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

Average Error: 2.1 → 2.1

Time: 11.7s

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	2.1
Target	2.1
Herbie	2.1

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

Derivation

1. Initial program 2.1

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

2. Simplified 10.7

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

   [Start] 2.1	\[ \frac{x - y}{z - y} \cdot t \]
   associate-*l/ [=>] 11.9	\[ \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]
   associate-*r/ [<=] 10.7	\[ \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

3. Applied egg-rr 2.1

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

4. Final simplification 2.1

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

Alternatives

Alternative 1
Error	15.9
Cost	1109

\[\begin{array}{l} t_1 := \frac{t}{\frac{y - z}{y}}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-169}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-66}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+135} \lor \neg \left(y \leq 1.8 \cdot 10^{+203}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \]

Alternative 2
Error	17.9
Cost	1108

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ t_2 := \left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-166}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-33}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+27}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	22.1
Cost	977

\[\begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+32}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-66} \lor \neg \left(y \leq 3 \cdot 10^{-33}\right) \land y \leq 1.4 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4
Error	16.2
Cost	977

\[\begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+33}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-66}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+135} \lor \neg \left(y \leq 1.52 \cdot 10^{+203}\right):\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5
Error	7.0
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+181}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+203}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{y - z}{y}}\\ \end{array} \]

Alternative 6
Error	17.7
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -9.4 \cdot 10^{+30} \lor \neg \left(y \leq 2.5 \cdot 10^{-66}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 7
Error	16.6
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+31} \lor \neg \left(y \leq 7.2 \cdot 10^{+27}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \end{array} \]

Alternative 8
Error	16.6
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \]

Alternative 9
Error	16.6
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \]

Alternative 10
Error	16.6
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{t}{\frac{y}{y - x}}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+27}:\\ \;\;\;\;\frac{t}{\frac{z}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \]

Alternative 11
Error	37.4
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-20}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-113}:\\ \;\;\;\;y \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12
Error	25.7
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+33}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 13
Error	24.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+30}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+27}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 14
Error	24.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+30}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+26}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15
Error	2.1
Cost	576

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

Alternative 16
Error	39.6
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023010 
(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))