Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Average Error: 12.4 → 1.7

Time: 6.6s

Precision: binary64

Cost: 1480

Math

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

↓

\[\begin{array}{l} t_0 := \frac{x \cdot \left(y + z\right)}{z}\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+298}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \end{array} \]

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 5e-168)
     (/ x (/ z (+ y z)))
     (if (<= t_0 2e+298) 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 <= 5e-168) {
		tmp = x / (z / (y + z));
	} else if (t_0 <= 2e+298) {
		tmp = t_0;
	} else {
		tmp = x * ((y + z) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (y + z)) / z
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x * (y + z)) / z
    if (t_0 <= 5d-168) then
        tmp = x / (z / (y + z))
    else if (t_0 <= 2d+298) then
        tmp = t_0
    else
        tmp = x * ((y + z) / z)
    end if
    code = tmp
end function

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 <= 5e-168) {
		tmp = x / (z / (y + z));
	} else if (t_0 <= 2e+298) {
		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 <= 5e-168:
		tmp = x / (z / (y + z))
	elif t_0 <= 2e+298:
		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 <= 5e-168)
		tmp = Float64(x / Float64(z / Float64(y + z)));
	elseif (t_0 <= 2e+298)
		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 <= 5e-168)
		tmp = x / (z / (y + z));
	elseif (t_0 <= 2e+298)
		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, 5e-168], N[(x / N[(z / N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 2e+298], t$95$0, N[(x * N[(N[(y + z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	12.4
Target	3.1
Herbie	1.7

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (+.f64 y z)) z) < 5.00000000000000001e-168

   1. Initial program 12.6

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

   2. Simplified 2.6

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

      [Start] 12.6	\[ \frac{x \cdot \left(y + z\right)}{z} \]
      associate-/l* [=>] 2.6	\[ \color{blue}{\frac{x}{\frac{z}{y + z}}} \]

   if 5.00000000000000001e-168 < (/.f64 (*.f64 x (+.f64 y z)) z) < 1.9999999999999999e298

   1. Initial program 0.4

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

   if 1.9999999999999999e298 < (/.f64 (*.f64 x (+.f64 y z)) z)

   1. Initial program 61.2

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

   2. Simplified 1.0

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

      [Start] 61.2	\[ \frac{x \cdot \left(y + z\right)}{z} \]
      associate-*r/ [<=] 1.0	\[ \color{blue}{x \cdot \frac{y + z}{z}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 1.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y + z\right)}{z} \leq 5 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y + z\right)}{z} \leq 2 \cdot 10^{+298}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \end{array} \]

Alternatives

Alternative 1
Error	19.0
Cost	850

\[\begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+138} \lor \neg \left(y \leq -6.2 \cdot 10^{+97} \lor \neg \left(y \leq -1.12 \cdot 10^{-13}\right) \land y \leq 4 \cdot 10^{+124}\right):\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	19.2
Cost	848

\[\begin{array}{l} t_0 := \frac{y}{\frac{z}{x}}\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+141}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+94}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+122}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	4.2
Cost	580

\[\begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+152}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \end{array} \]

Alternative 4
Error	3.7
Cost	580

\[\begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+32}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + z}{z}\\ \end{array} \]

Alternative 5
Error	3.2
Cost	580

\[\begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+125}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y + z}}\\ \end{array} \]

Alternative 6
Error	25.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023039 
(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))