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

Average Error: 2.1 → 2.1

Time: 8.0s

Precision: binary64

Cost: 841

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-160} \lor \neg \left(t \leq 3.5 \cdot 10^{-203}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z - t}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.35e-160) (not (<= t 3.5e-203)))
   (+ t (* (/ x y) (- z t)))
   (+ t (/ x (/ y (- z 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 tmp;
	if ((t <= -1.35e-160) || !(t <= 3.5e-203)) {
		tmp = t + ((x / y) * (z - t));
	} else {
		tmp = t + (x / (y / (z - t)));
	}
	return tmp;
}

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) :: tmp
    if ((t <= (-1.35d-160)) .or. (.not. (t <= 3.5d-203))) then
        tmp = t + ((x / y) * (z - t))
    else
        tmp = t + (x / (y / (z - t)))
    end if
    code = tmp
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 tmp;
	if ((t <= -1.35e-160) || !(t <= 3.5e-203)) {
		tmp = t + ((x / y) * (z - t));
	} else {
		tmp = t + (x / (y / (z - t)));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.35e-160) or not (t <= 3.5e-203):
		tmp = t + ((x / y) * (z - t))
	else:
		tmp = t + (x / (y / (z - t)))
	return tmp

Julia

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

↓

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.35e-160) || !(t <= 3.5e-203))
		tmp = Float64(t + Float64(Float64(x / y) * Float64(z - t)));
	else
		tmp = Float64(t + Float64(x / Float64(y / Float64(z - t))));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.35e-160) || ~((t <= 3.5e-203)))
		tmp = t + ((x / y) * (z - t));
	else
		tmp = t + (x / (y / (z - t)));
	end
	tmp_2 = tmp;
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_] := If[Or[LessEqual[t, -1.35e-160], N[Not[LessEqual[t, 3.5e-203]], $MachinePrecision]], N[(t + N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x / N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	2.1
Target	2.5
Herbie	2.1

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

Derivation

1. Split input into 2 regimes

2. if t < -1.35000000000000005e-160 or 3.5000000000000001e-203 < t

   1. Initial program 1.2

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

   if -1.35000000000000005e-160 < t < 3.5000000000000001e-203

   1. Initial program 5.3

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

   2. Applied egg-rr 5.3

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{z - t}}} + t \]
3. Recombined 2 regimes into one program.

4. Final simplification 2.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-160} \lor \neg \left(t \leq 3.5 \cdot 10^{-203}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z - t}}\\ \end{array} \]

Alternatives

Alternative 1
Error	22.1
Cost	1945

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-21}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10000000000:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+51} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+134}\right) \land \frac{x}{y} \leq 10^{+184}:\\ \;\;\;\;\frac{-t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \end{array} \]

Alternative 2
Error	22.2
Cost	1945

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{-21}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10000000000:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+51}:\\ \;\;\;\;\frac{-t}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+134} \lor \neg \left(\frac{x}{y} \leq 10^{+184}\right):\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \end{array} \]

Alternative 3
Error	14.3
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-32} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-21}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4
Error	6.6
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+19} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-21}\right):\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \end{array} \]

Alternative 5
Error	6.6
Cost	968

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-14}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \]

Alternative 6
Error	21.9
Cost	841

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-25} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7
Error	2.1
Cost	576

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

Alternative 8
Error	31.9
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023039 
(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))