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

Average Error: 2.1 → 1.2

Time: 17.2s

Precision: binary64

Cost: 1736

Math

\[\frac{x - y}{z - y} \cdot t \]

↓

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t_1 \cdot t\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{-296}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 10^{-244}:\\ \;\;\;\;\frac{1}{\frac{z - y}{\left(x - y\right) \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* t_1 t)))
   (if (<= t_1 -4e-296)
     t_2
     (if (<= t_1 1e-244) (/ 1.0 (/ (- z y) (* (- x y) t))) t_2))))

C

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

↓

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t_1 * t;
	double tmp;
	if (t_1 <= -4e-296) {
		tmp = t_2;
	} else if (t_1 <= 1e-244) {
		tmp = 1.0 / ((z - y) / ((x - y) * t));
	} else {
		tmp = t_2;
	}
	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 - y)) * 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) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = t_1 * t
    if (t_1 <= (-4d-296)) then
        tmp = t_2
    else if (t_1 <= 1d-244) then
        tmp = 1.0d0 / ((z - y) / ((x - y) * t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = t_1 * t;
	double tmp;
	if (t_1 <= -4e-296) {
		tmp = t_2;
	} else if (t_1 <= 1e-244) {
		tmp = 1.0 / ((z - y) / ((x - y) * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = t_1 * t
	tmp = 0
	if t_1 <= -4e-296:
		tmp = t_2
	elif t_1 <= 1e-244:
		tmp = 1.0 / ((z - y) / ((x - y) * t))
	else:
		tmp = t_2
	return tmp

Julia

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

↓

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(t_1 * t)
	tmp = 0.0
	if (t_1 <= -4e-296)
		tmp = t_2;
	elseif (t_1 <= 1e-244)
		tmp = Float64(1.0 / Float64(Float64(z - y) / Float64(Float64(x - y) * t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = t_1 * t;
	tmp = 0.0;
	if (t_1 <= -4e-296)
		tmp = t_2;
	elseif (t_1 <= 1e-244)
		tmp = 1.0 / ((z - y) / ((x - y) * t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-296], t$95$2, If[LessEqual[t$95$1, 1e-244], N[(1.0 / N[(N[(z - y), $MachinePrecision] / N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Target

Original	2.1
Target	2.1
Herbie	1.2

\[\frac{t}{\frac{z - y}{x - y}} \]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -4e-296 or 9.9999999999999993e-245 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 1.2

      \[\frac{x - y}{z - y} \cdot t \]

   if -4e-296 < (/.f64 (-.f64 x y) (-.f64 z y)) < 9.9999999999999993e-245

   1. Initial program 16.6

      \[\frac{x - y}{z - y} \cdot t \]

   2. Simplified 0.2

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
      Proof
      (*.f64 (-.f64 x y) (/.f64 t (-.f64 z y))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (-.f64 x y) t) (-.f64 z y))): 72 points increase in error, 69 points decrease in error
      (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)): 30 points increase in error, 80 points decrease in error

   3. Applied egg-rr 1.0

      \[\leadsto \color{blue}{\frac{1}{\frac{z - y}{\left(x - y\right) \cdot t}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 1.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -4 \cdot 10^{-296}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 10^{-244}:\\ \;\;\;\;\frac{1}{\frac{z - y}{\left(x - y\right) \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \end{array} \]

Alternatives

Alternative 1
Error	1.1
Cost	1608

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := t_1 \cdot t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-303}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 10^{-244}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	8.6
Cost	1104

\[\begin{array}{l} t_1 := \frac{x - y}{\frac{z - y}{t}}\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;y \leq -5.30827302909328 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.0761288601261743 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.14782423233367 \cdot 10^{-239}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 1.6263320507004392 \cdot 10^{+236}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	18.7
Cost	976

\[\begin{array}{l} t_1 := t - x \cdot \frac{t}{y}\\ \mathbf{if}\;y \leq -6.76175028788724 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.6447982018471912 \cdot 10^{-35}:\\ \;\;\;\;\frac{x - y}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq -5.499696867305942 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.733382224330407 \cdot 10^{-39}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	20.2
Cost	844

\[\begin{array}{l} t_1 := t - x \cdot \frac{t}{y}\\ \mathbf{if}\;y \leq -2.0582184291817826 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.0761288601261743 \cdot 10^{-146}:\\ \;\;\;\;\frac{x}{\frac{z - y}{t}}\\ \mathbf{elif}\;y \leq 9.733382224330407 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	16.1
Cost	844

\[\begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -1.267658374803502 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.0761288601261743 \cdot 10^{-146}:\\ \;\;\;\;\frac{x}{\frac{z - y}{t}}\\ \mathbf{elif}\;y \leq 9.733382224330407 \cdot 10^{-39}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	16.2
Cost	844

\[\begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -1.267658374803502 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.7464807791840774 \cdot 10^{-235}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 9.733382224330407 \cdot 10^{-39}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	16.1
Cost	844

\[\begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -1.267658374803502 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.0761288601261743 \cdot 10^{-146}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 9.733382224330407 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	24.2
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -2.0582184291817826 \cdot 10^{+23}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.0761288601261743 \cdot 10^{-146}:\\ \;\;\;\;\frac{x}{\frac{z - y}{t}}\\ \mathbf{elif}\;y \leq 9.733382224330407 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9
Error	18.8
Cost	712

\[\begin{array}{l} t_1 := t - x \cdot \frac{t}{y}\\ \mathbf{if}\;y \leq -5.499696867305942 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.733382224330407 \cdot 10^{-39}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	38.0
Cost	584

\[\begin{array}{l} t_1 := y \cdot \frac{t}{z}\\ \mathbf{if}\;z \leq -2.70021146591632 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.856326558195935 \cdot 10^{+137}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	25.7
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -9.386291941378559 \cdot 10^{-54}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.733382224330407 \cdot 10^{-39}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12
Error	25.7
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -9.386291941378559 \cdot 10^{-54}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 9.733382224330407 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13
Error	2.1
Cost	576

\[\frac{t}{\frac{z - y}{x - y}} \]

Alternative 14
Error	39.8
Cost	64

\[t \]

Reproduce

herbie shell --seed 2022316 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

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