\right)}{z} \]

↓

\[\begin{array}{l} t_0 := \frac{x \cdot \left(y + z\right)}{z}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;t_0 \leq -50000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+290}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (+ y z)) z))

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x (+ y z)) z)))
   (if (<= t_0 (- INFINITY))
     (* (+ y z) (/ x z))
     (if (<= t_0 -50000.0)
       t_0
       (if (<= t_0 2e+18)
         (/ x (/ z (+ y z)))
         (if (<= t_0 5e+290) t_0 (* x (/ (+ y z) z))))))))

C

double code(double x, double y, double z) {
	return (x * (y + z)) / z;
}

↓

double code(double x, double y, double z) {
	double t_0 = (x * (y + z)) / z;
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = (y + z) * (x / z);
	} else if (t_0 <= -50000.0) {
		tmp = t_0;
	} else if (t_0 <= 2e+18) {
		tmp = x / (z / (y + z));
	} else if (t_0 <= 5e+290) {
		tmp = t_0;
	} else {
		tmp = x * ((y + z) / z);
	}
	return tmp;
}

Java

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

↓

public static double code(double x, double y, double z) {
	double t_0 = (x * (y + z)) / z;
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = (y + z) * (x / z);
	} else if (t_0 <= -50000.0) {
		tmp = t_0;
	} else if (t_0 <= 2e+18) {
		tmp = x / (z / (y + z));
	} else if (t_0 <= 5e+290) {
		tmp = t_0;
	} else {
		tmp = x * ((y + z) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	return (x * (y + z)) / z

↓

def code(x, y, z):
	t_0 = (x * (y + z)) / z
	tmp = 0
	if t_0 <= -math.inf:
		tmp = (y + z) * (x / z)
	elif t_0 <= -50000.0:
		tmp = t_0
	elif t_0 <= 2e+18:
		tmp = x / (z / (y + z))
	elif t_0 <= 5e+290:
		tmp = t_0
	else:
		tmp = x * ((y + z) / z)
	return tmp

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y + z)) / z)
end

↓

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(y + z)) / z)
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(Float64(y + z) * Float64(x / z));
	elseif (t_0 <= -50000.0)
		tmp = t_0;
	elseif (t_0 <= 2e+18)
		tmp = Float64(x / Float64(z / Float64(y + z)));
	elseif (t_0 <= 5e+290)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(Float64(y + z) / z));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y + z)) / z;
end

↓

function tmp_2 = code(x, y, z)
	t_0 = (x * (y + z)) / z;
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = (y + z) * (x / z);
	elseif (t_0 <= -50000.0)
		tmp = t_0;
	elseif (t_0 <= 2e+18)
		tmp = x / (z / (y + z));
	elseif (t_0 <= 5e+290)
		tmp = t_0;
	else
		tmp = x * ((y + z) / z);
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(N[(y + z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, -50000.0], t$95$0, If[LessEqual[t$95$0, 2e+18], N[(x / N[(z / N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+290], t$95$0, N[(x * N[(N[(y + z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	12.2
Target	2.8
Herbie	0.3

\[\frac{x}{\frac{z}{y + z}} \]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 64.0

      \[\frac{x \cdot \left(y + z\right)}{z} \]

   2. Simplified 0.1

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

      [Start] 64.0	\[ \frac{x \cdot \left(y + z\right)}{z} \]
      associate-*l/ [<=] 0.1	\[ \color{blue}{\frac{x}{z} \cdot \left(y + z\right)} \]

   if -inf.0 < (/.f64 (*.f64 x (+.f64 y z)) z) < -5e4 or 2e18 < (/.f64 (*.f64 x (+.f64 y z)) z) < 4.9999999999999998e290

   1. Initial program 0.2

      \[\frac{x \cdot \left(y + z\right)}{z} \]

   if -5e4 < (/.f64 (*.f64 x (+.f64 y z)) z) < 2e18

   1. Initial program 6.2

      \[\frac{x \cdot \left(y + z\right)}{z} \]

   2. Simplified 0.1

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y + z}}} \]
      Proof

      [Start] 6.2	\[ \frac{x \cdot \left(y + z\right)}{z} \]
      associate-/l* [=>] 0.1	\[ \color{blue}{\frac{x}{\frac{z}{y + z}}} \]

   if 4.9999999999999998e290 < (/.f64 (*.f64 x (+.f64 y z)) z)

   1. Initial program 57.6

      \[\frac{x \cdot \left(y + z\right)}{z} \]

   2. Simplified 1.9

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

      [Start] 57.6	\[ \frac{x \cdot \left(y + z\right)}{z} \]
      associate-*r/ [<=] 1.9	\[ \color{blue}{x \cdot \frac{y + z}{z}} \]

3. Recombined 4 regimes into one program.

4. Final simplification 0.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \leq -\infty:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{x \cdot \left(y + z\right)}{z} \leq -50000:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \mathbf{elif}\;\frac{x \cdot \left(y + z\right)}{z} \leq 2 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y + z\right)}{z} \leq 5 \cdot 10^{+290}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \end{array} \]

Alternatives

Alternative 1
Error	19.3
Cost	848

\[\begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{+47}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	19.3
Cost	848

\[\begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-70}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]

Alternative 3
Error	3.4
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-185} \lor \neg \left(z \leq -2.1 \cdot 10^{-290}\right):\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array} \]

Alternative 4
Error	3.8
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+34} \lor \neg \left(y \leq 5.2 \cdot 10^{+101}\right):\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \end{array} \]

Alternative 5
Error	18.9
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+47} \lor \neg \left(y \leq 6.2 \cdot 10^{+64}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6
Error	25.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023055 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

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

  (/ (* x (+ y z)) z))