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

Average Accuracy: 96.9% → 96.7%

Time: 12.0s

Precision: binary64

Cost: 841

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-137} \lor \neg \left(t \leq 1.2 \cdot 10^{-150}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1e-137) (not (<= t 1.2e-150)))
   (+ t (* (/ x y) (- z t)))
   (+ t (* 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 tmp;
	if ((t <= -1e-137) || !(t <= 1.2e-150)) {
		tmp = t + ((x / y) * (z - t));
	} else {
		tmp = t + (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) :: tmp
    if ((t <= (-1d-137)) .or. (.not. (t <= 1.2d-150))) then
        tmp = t + ((x / y) * (z - t))
    else
        tmp = t + (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 tmp;
	if ((t <= -1e-137) || !(t <= 1.2e-150)) {
		tmp = t + ((x / y) * (z - t));
	} else {
		tmp = t + (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):
	tmp = 0
	if (t <= -1e-137) or not (t <= 1.2e-150):
		tmp = t + ((x / y) * (z - t))
	else:
		tmp = t + (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)
	tmp = 0.0
	if ((t <= -1e-137) || !(t <= 1.2e-150))
		tmp = Float64(t + Float64(Float64(x / y) * Float64(z - t)));
	else
		tmp = Float64(t + Float64(x * Float64(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)
	tmp = 0.0;
	if ((t <= -1e-137) || ~((t <= 1.2e-150)))
		tmp = t + ((x / y) * (z - t));
	else
		tmp = t + (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_] := If[Or[LessEqual[t, -1e-137], N[Not[LessEqual[t, 1.2e-150]], $MachinePrecision]], N[(t + N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	96.9%
Target	96.3%
Herbie	96.7%

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

Derivation

1. Split input into 2 regimes

2. if t < -9.99999999999999978e-138 or 1.2e-150 < t

   1. Initial program 98.7%

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

   if -9.99999999999999978e-138 < t < 1.2e-150

   1. Initial program 92.6%

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

   2. Simplified 92.0%

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

      [Start] 92.6	\[ \frac{x}{y} \cdot \left(z - t\right) + t \]
      associate-*l/ [=>] 91.4	\[ \color{blue}{\frac{x \cdot \left(z - t\right)}{y}} + t \]
      *-commutative [=>] 91.4	\[ \frac{\color{blue}{\left(z - t\right) \cdot x}}{y} + t \]
      associate-*l/ [<=] 92.0	\[ \color{blue}{\frac{z - t}{y} \cdot x} + t \]
      *-commutative [=>] 92.0	\[ \color{blue}{x \cdot \frac{z - t}{y}} + t \]
      fma-def [=>] 92.0	\[ \color{blue}{\mathsf{fma}\left(x, \frac{z - t}{y}, t\right)} \]

   3. Applied egg-rr 92.0%

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

      [Start] 92.0	\[ \mathsf{fma}\left(x, \frac{z - t}{y}, t\right) \]
      fma-udef [=>] 92.0	\[ \color{blue}{x \cdot \frac{z - t}{y} + t} \]

3. Recombined 2 regimes into one program.

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-137} \lor \neg \left(t \leq 1.2 \cdot 10^{-150}\right):\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z - t}{y}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	82.0%
Cost	2008

\[\begin{array}{l} t_1 := t + \frac{x}{y} \cdot z\\ t_2 := \frac{t \cdot x}{-y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-310}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Accuracy	81.9%
Cost	2008

\[\begin{array}{l} t_1 := t + \frac{x}{y} \cdot z\\ t_2 := \frac{t \cdot x}{-y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2.5 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-310}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	65.1%
Cost	1944

\[\begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ t_2 := t \cdot \frac{-x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-51}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+108}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Accuracy	65.7%
Cost	1944

\[\begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ t_2 := x \cdot \frac{-t}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-51}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+108}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	65.7%
Cost	1944

\[\begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+165}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-51}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+108}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-y}{t}}\\ \end{array} \]

Alternative 6
Accuracy	65.7%
Cost	1944

\[\begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ t_2 := \frac{t \cdot x}{-y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-51}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+108}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Accuracy	93.3%
Cost	1748

\[\begin{array}{l} t_1 := t + \frac{x}{y} \cdot z\\ t_2 := t + x \cdot \frac{z - t}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-291}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-310}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+76}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{z - t}}\\ \end{array} \]

Alternative 8
Accuracy	81.3%
Cost	1488

\[\begin{array}{l} t_1 := t + \frac{x}{y} \cdot z\\ t_2 := \frac{t \cdot x}{-y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \frac{-x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Accuracy	90.6%
Cost	969

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -200 \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{\frac{y}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \end{array} \]

Alternative 10
Accuracy	92.2%
Cost	968

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -200:\\ \;\;\;\;\frac{x}{\frac{y}{z - t}}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+34}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \]

Alternative 11
Accuracy	65.0%
Cost	841

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-21} \lor \neg \left(\frac{x}{y} \leq 10^{-51}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12
Accuracy	50.2%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023151 
(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))