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

Average Accuracy: 96.6% → 98.0%

Time: 11.0s

Precision: binary64

Cost: 1608

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-215}:\\ \;\;\;\;\frac{t_1}{\frac{1}{t}}\\ \mathbf{elif}\;t_1 \leq 10^{-276}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot t\\ \end{array} \]

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-215)
     (/ t_1 (/ 1.0 t))
     (if (<= t_1 1e-276) (/ (* (- x y) t) z) (* t_1 t)))))

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-215) {
		tmp = t_1 / (1.0 / t);
	} else if (t_1 <= 1e-276) {
		tmp = ((x - y) * t) / z;
	} else {
		tmp = t_1 * 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 - 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-215)) then
        tmp = t_1 / (1.0d0 / t)
    else if (t_1 <= 1d-276) then
        tmp = ((x - y) * t) / z
    else
        tmp = t_1 * t
    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-215) {
		tmp = t_1 / (1.0 / t);
	} else if (t_1 <= 1e-276) {
		tmp = ((x - y) * t) / z;
	} else {
		tmp = t_1 * t;
	}
	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-215:
		tmp = t_1 / (1.0 / t)
	elif t_1 <= 1e-276:
		tmp = ((x - y) * t) / z
	else:
		tmp = t_1 * t
	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-215)
		tmp = Float64(t_1 / Float64(1.0 / t));
	elseif (t_1 <= 1e-276)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	else
		tmp = Float64(t_1 * t);
	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-215)
		tmp = t_1 / (1.0 / t);
	elseif (t_1 <= 1e-276)
		tmp = ((x - y) * t) / z;
	else
		tmp = t_1 * t;
	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-215], N[(t$95$1 / N[(1.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-276], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], N[(t$95$1 * t), $MachinePrecision]]]]

Target

Original	96.6%
Target	96.6%
Herbie	98.0%

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -4.99999999999999956e-215

   1. Initial program 96.4%

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

   2. Simplified 86.0%

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

      [Start] 96.4	\[ \frac{x - y}{z - y} \cdot t \]
      associate-*l/ [=>] 85.9	\[ \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]
      associate-*r/ [<=] 86.0	\[ \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Applied egg-rr 96.3%

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

   if -4.99999999999999956e-215 < (/.f64 (-.f64 x y) (-.f64 z y)) < 1e-276

   1. Initial program 82.5%

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

   2. Simplified 99.5%

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

      [Start] 82.5	\[ \frac{x - y}{z - y} \cdot t \]
      associate-*l/ [=>] 98.8	\[ \color{blue}{\frac{\left(x - y\right) \cdot t}{z - y}} \]
      associate-*r/ [<=] 99.5	\[ \color{blue}{\left(x - y\right) \cdot \frac{t}{z - y}} \]

   3. Taylor expanded in z around inf 98.8%

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

   if 1e-276 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 98.5%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{z - y} \leq -5 \cdot 10^{-215}:\\ \;\;\;\;\frac{\frac{x - y}{z - y}}{\frac{1}{t}}\\ \mathbf{elif}\;\frac{x - y}{z - y} \leq 10^{-276}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z - y} \cdot t\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	98.0%
Cost	1609

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-215} \lor \neg \left(t_1 \leq 10^{-276}\right):\\ \;\;\;\;t_1 \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \end{array} \]

Alternative 2
Accuracy	72.1%
Cost	1109

\[\begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ t_2 := \frac{t}{\frac{z}{x - y}}\\ \mathbf{if}\;z \leq -5.9 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-9}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+52} \lor \neg \left(z \leq 2.7 \cdot 10^{+163}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	72.6%
Cost	1108

\[\begin{array}{l} t_1 := t \cdot \left(1 - \frac{x}{y}\right)\\ t_2 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -9.4 \cdot 10^{-85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-54}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+120}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+159}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	89.0%
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+113}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+155}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 5
Accuracy	66.5%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-83} \lor \neg \left(y \leq 1.25 \cdot 10^{-142}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \end{array} \]

Alternative 6
Accuracy	74.1%
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-33} \lor \neg \left(x \leq 750000000000\right):\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]

Alternative 7
Accuracy	68.6%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-108}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-142}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 8
Accuracy	68.6%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-107}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-142}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \end{array} \]

Alternative 9
Accuracy	58.9%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-83}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-20}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10
Accuracy	58.8%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{-83}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-20}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11
Accuracy	58.8%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-83}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-53}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 12
Accuracy	37.4%
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023129 
(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))