Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1

Average Error: 1.9 → 1.6

Time: 22.7s

Precision: binary64

Cost: 968

Math

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

↓

\[\begin{array}{l} t_1 := x \cdot \left(z - t\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{+14}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;x \ne 0:\\ \;\;\;\;\frac{z - t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{y}\\ \end{array} + t\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+56}:\\ \;\;\;\;\frac{1}{y} \cdot t_1 + t\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{y} \cdot x + t\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (- z t))))
   (if (<= y -1e+14)
     (+ (if (!= x 0.0) (/ (- z t) (/ y x)) (/ t_1 y)) t)
     (if (<= y 6.5e+56) (+ (* (/ 1.0 y) t_1) t) (+ (* (/ (- z t) y) x) t)))))

C

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

↓

double code(double x, double y, double z, double t) {
	double t_1 = x * (z - t);
	double tmp_1;
	if (y <= -1e+14) {
		double tmp_2;
		if (x != 0.0) {
			tmp_2 = (z - t) / (y / x);
		} else {
			tmp_2 = t_1 / y;
		}
		tmp_1 = tmp_2 + t;
	} else if (y <= 6.5e+56) {
		tmp_1 = ((1.0 / y) * t_1) + t;
	} else {
		tmp_1 = (((z - t) / y) * x) + t;
	}
	return tmp_1;
}

Fortran

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

↓

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    real(8) :: tmp_1
    real(8) :: tmp_2
    t_1 = x * (z - t)
    if (y <= (-1d+14)) then
        if (x /= 0.0d0) then
            tmp_2 = (z - t) / (y / x)
        else
            tmp_2 = t_1 / y
        end if
        tmp_1 = tmp_2 + t
    else if (y <= 6.5d+56) then
        tmp_1 = ((1.0d0 / y) * t_1) + t
    else
        tmp_1 = (((z - t) / y) * x) + t
    end if
    code = tmp_1
end function

Java

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

↓

public static double code(double x, double y, double z, double t) {
	double t_1 = x * (z - t);
	double tmp_1;
	if (y <= -1e+14) {
		double tmp_2;
		if (x != 0.0) {
			tmp_2 = (z - t) / (y / x);
		} else {
			tmp_2 = t_1 / y;
		}
		tmp_1 = tmp_2 + t;
	} else if (y <= 6.5e+56) {
		tmp_1 = ((1.0 / y) * t_1) + t;
	} else {
		tmp_1 = (((z - t) / y) * x) + t;
	}
	return tmp_1;
}

Python

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

↓

def code(x, y, z, t):
	t_1 = x * (z - t)
	tmp_1 = 0
	if y <= -1e+14:
		tmp_2 = 0
		if x != 0.0:
			tmp_2 = (z - t) / (y / x)
		else:
			tmp_2 = t_1 / y
		tmp_1 = tmp_2 + t
	elif y <= 6.5e+56:
		tmp_1 = ((1.0 / y) * t_1) + t
	else:
		tmp_1 = (((z - t) / y) * x) + t
	return tmp_1

Julia

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

↓

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z - t))
	tmp_1 = 0.0
	if (y <= -1e+14)
		tmp_2 = 0.0
		if (x != 0.0)
			tmp_2 = Float64(Float64(z - t) / Float64(y / x));
		else
			tmp_2 = Float64(t_1 / y);
		end
		tmp_1 = Float64(tmp_2 + t);
	elseif (y <= 6.5e+56)
		tmp_1 = Float64(Float64(Float64(1.0 / y) * t_1) + t);
	else
		tmp_1 = Float64(Float64(Float64(Float64(z - t) / y) * x) + t);
	end
	return tmp_1
end

MATLAB

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

↓

function tmp_4 = code(x, y, z, t)
	t_1 = x * (z - t);
	tmp_2 = 0.0;
	if (y <= -1e+14)
		tmp_3 = 0.0;
		if (x ~= 0.0)
			tmp_3 = (z - t) / (y / x);
		else
			tmp_3 = t_1 / y;
		end
		tmp_2 = tmp_3 + t;
	elseif (y <= 6.5e+56)
		tmp_2 = ((1.0 / y) * t_1) + t;
	else
		tmp_2 = (((z - t) / y) * x) + t;
	end
	tmp_4 = tmp_2;
end

Wolfram

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

↓

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+14], N[(If[Unequal[x, 0.0], N[(N[(z - t), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / y), $MachinePrecision]] + t), $MachinePrecision], If[LessEqual[y, 6.5e+56], N[(N[(N[(1.0 / y), $MachinePrecision] * t$95$1), $MachinePrecision] + t), $MachinePrecision], N[(N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision] + t), $MachinePrecision]]]]

Target

Original	1.9
Target	2.1
Herbie	1.6

\[\begin{array}{l} \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if y < -1e14

   1. Initial program 1.0

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

   2. Applied egg-rr 1.1

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

   if -1e14 < y < 6.5000000000000001e56

   1. Initial program 2.9

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

   2. Applied egg-rr 2.2

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

   if 6.5000000000000001e56 < y

   1. Initial program 1.3

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

   2. Applied egg-rr 1.2

      \[\leadsto \color{blue}{\frac{z - t}{y} \cdot x} + t \]
3. Recombined 3 regimes into one program.

Alternatives

Alternative 1
Error	4.7
Cost	2008

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ t_2 := \frac{x}{y} \cdot z + t\\ t_3 := \frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -100:\\ \;\;\;\;t_3\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-200}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-129}:\\ \;\;\;\;\frac{z \cdot x}{y} + t\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Error	20.7
Cost	1240

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ t_2 := \frac{x}{y} \cdot z\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+176}:\\ \;\;\;\;t\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{+65}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 640000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.68 \cdot 10^{+100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+232}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{y} \cdot x\\ \end{array} \]

Alternative 3
Error	1.5
Cost	1096

\[\begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-129}:\\ \;\;\;\;\frac{z \cdot x}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	1.6
Cost	968

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+55}:\\ \;\;\;\;\frac{1}{y} \cdot \left(x \cdot \left(z - t\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{y} \cdot x + t\\ \end{array} \]

Alternative 5
Error	22.0
Cost	904

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-13}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-\frac{x}{y}\right)\\ \end{array} \]

Alternative 6
Error	21.6
Cost	840

\[\begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-22}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	8.0
Cost	712

\[\begin{array}{l} t_1 := \frac{x}{y} \cdot z + t\\ \mathbf{if}\;z \leq -1.46 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-109}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	31.1
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023010 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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