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

Average Accuracy: 96.4% → 96.4%

Time: 11.4s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z t) :precision binary64 (/ 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) {
	return t / ((z - y) / (x - y));
}

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
    code = t / ((z - y) / (x - y))
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) {
	return t / ((z - y) / (x - y));
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

function tmp = code(x, y, z, t)
	tmp = t / ((z - y) / (x - y));
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_] := N[(t / N[(N[(z - y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	96.4%
Target	96.4%
Herbie	96.4%

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

Derivation

1. Initial program 96.4%

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

2. Simplified 84.0%

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

   [Start] 96.4	\[ \frac{x - y}{z - y} \cdot t \]
   associate-*l/ [=>] 81.5	\[ \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]
   associate-*r/ [<=] 84.0	\[ \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

3. Applied egg-rr 96.4%

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

   [Start] 84.0	\[ \left(x - y\right) \cdot \frac{t}{z - y} \]
   associate-*r/ [=>] 81.5	\[ \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]
   *-commutative [=>] 81.5	\[ \frac{\color{blue}{t \cdot \left(x - y\right)}}{z - y} \]
   associate-/l* [=>] 96.4	\[ \color{blue}{\frac{t}{\frac{z - y}{x - y}}} \]

4. Final simplification 96.4%

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

Alternatives

Alternative 1
Accuracy	66.2%
Cost	1108

\[\begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+174}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-94}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+26}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 2
Accuracy	72.7%
Cost	976

\[\begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{t}{z}\\ t_2 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -1 \cdot 10^{-113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+24}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	89.3%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+154} \lor \neg \left(y \leq 5.6 \cdot 10^{+92}\right):\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 4
Accuracy	63.7%
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+171}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-105}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+40}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5
Accuracy	74.8%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-94} \lor \neg \left(y \leq 2.45 \cdot 10^{+41}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \end{array} \]

Alternative 6
Accuracy	74.9%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-114} \lor \neg \left(y \leq 1.1 \cdot 10^{+41}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \]

Alternative 7
Accuracy	40.6%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+92} \lor \neg \left(z \leq 1.7 \cdot 10^{+236}\right):\\ \;\;\;\;y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8
Accuracy	59.9%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9
Accuracy	61.0%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -2.08 \cdot 10^{-94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10
Accuracy	61.0%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -2.08 \cdot 10^{-94}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+41}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11
Accuracy	96.4%
Cost	576

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

Alternative 12
Accuracy	38.9%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023135 
(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))