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

Average Error: 2.4 → 2.4

Time: 19.1s

Precision: binary64

Cost: 968

Math

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

↓

\[\begin{array}{l} t_1 := \frac{t}{\frac{z - y}{x - y}}\\ \mathbf{if}\;y \leq -1 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.753294143698218 \cdot 10^{-32}:\\ \;\;\;\;\frac{1}{\frac{z - y}{t \cdot \left(x - y\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (/ (- z y) (- x y)))))
   (if (<= y -1e-150)
     t_1
     (if (<= y 6.753294143698218e-32) (/ 1.0 (/ (- z y) (* t (- x y)))) t_1))))

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 = t / ((z - y) / (x - y));
	double tmp;
	if (y <= -1e-150) {
		tmp = t_1;
	} else if (y <= 6.753294143698218e-32) {
		tmp = 1.0 / ((z - y) / (t * (x - y)));
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_1 = t / ((z - y) / (x - y))
    if (y <= (-1d-150)) then
        tmp = t_1
    else if (y <= 6.753294143698218d-32) then
        tmp = 1.0d0 / ((z - y) / (t * (x - y)))
    else
        tmp = t_1
    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 = t / ((z - y) / (x - y));
	double tmp;
	if (y <= -1e-150) {
		tmp = t_1;
	} else if (y <= 6.753294143698218e-32) {
		tmp = 1.0 / ((z - y) / (t * (x - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	t_1 = t / ((z - y) / (x - y))
	tmp = 0
	if y <= -1e-150:
		tmp = t_1
	elif y <= 6.753294143698218e-32:
		tmp = 1.0 / ((z - y) / (t * (x - y)))
	else:
		tmp = t_1
	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(t / Float64(Float64(z - y) / Float64(x - y)))
	tmp = 0.0
	if (y <= -1e-150)
		tmp = t_1;
	elseif (y <= 6.753294143698218e-32)
		tmp = Float64(1.0 / Float64(Float64(z - y) / Float64(t * Float64(x - y))));
	else
		tmp = t_1;
	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 = t / ((z - y) / (x - y));
	tmp = 0.0;
	if (y <= -1e-150)
		tmp = t_1;
	elseif (y <= 6.753294143698218e-32)
		tmp = 1.0 / ((z - y) / (t * (x - y)));
	else
		tmp = t_1;
	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[(t / N[(N[(z - y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e-150], t$95$1, If[LessEqual[y, 6.753294143698218e-32], N[(1.0 / N[(N[(z - y), $MachinePrecision] / N[(t * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Target

Original	2.4
Target	2.4
Herbie	2.4

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

Derivation

1. Split input into 2 regimes

2. if y < -1.00000000000000001e-150 or 6.7532941436982183e-32 < y

   1. Initial program 0.7

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

   2. Applied egg-rr 0.7

      \[\leadsto \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]

   if -1.00000000000000001e-150 < y < 6.7532941436982183e-32

   1. Initial program 5.8

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

   2. Simplified 5.6

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
      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))): 74 points increase in error, 64 points decrease in error
      (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)): 37 points increase in error, 82 points decrease in error

   3. Applied egg-rr 5.9

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

4. Final simplification 2.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-150}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x - y}}\\ \mathbf{elif}\;y \leq 6.753294143698218 \cdot 10^{-32}:\\ \;\;\;\;\frac{1}{\frac{z - y}{t \cdot \left(x - y\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x - y}}\\ \end{array} \]

Alternatives

Alternative 1
Error	16.9
Cost	1768

\[\begin{array}{l} t_1 := t - x \cdot \frac{t}{y}\\ t_2 := \frac{t}{1 - \frac{z}{y}}\\ t_3 := \frac{t}{\frac{z - y}{x}}\\ \mathbf{if}\;y \leq -2.1963329388440706 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.5940052964382227 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.873308293336638 \cdot 10^{-53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-155}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-302}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-84}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.4629017003547966 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.181075230969806 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 3.3738186294770597 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.276293077517256 \cdot 10^{+40}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	17.0
Cost	1636

\[\begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ t_2 := \frac{t}{\frac{z - y}{x}}\\ \mathbf{if}\;y \leq -1.5940052964382227 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -7.873308293336638 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-302}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.4629017003547966 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.181075230969806 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 3.3738186294770597 \cdot 10^{-15}:\\ \;\;\;\;t - x \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 1.276293077517256 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	16.7
Cost	1436

\[\begin{array}{l} t_1 := t \cdot \frac{-y}{z - y}\\ t_2 := \frac{t}{\frac{z - y}{x}}\\ \mathbf{if}\;y \leq -1.5940052964382227 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -7.873308293336638 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-302}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.972274425262684 \cdot 10^{-60}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.276293077517256 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	16.7
Cost	1372

\[\begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ t_2 := \frac{t}{\frac{z - y}{x}}\\ \mathbf{if}\;y \leq -1.5940052964382227 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -7.873308293336638 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-210}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-84}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{elif}\;y \leq 1.4629017003547966 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.276293077517256 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	16.7
Cost	1372

\[\begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ t_2 := \frac{t}{\frac{z - y}{x}}\\ \mathbf{if}\;y \leq -1.5940052964382227 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -7.873308293336638 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-302}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.972274425262684 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.276293077517256 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	16.7
Cost	1372

\[\begin{array}{l} t_1 := \frac{t}{\frac{z - y}{x}}\\ t_2 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -1.5940052964382227 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -7.873308293336638 \cdot 10^{-53}:\\ \;\;\;\;\frac{-y}{\frac{z - y}{t}}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-302}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.972274425262684 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.276293077517256 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	16.6
Cost	1240

\[\begin{array}{l} t_1 := t - x \cdot \frac{t}{y}\\ t_2 := \frac{t}{1 - \frac{z}{y}}\\ t_3 := \frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{if}\;y \leq -2.1963329388440706 \cdot 10^{+90}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.5940052964382227 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.873308293336638 \cdot 10^{-53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.181075230969806 \cdot 10^{-52}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 6.996530386193786 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5223141848086050:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	1.9
Cost	1092

\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{+166}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x - y}}\\ \end{array} \]

Alternative 9
Error	21.8
Cost	976

\[\begin{array}{l} t_1 := \frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{if}\;y \leq -1.4534783080565825 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 5223141848086050:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10
Error	16.4
Cost	712

\[\begin{array}{l} t_1 := \frac{t}{1 - \frac{z}{y}}\\ \mathbf{if}\;y \leq -7.873308293336638 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5223141848086050:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	25.7
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -2.052961418912939 \cdot 10^{-15}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5223141848086050:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12
Error	25.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.4534783080565825 \cdot 10^{+38}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.674238217793942 \cdot 10^{+38}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13
Error	40.1
Cost	64

\[t \]

Reproduce

herbie shell --seed 2022294 
(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))