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

Percentage Accurate: 96.9% → 97.3%

Time: 12.5s

Precision: binary64

Cost: 1092

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{+191}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x - y}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ (- x y) (- z y)) -1e+191)
   (* x (/ t (- z y)))
   (/ t (/ (- z y) (- x y)))))

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 tmp;
	if (((x - y) / (z - y)) <= -1e+191) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t / ((z - y) / (x - y));
	}
	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) :: tmp
    if (((x - y) / (z - y)) <= (-1d+191)) then
        tmp = x * (t / (z - y))
    else
        tmp = t / ((z - y) / (x - y))
    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 tmp;
	if (((x - y) / (z - y)) <= -1e+191) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t / ((z - y) / (x - y));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	tmp = 0
	if ((x - y) / (z - y)) <= -1e+191:
		tmp = x * (t / (z - y))
	else:
		tmp = t / ((z - y) / (x - y))
	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)
	tmp = 0.0
	if (Float64(Float64(x - y) / Float64(z - y)) <= -1e+191)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t / Float64(Float64(z - y) / Float64(x - y)));
	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)
	tmp = 0.0;
	if (((x - y) / (z - y)) <= -1e+191)
		tmp = x * (t / (z - y));
	else
		tmp = t / ((z - y) / (x - y));
	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_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], -1e+191], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(N[(z - y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	96.9%
Target	96.8%
Herbie	97.3%

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -1.00000000000000007e191

   1. Initial program 66.5%

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

   2. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
      Step-by-step derivation

      [Start] 66.5%	\[ \frac{x - y}{z - y} \cdot t \]
      associate-*l/ [=>] 94.4%	\[ \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]
      associate-*r/ [<=] 99.9%	\[ \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Taylor expanded in x around inf 94.4%

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

   4. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{t}{z - y}} \]
      Step-by-step derivation

      [Start] 94.4%	\[ \frac{t \cdot x}{z - y} \]
      associate-*l/ [<=] 99.9%	\[ \color{blue}{\frac{t}{z - y} \cdot x} \]
      *-commutative [=>] 99.9%	\[ \color{blue}{x \cdot \frac{t}{z - y}} \]

   if -1.00000000000000007e191 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 99.0%

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

   2. Simplified 86.4%

      \[\leadsto \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]
      Step-by-step derivation

      [Start] 99.0%	\[ \frac{x - y}{z - y} \cdot t \]
      associate-*l/ [=>] 84.6%	\[ \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]
      associate-*r/ [<=] 86.4%	\[ \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]
      Step-by-step derivation

      [Start] 86.4%	\[ \left(x - y\right) \cdot \frac{t}{z - y} \]
      associate-*r/ [=>] 84.6%	\[ \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]
      associate-*l/ [<=] 99.0%	\[ \color{blue}{\frac{x - y}{z - y} \cdot t} \]
      *-commutative [=>] 99.0%	\[ \color{blue}{t \cdot \frac{x - y}{z - y}} \]
      clear-num [=>] 98.9%	\[ t \cdot \color{blue}{\frac{1}{\frac{z - y}{x - y}}} \]
      un-div-inv [=>] 99.1%	\[ \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{+191}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x - y}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	97.3%
Cost	1092

\[\begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -1 \cdot 10^{+191}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x - y}}\\ \end{array} \]

Alternative 2
Accuracy	70.0%
Cost	1173

\[\begin{array}{l} t_1 := t - \frac{x \cdot t}{y}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-172}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+30}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{+91} \lor \neg \left(y \leq 8.6 \cdot 10^{+238}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{z - y}{t}}\\ \end{array} \]

Alternative 3
Accuracy	97.4%
Cost	1092

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+158}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot t\\ \end{array} \]

Alternative 4
Accuracy	73.1%
Cost	1040

\[\begin{array}{l} t_1 := t - \frac{x \cdot t}{y}\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-172}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{z - y}\\ \end{array} \]

Alternative 5
Accuracy	74.9%
Cost	1040

\[\begin{array}{l} t_1 := t \cdot \frac{y - x}{y}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-172}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{z - y}\\ \end{array} \]

Alternative 6
Accuracy	68.0%
Cost	976

\[\begin{array}{l} t_1 := x \cdot \frac{t}{z - y}\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-288}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7
Accuracy	69.0%
Cost	976

\[\begin{array}{l} t_1 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;y \leq -2 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+33}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8
Accuracy	87.3%
Cost	972

\[\begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-287}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{z - y}\\ \end{array} \]

Alternative 9
Accuracy	61.1%
Cost	848

\[\begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-7}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10
Accuracy	60.9%
Cost	848

\[\begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+30}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11
Accuracy	71.9%
Cost	844

\[\begin{array}{l} t_1 := t - \frac{x \cdot t}{y}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.55 \cdot 10^{-115}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+26}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Accuracy	71.8%
Cost	844

\[\begin{array}{l} t_1 := t - \frac{x \cdot t}{y}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-113}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.82 \cdot 10^{+28}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Accuracy	71.4%
Cost	844

\[\begin{array}{l} t_1 := t - \frac{x \cdot t}{y}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-172}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Accuracy	69.5%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+96}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+120}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15
Accuracy	60.7%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-38}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16
Accuracy	61.4%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-37}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 17
Accuracy	61.3%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-36}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+30}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 18
Accuracy	35.9%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023165 
(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))