Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Average Error: 19.99% → 1.63%

Time: 6.2s

Precision: binary64

Cost: 2513

Math

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

↓

\[\begin{array}{l} t_0 := \frac{x \cdot \left(y + z\right)}{z}\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{elif}\;t_0 \leq -5 \cdot 10^{+103} \lor \neg \left(t_0 \leq 5 \cdot 10^{+58}\right) \land t_0 \leq 5 \cdot 10^{+221}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \end{array} \]

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))
     (* x (/ (+ y z) z))
     (if (or (<= t_0 -5e+103) (and (not (<= t_0 5e+58)) (<= t_0 5e+221)))
       t_0
       (/ x (/ z (+ y 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 = x * ((y + z) / z);
	} else if ((t_0 <= -5e+103) || (!(t_0 <= 5e+58) && (t_0 <= 5e+221))) {
		tmp = t_0;
	} else {
		tmp = x / (z / (y + 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 = x * ((y + z) / z);
	} else if ((t_0 <= -5e+103) || (!(t_0 <= 5e+58) && (t_0 <= 5e+221))) {
		tmp = t_0;
	} else {
		tmp = x / (z / (y + 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 = x * ((y + z) / z)
	elif (t_0 <= -5e+103) or (not (t_0 <= 5e+58) and (t_0 <= 5e+221)):
		tmp = t_0
	else:
		tmp = x / (z / (y + 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(x * Float64(Float64(y + z) / z));
	elseif ((t_0 <= -5e+103) || (!(t_0 <= 5e+58) && (t_0 <= 5e+221)))
		tmp = t_0;
	else
		tmp = Float64(x / Float64(z / Float64(y + 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 = x * ((y + z) / z);
	elseif ((t_0 <= -5e+103) || (~((t_0 <= 5e+58)) && (t_0 <= 5e+221)))
		tmp = t_0;
	else
		tmp = x / (z / (y + 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[(x * N[(N[(y + z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$0, -5e+103], And[N[Not[LessEqual[t$95$0, 5e+58]], $MachinePrecision], LessEqual[t$95$0, 5e+221]]], t$95$0, N[(x / N[(z / N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	19.99%
Target	5.06%
Herbie	1.63%

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 100

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

   2. Simplified 0.09

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

      [Start] 100	\[ \frac{x \cdot \left(y + z\right)}{z} \]
      associate-*r/ [<=] 0.09	\[ \color{blue}{x \cdot \frac{y + z}{z}} \]

   if -inf.0 < (/.f64 (*.f64 x (+.f64 y z)) z) < -5e103 or 4.99999999999999986e58 < (/.f64 (*.f64 x (+.f64 y z)) z) < 5.0000000000000002e221

   1. Initial program 0.34

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

   if -5e103 < (/.f64 (*.f64 x (+.f64 y z)) z) < 4.99999999999999986e58 or 5.0000000000000002e221 < (/.f64 (*.f64 x (+.f64 y z)) z)

   1. Initial program 18.18

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

   2. Simplified 2.28

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

      [Start] 18.18	\[ \frac{x \cdot \left(y + z\right)}{z} \]
      associate-/l* [=>] 2.28	\[ \color{blue}{\frac{x}{\frac{z}{y + z}}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 1.63

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \leq -\infty:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{elif}\;\frac{x \cdot \left(y + z\right)}{z} \leq -5 \cdot 10^{+103} \lor \neg \left(\frac{x \cdot \left(y + z\right)}{z} \leq 5 \cdot 10^{+58}\right) \land \frac{x \cdot \left(y + z\right)}{z} \leq 5 \cdot 10^{+221}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \end{array} \]

Alternatives

Alternative 1
Error	30.3%
Cost	1114

\[\begin{array}{l} \mathbf{if}\;z \leq -27.5:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-22} \lor \neg \left(z \leq -2.15 \cdot 10^{-67}\right) \land \left(z \leq 1.36 \cdot 10^{-35} \lor \neg \left(z \leq 1550000000000\right) \land z \leq 3.9 \cdot 10^{+46}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	30.52%
Cost	1113

\[\begin{array}{l} \mathbf{if}\;z \leq -21:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-31} \lor \neg \left(z \leq 1550000000000\right) \land z \leq 3.9 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Error	30.28%
Cost	1112

\[\begin{array}{l} \mathbf{if}\;z \leq -35:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.44 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-28}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;z \leq 1450000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+46}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4
Error	5.37%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq 2.5 \cdot 10^{-284} \lor \neg \left(z \leq 1.5 \cdot 10^{-96}\right):\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 5
Error	4.96%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-288} \lor \neg \left(z \leq 10^{-105}\right):\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \end{array} \]

Alternative 6
Error	5.47%
Cost	448

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

Alternative 7
Error	40.29%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023121 
(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))