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

Average Error: 3.67% → 2.93%

Time: 10.2s

Precision: binary64

Cost: 1092

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+127}:\\ \;\;\;\;t_1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x y) (- z y))))
   (if (<= t_1 5e+127) (* t_1 t) (/ (* x t) (- z y)))))

C

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

↓

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e+127) {
		tmp = t_1 * t;
	} else {
		tmp = (x * t) / (z - 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 - y)) * 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 = (x - y) / (z - y)
    if (t_1 <= 5d+127) then
        tmp = t_1 * t
    else
        tmp = (x * t) / (z - y)
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 5e+127) {
		tmp = t_1 * t;
	} else {
		tmp = (x * t) / (z - y);
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 5e+127:
		tmp = t_1 * t
	else:
		tmp = (x * t) / (z - y)
	return tmp

Julia

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

↓

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 5e+127)
		tmp = Float64(t_1 * t);
	else
		tmp = Float64(Float64(x * t) / Float64(z - y));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 5e+127)
		tmp = t_1 * t;
	else
		tmp = (x * t) / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+127], N[(t$95$1 * t), $MachinePrecision], N[(N[(x * t), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]

Target

Original	3.67%
Target	3.52%
Herbie	2.93%

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 5.0000000000000004e127

   1. Initial program 2.72

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

   if 5.0000000000000004e127 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 20.23

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

   2. Simplified 5.36

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

      [Start] 20.23	\[ \frac{x - y}{z - y} \cdot t \]
      associate-*l/ [=>] 6.66	\[ \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]
      associate-*r/ [<=] 5.36	\[ \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Taylor expanded in x around inf 6.66

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

4. Final simplification 2.93

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq 5 \cdot 10^{+127}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \end{array} \]

Alternatives

Alternative 1
Error	29.47%
Cost	978

\[\begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+88} \lor \neg \left(y \leq 3.65 \cdot 10^{-153} \lor \neg \left(y \leq 3 \cdot 10^{-74}\right) \land y \leq 2.75 \cdot 10^{+82}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \end{array} \]

Alternative 2
Error	29.5%
Cost	977

\[\begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -1.52 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.65 \cdot 10^{-153}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-74} \lor \neg \left(y \leq 2.75 \cdot 10^{+82}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z - y}\\ \end{array} \]

Alternative 3
Error	10.86%
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+155}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+124}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]

Alternative 4
Error	33.55%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+88}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5
Error	58.49%
Cost	585

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+227} \lor \neg \left(z \leq 1.5 \cdot 10^{+205}\right):\\ \;\;\;\;t \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6
Error	41.39%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{+88}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7
Error	40.16%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+88}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+71}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8
Error	61.51%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023088 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

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