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

Percentage Accurate: 97.7% → 98.4%

Time: 12.6s

Precision: binary64

Cost: 1220

• 24.9% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

\[\begin{array}{l} t_1 := t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* (/ x y) (- z t)))))
   (if (<= t_1 5e+306) t_1 (/ (* x (- z t)) y))))

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 t_1 = t + ((x / y) * (z - t));
	double tmp;
	if (t_1 <= 5e+306) {
		tmp = t_1;
	} else {
		tmp = (x * (z - t)) / y;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = t + ((x / y) * (z - t))
    if (t_1 <= 5d+306) then
        tmp = t_1
    else
        tmp = (x * (z - t)) / y
    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 t_1 = t + ((x / y) * (z - t));
	double tmp;
	if (t_1 <= 5e+306) {
		tmp = t_1;
	} else {
		tmp = (x * (z - t)) / y;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	t_1 = t + ((x / y) * (z - t))
	tmp = 0
	if t_1 <= 5e+306:
		tmp = t_1
	else:
		tmp = (x * (z - t)) / y
	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)
	t_1 = Float64(t + Float64(Float64(x / y) * Float64(z - t)))
	tmp = 0.0
	if (t_1 <= 5e+306)
		tmp = t_1;
	else
		tmp = Float64(Float64(x * Float64(z - t)) / y);
	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)
	t_1 = t + ((x / y) * (z - t));
	tmp = 0.0;
	if (t_1 <= 5e+306)
		tmp = t_1;
	else
		tmp = (x * (z - t)) / y;
	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_] := Block[{t$95$1 = N[(t + N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+306], t$95$1, N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Target

Original	97.7%
Target	97.3%
Herbie	98.4%

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t) < 4.99999999999999993e306

   1. Initial program 98.2%

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

   if 4.99999999999999993e306 < (+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

   1. Initial program 87.5%

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

   2. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{z - t}{y}, t\right)} \]
      Step-by-step derivation

      [Start] 87.5%	\[ \frac{x}{y} \cdot \left(z - t\right) + t \]
      associate-*l/ [=>] 100.0%	\[ \color{blue}{\frac{x \cdot \left(z - t\right)}{y}} + t \]
      *-commutative [=>] 100.0%	\[ \frac{\color{blue}{\left(z - t\right) \cdot x}}{y} + t \]
      associate-*l/ [<=] 99.9%	\[ \color{blue}{\frac{z - t}{y} \cdot x} + t \]
      *-commutative [=>] 99.9%	\[ \color{blue}{x \cdot \frac{z - t}{y}} + t \]
      fma-def [=>] 99.9%	\[ \color{blue}{\mathsf{fma}\left(x, \frac{z - t}{y}, t\right)} \]

   3. Applied egg-rr 99.9%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{\frac{1}{y} \cdot \left(z - t\right)}, t\right) \]
      Step-by-step derivation

      [Start] 99.9%	\[ \mathsf{fma}\left(x, \frac{z - t}{y}, t\right) \]
      clear-num [=>] 99.9%	\[ \mathsf{fma}\left(x, \color{blue}{\frac{1}{\frac{y}{z - t}}}, t\right) \]
      associate-/r/ [=>] 99.9%	\[ \mathsf{fma}\left(x, \color{blue}{\frac{1}{y} \cdot \left(z - t\right)}, t\right) \]

   4. Taylor expanded in x around -inf 100.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + \frac{x}{y} \cdot \left(z - t\right) \leq 5 \cdot 10^{+306}:\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	98.4%
Cost	1220

\[\begin{array}{l} t_1 := t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \]

Alternative 2
Accuracy	63.6%
Cost	2205

\[\begin{array}{l} t_1 := \frac{x}{y} \cdot \left(-t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+124}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -0.0005:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-28}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+89} \lor \neg \left(\frac{x}{y} \leq 10^{+142}\right) \land \frac{x}{y} \leq 5 \cdot 10^{+206}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	63.4%
Cost	2205

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+124}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+62}:\\ \;\;\;\;\frac{x \cdot \left(-t\right)}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -0.0005:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-28}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+89} \lor \neg \left(\frac{x}{y} \leq 10^{+142}\right) \land \frac{x}{y} \leq 5 \cdot 10^{+206}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \]

Alternative 4
Accuracy	62.8%
Cost	1425

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.0005:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-28}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+89} \lor \neg \left(\frac{x}{y} \leq 10^{+142}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \end{array} \]

Alternative 5
Accuracy	94.1%
Cost	1096

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -40000000000:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+27}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - t\right) \cdot \frac{1}{y}\right)\\ \end{array} \]

Alternative 6
Accuracy	94.3%
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -40000000000 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 7
Accuracy	64.4%
Cost	841

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.0005 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-28}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8
Accuracy	64.3%
Cost	840

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.0005:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-28}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \]

Alternative 9
Accuracy	63.1%
Cost	840

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.0005:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-28}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \]

Alternative 10
Accuracy	85.3%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -6.7 \cdot 10^{-35} \lor \neg \left(z \leq 1.5 \cdot 10^{-115}\right):\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \end{array} \]

Alternative 11
Accuracy	76.3%
Cost	448

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

Alternative 12
Accuracy	37.8%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023263 
(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))