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

Average Error: 3.16% → 2.46%

Time: 9.0s

Precision: binary64

Cost: 836

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+120}:\\ \;\;\;\;x \cdot \left(\frac{z}{y} - \frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+120) (* x (- (/ z y) (/ t y))) (+ t (* (/ x y) (- 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) {
	double tmp;
	if ((x / y) <= -5e+120) {
		tmp = x * ((z / y) - (t / y));
	} else {
		tmp = t + ((x / y) * (z - t));
	}
	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 - 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
    real(8) :: tmp
    if ((x / y) <= (-5d+120)) then
        tmp = x * ((z / y) - (t / y))
    else
        tmp = t + ((x / y) * (z - t))
    end if
    code = tmp
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) {
	double tmp;
	if ((x / y) <= -5e+120) {
		tmp = x * ((z / y) - (t / y));
	} else {
		tmp = t + ((x / y) * (z - t));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+120:
		tmp = x * ((z / y) - (t / y))
	else:
		tmp = t + ((x / y) * (z - t))
	return tmp

Julia

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

↓

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+120)
		tmp = Float64(x * Float64(Float64(z / y) - Float64(t / y)));
	else
		tmp = Float64(t + Float64(Float64(x / y) * Float64(z - t)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e+120)
		tmp = x * ((z / y) - (t / y));
	else
		tmp = t + ((x / y) * (z - t));
	end
	tmp_2 = tmp;
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_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+120], N[(x * N[(N[(z / y), $MachinePrecision] - N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	3.16%
Target	3.53%
Herbie	2.46%

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.00000000000000019e120

   1. Initial program 16.75

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

   2. Taylor expanded in x around inf 6.83

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

   if -5.00000000000000019e120 < (/.f64 x y)

   1. Initial program 2.12

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
3. Recombined 2 regimes into one program.

4. Final simplification 2.46

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+120}:\\ \;\;\;\;x \cdot \left(\frac{z}{y} - \frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	48.1%
Cost	1113

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+58}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-180}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 3.45 \cdot 10^{-249}:\\ \;\;\;\;-\frac{t}{\frac{y}{x}}\\ \mathbf{elif}\;y \leq 245000000000 \lor \neg \left(y \leq 3.2 \cdot 10^{+91}\right) \land y \leq 1.12 \cdot 10^{+136}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 2
Error	34.37%
Cost	1101

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \left(-\frac{t}{y}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-70} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3
Error	7.23%
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1000 \lor \neg \left(\frac{x}{y} \leq 2\right):\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 4
Error	7.28%
Cost	968

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1000:\\ \;\;\;\;x \cdot \left(\frac{z}{y} - \frac{t}{y}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \]

Alternative 5
Error	41.07%
Cost	849

\[\begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-75}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-153} \lor \neg \left(t \leq 1.75 \cdot 10^{-114}\right) \land t \leq 1.8 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6
Error	40.95%
Cost	848

\[\begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{-78}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-113}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7
Error	40.03%
Cost	848

\[\begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-75}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-136}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-113}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8
Error	41.05%
Cost	848

\[\begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-75}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-143}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-115}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9
Error	13.18%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{-33} \lor \neg \left(z \leq 4.3 \cdot 10^{-107}\right):\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \end{array} \]

Alternative 10
Error	13.05%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{-33} \lor \neg \left(z \leq 4.4 \cdot 10^{-106}\right):\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]

Alternative 11
Error	18.63%
Cost	708

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \left(-\frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 12
Error	49.34%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023090 
(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))