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

Average Accuracy: 96.8% → 96.9%

Time: 8.0s

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	96.8%
Target	96.4%
Herbie	96.9%

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

Derivation

1. Initial program 96.8%

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

2. Applied egg-rr 96.9%

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

3. Final simplification 96.9%

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

Alternatives

Alternative 1
Accuracy	65.8%
Cost	1424

\[\begin{array}{l} t_1 := \frac{-t}{\frac{y}{x}}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+214}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-34}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-7}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	65.6%
Cost	1424

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+214}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+142}:\\ \;\;\;\;\frac{t \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-34}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-7}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{y}{x}}\\ \end{array} \]

Alternative 3
Accuracy	65.7%
Cost	1424

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+214}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+142}:\\ \;\;\;\;\frac{-x}{\frac{y}{t}}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-34}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-7}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{-t}{\frac{y}{x}}\\ \end{array} \]

Alternative 4
Accuracy	94.1%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -50000:\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-16}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array} \]

Alternative 5
Accuracy	80.8%
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-34} \lor \neg \left(\frac{x}{y} \leq 10000000000000\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 6
Accuracy	91.8%
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-34} \lor \neg \left(\frac{x}{y} \leq 10^{-7}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]

Alternative 7
Accuracy	95.2%
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -50000 \lor \neg \left(\frac{x}{y} \leq 10^{-7}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 8
Accuracy	66.7%
Cost	841

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-34} \lor \neg \left(\frac{x}{y} \leq 10^{-7}\right):\\ \;\;\;\;z \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9
Accuracy	66.8%
Cost	841

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-34} \lor \neg \left(\frac{x}{y} \leq 10^{-7}\right):\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10
Accuracy	73.2%
Cost	713

\[\begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{-138} \lor \neg \left(t \leq 9 \cdot 10^{-116}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 11
Accuracy	96.8%
Cost	576

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

Alternative 12
Accuracy	51.5%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023141 
(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))