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

Average Accuracy: 96.4% → 96.5%

Time: 9.8s

Precision: binary64

Cost: 704

Math

\[\frac{x}{y} \cdot \left(z - t\right) + t \]

↓

\[t + \frac{1}{\frac{\frac{y}{x}}{z - t}} \]

FPCore

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

↓

(FPCore (x y z t) :precision binary64 (+ t (/ 1.0 (/ (/ y x) (- z t)))))

C

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

↓

double code(double x, double y, double z, double t) {
	return t + (1.0 / ((y / x) / (z - t)));
}

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 - t)) + 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 + (1.0d0 / ((y / x) / (z - t)))
end function

Java

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

↓

public static double code(double x, double y, double z, double t) {
	return t + (1.0 / ((y / x) / (z - t)));
}

Python

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

↓

def code(x, y, z, t):
	return t + (1.0 / ((y / x) / (z - t)))

Julia

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

↓

function code(x, y, z, t)
	return Float64(t + Float64(1.0 / Float64(Float64(y / x) / Float64(z - t))))
end

MATLAB

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

↓

function tmp = code(x, y, z, t)
	tmp = t + (1.0 / ((y / x) / (z - t)));
end

Wolfram

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

↓

code[x_, y_, z_, t_] := N[(t + N[(1.0 / N[(N[(y / x), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	96.4%
Target	95.8%
Herbie	96.5%

\[\begin{array}{l} \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array} \]

Derivation

1. Initial program 96.4%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]

2. Applied egg-rr 96.5%

   \[\leadsto \color{blue}{\frac{1}{\frac{\frac{y}{x}}{z - t}}} + t \]
   Proof

   [Start] 96.4	\[ \frac{x}{y} \cdot \left(z - t\right) + t \]
   associate-*l/ [=>] 90.1	\[ \color{blue}{\frac{x \cdot \left(z - t\right)}{y}} + t \]
   clear-num [=>] 90.0	\[ \color{blue}{\frac{1}{\frac{y}{x \cdot \left(z - t\right)}}} + t \]
   associate-/r* [=>] 96.5	\[ \frac{1}{\color{blue}{\frac{\frac{y}{x}}{z - t}}} + t \]

3. Final simplification 96.5%

   \[\leadsto t + \frac{1}{\frac{\frac{y}{x}}{z - t}} \]

Alternatives

Alternative 1
Accuracy	63.9%
Cost	1360

\[\begin{array}{l} t_1 := z \cdot \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+21}:\\ \;\;\;\;-\frac{t}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq -0.0005:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-87}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 2
Accuracy	63.4%
Cost	1360

\[\begin{array}{l} t_1 := z \cdot \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+21}:\\ \;\;\;\;\frac{x \cdot t}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq -0.0005:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-87}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 3
Accuracy	79.0%
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.0005 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-87}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4
Accuracy	94.7%
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -20 \lor \neg \left(\frac{x}{y} \leq 0.001\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 5
Accuracy	94.8%
Cost	968

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -20:\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.001:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{\frac{y}{x}}\\ \end{array} \]

Alternative 6
Accuracy	63.4%
Cost	841

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.0005 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-87}\right):\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7
Accuracy	63.5%
Cost	840

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.0005:\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-87}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 8
Accuracy	96.4%
Cost	576

\[t + \left(z - t\right) \cdot \frac{x}{y} \]

Alternative 9
Accuracy	49.9%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023133 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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