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

Average Error: 2.0 → 2.5

Time: 13.9s

Precision: binary64

Cost: 840

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{-222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-233}:\\ \;\;\;\;\frac{z \cdot x}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* (/ x y) (- z t)) t)))
   (if (<= t -2.8e-222) t_1 (if (<= t 7e-233) (+ (/ (* z x) y) t) t_1))))

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 = ((x / y) * (z - t)) + t;
	double tmp;
	if (t <= -2.8e-222) {
		tmp = t_1;
	} else if (t <= 7e-233) {
		tmp = ((z * x) / y) + t;
	} else {
		tmp = t_1;
	}
	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 = ((x / y) * (z - t)) + t
    if (t <= (-2.8d-222)) then
        tmp = t_1
    else if (t <= 7d-233) then
        tmp = ((z * x) / y) + t
    else
        tmp = t_1
    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 = ((x / y) * (z - t)) + t;
	double tmp;
	if (t <= -2.8e-222) {
		tmp = t_1;
	} else if (t <= 7e-233) {
		tmp = ((z * x) / y) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	t_1 = ((x / y) * (z - t)) + t
	tmp = 0
	if t <= -2.8e-222:
		tmp = t_1
	elif t <= 7e-233:
		tmp = ((z * x) / y) + t
	else:
		tmp = t_1
	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(Float64(Float64(x / y) * Float64(z - t)) + t)
	tmp = 0.0
	if (t <= -2.8e-222)
		tmp = t_1;
	elseif (t <= 7e-233)
		tmp = Float64(Float64(Float64(z * x) / y) + t);
	else
		tmp = t_1;
	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 = ((x / y) * (z - t)) + t;
	tmp = 0.0;
	if (t <= -2.8e-222)
		tmp = t_1;
	elseif (t <= 7e-233)
		tmp = ((z * x) / y) + t;
	else
		tmp = t_1;
	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[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[t, -2.8e-222], t$95$1, If[LessEqual[t, 7e-233], N[(N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Target

Original	2.0
Target	2.3
Herbie	2.5

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

Derivation

1. Split input into 2 regimes

2. if t < -2.80000000000000007e-222 or 6.99999999999999982e-233 < t

   1. Initial program 1.4

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

   if -2.80000000000000007e-222 < t < 6.99999999999999982e-233

   1. Initial program 5.7

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

   2. Taylor expanded in z around inf 8.9

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

4. Final simplification 2.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-222}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-233}:\\ \;\;\;\;\frac{z \cdot x}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array} \]

Alternatives

Alternative 1
Error	18.5
Cost	1372

\[\begin{array}{l} t_1 := \frac{z}{y} \cdot x\\ t_2 := t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{if}\;t \leq -8 \cdot 10^{-143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-223}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-156}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-54}:\\ \;\;\;\;-\frac{t \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	23.5
Cost	1360

\[\begin{array}{l} t_1 := \frac{z \cdot x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+205}:\\ \;\;\;\;\frac{z}{y} \cdot x\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{+28}:\\ \;\;\;\;t \cdot \left(-\frac{x}{y}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-19}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	30.5
Cost	1112

\[\begin{array}{l} t_1 := \frac{z \cdot x}{y}\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+58}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-292}:\\ \;\;\;\;-\frac{t \cdot x}{y}\\ \mathbf{elif}\;y \leq 780000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{+91}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4
Error	6.3
Cost	968

\[\begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -1000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-19}:\\ \;\;\;\;\frac{z \cdot x}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	6.4
Cost	968

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1000:\\ \;\;\;\;\left(\frac{z}{y} - \frac{t}{y}\right) \cdot x\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-19}:\\ \;\;\;\;\frac{z \cdot x}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot x}{y}\\ \end{array} \]

Alternative 6
Error	26.3
Cost	848

\[\begin{array}{l} t_1 := \frac{z}{y} \cdot x\\ \mathbf{if}\;t \leq -1.16 \cdot 10^{-77}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-113}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7
Error	26.2
Cost	848

\[\begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-75}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-142}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-112}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-58}:\\ \;\;\;\;\frac{z}{y} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8
Error	10.9
Cost	712

\[\begin{array}{l} t_1 := \frac{z \cdot x}{y} + t\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-90}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	10.9
Cost	712

\[\begin{array}{l} t_1 := \frac{z \cdot x}{y} + t\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-90}:\\ \;\;\;\;t - t \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	31.6
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))