Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Average Error: 12.4 → 0.5

Time: 15.2s

Precision: binary64

Cost: 2772

Math

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

↓

\[\begin{array}{l} t_0 := \frac{x \cdot \left(y + z\right)}{z}\\ t_1 := \begin{array}{l} \mathbf{if}\;y + z \ne 0:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y + z\right) \cdot x}{z}\\ \end{array}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;\left(1 + \frac{y}{z}\right) \cdot x\\ \mathbf{elif}\;t_0 \leq -5 \cdot 10^{-105}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+270}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x (+ y z)) z))
        (t_1 (if (!= (+ y z) 0.0) (/ x (/ z (+ y z))) (/ (* (+ y z) x) z))))
   (if (<= t_0 (- INFINITY))
     (* (+ 1.0 (/ y z)) x)
     (if (<= t_0 -5e-105)
       t_0
       (if (<= t_0 1e-153) t_1 (if (<= t_0 5e+270) t_0 t_1))))))

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 ((y + z) != 0.0) {
		tmp = x / (z / (y + z));
	} else {
		tmp = ((y + z) * x) / z;
	}
	double t_1 = tmp;
	double tmp_1;
	if (t_0 <= -((double) INFINITY)) {
		tmp_1 = (1.0 + (y / z)) * x;
	} else if (t_0 <= -5e-105) {
		tmp_1 = t_0;
	} else if (t_0 <= 1e-153) {
		tmp_1 = t_1;
	} else if (t_0 <= 5e+270) {
		tmp_1 = t_0;
	} else {
		tmp_1 = t_1;
	}
	return tmp_1;
}

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 ((y + z) != 0.0) {
		tmp = x / (z / (y + z));
	} else {
		tmp = ((y + z) * x) / z;
	}
	double t_1 = tmp;
	double tmp_1;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp_1 = (1.0 + (y / z)) * x;
	} else if (t_0 <= -5e-105) {
		tmp_1 = t_0;
	} else if (t_0 <= 1e-153) {
		tmp_1 = t_1;
	} else if (t_0 <= 5e+270) {
		tmp_1 = t_0;
	} else {
		tmp_1 = t_1;
	}
	return tmp_1;
}

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 (y + z) != 0.0:
		tmp = x / (z / (y + z))
	else:
		tmp = ((y + z) * x) / z
	t_1 = tmp
	tmp_1 = 0
	if t_0 <= -math.inf:
		tmp_1 = (1.0 + (y / z)) * x
	elif t_0 <= -5e-105:
		tmp_1 = t_0
	elif t_0 <= 1e-153:
		tmp_1 = t_1
	elif t_0 <= 5e+270:
		tmp_1 = t_0
	else:
		tmp_1 = t_1
	return tmp_1

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 (Float64(y + z) != 0.0)
		tmp = Float64(x / Float64(z / Float64(y + z)));
	else
		tmp = Float64(Float64(Float64(y + z) * x) / z);
	end
	t_1 = tmp
	tmp_1 = 0.0
	if (t_0 <= Float64(-Inf))
		tmp_1 = Float64(Float64(1.0 + Float64(y / z)) * x);
	elseif (t_0 <= -5e-105)
		tmp_1 = t_0;
	elseif (t_0 <= 1e-153)
		tmp_1 = t_1;
	elseif (t_0 <= 5e+270)
		tmp_1 = t_0;
	else
		tmp_1 = t_1;
	end
	return tmp_1
end

MATLAB

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

↓

function tmp_3 = code(x, y, z)
	t_0 = (x * (y + z)) / z;
	tmp = 0.0;
	if ((y + z) ~= 0.0)
		tmp = x / (z / (y + z));
	else
		tmp = ((y + z) * x) / z;
	end
	t_1 = tmp;
	tmp_2 = 0.0;
	if (t_0 <= -Inf)
		tmp_2 = (1.0 + (y / z)) * x;
	elseif (t_0 <= -5e-105)
		tmp_2 = t_0;
	elseif (t_0 <= 1e-153)
		tmp_2 = t_1;
	elseif (t_0 <= 5e+270)
		tmp_2 = t_0;
	else
		tmp_2 = t_1;
	end
	tmp_3 = tmp_2;
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]}, Block[{t$95$1 = If[Unequal[N[(y + z), $MachinePrecision], 0.0], N[(x / N[(z / N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]]}, If[LessEqual[t$95$0, (-Infinity)], N[(N[(1.0 + N[(y / z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$0, -5e-105], t$95$0, If[LessEqual[t$95$0, 1e-153], t$95$1, If[LessEqual[t$95$0, 5e+270], t$95$0, t$95$1]]]]]]

Target

Original	12.4
Target	3.1
Herbie	0.5

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

Derivation

1. Split input into 3 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. Applied egg-rr 0.1

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

   3. Taylor expanded in y around 0 0.1

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

   if -inf.0 < (/.f64 (*.f64 x (+.f64 y z)) z) < -4.99999999999999963e-105 or 1.00000000000000004e-153 < (/.f64 (*.f64 x (+.f64 y z)) z) < 4.99999999999999976e270

   1. Initial program 0.3

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

   if -4.99999999999999963e-105 < (/.f64 (*.f64 x (+.f64 y z)) z) < 1.00000000000000004e-153 or 4.99999999999999976e270 < (/.f64 (*.f64 x (+.f64 y z)) z)

   1. Initial program 22.7

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

   2. Applied egg-rr 1.0

      \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;y + z \ne 0:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ } \end{array}} \]

   3. Simplified 1.0

      \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;y + z \ne 0:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y + z\right) \cdot x}{z}\\ } \end{array}} \]
      Proof
3. Recombined 3 regimes into one program.

Alternatives

Alternative 1
Error	0.6
Cost	2512

\[\begin{array}{l} t_0 := \frac{x \cdot \left(y + z\right)}{z}\\ t_1 := \left(1 + \frac{y}{z}\right) \cdot x\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq -2 \cdot 10^{-232}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+270}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	4.4
Cost	712

\[\begin{array}{l} t_0 := \left(1 + \frac{y}{z}\right) \cdot x\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-299}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-127}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	19.5
Cost	584

\[\begin{array}{l} t_0 := \frac{x}{z} \cdot y\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+113}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	20.3
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+113}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+108}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array} \]

Alternative 5
Error	19.5
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+114}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]

Alternative 6
Error	25.5
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023010 
(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))