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

Average Error: 1.9 → 1.4

Time: 1.6min

Precision: binary64

Cost: 7692

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right)\\ t_2 := x \cdot \left(z - t\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+114}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;x \ne 0:\\ \;\;\;\;\frac{z - t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} + t\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+40}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;t_2 \ne 0:\\ \;\;\;\;{\left(\frac{y}{t_2}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{z - t}{y} \cdot x + t\\ \end{array} \]

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_2 (* x (- z t))))
   (if (<= y -2e+114)
     (+ (if (!= x 0.0) (/ (- z t) (/ y x)) t_1) t)
     (if (<= y 5e+40)
       (+ (if (!= t_2 0.0) (pow (/ y t_2) -1.0) t_1) t)
       (+ (* (/ (- z t) y) x) t)))))

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);
	double t_2 = x * (z - t);
	double tmp_1;
	if (y <= -2e+114) {
		double tmp_2;
		if (x != 0.0) {
			tmp_2 = (z - t) / (y / x);
		} else {
			tmp_2 = t_1;
		}
		tmp_1 = tmp_2 + t;
	} else if (y <= 5e+40) {
		double tmp_3;
		if (t_2 != 0.0) {
			tmp_3 = pow((y / t_2), -1.0);
		} else {
			tmp_3 = t_1;
		}
		tmp_1 = tmp_3 + t;
	} else {
		tmp_1 = (((z - t) / y) * x) + t;
	}
	return tmp_1;
}

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) :: t_2
    real(8) :: tmp
    real(8) :: tmp_1
    real(8) :: tmp_2
    real(8) :: tmp_3
    t_1 = (x / y) * (z - t)
    t_2 = x * (z - t)
    if (y <= (-2d+114)) then
        if (x /= 0.0d0) then
            tmp_2 = (z - t) / (y / x)
        else
            tmp_2 = t_1
        end if
        tmp_1 = tmp_2 + t
    else if (y <= 5d+40) then
        if (t_2 /= 0.0d0) then
            tmp_3 = (y / t_2) ** (-1.0d0)
        else
            tmp_3 = t_1
        end if
        tmp_1 = tmp_3 + t
    else
        tmp_1 = (((z - t) / y) * x) + t
    end if
    code = tmp_1
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);
	double t_2 = x * (z - t);
	double tmp_1;
	if (y <= -2e+114) {
		double tmp_2;
		if (x != 0.0) {
			tmp_2 = (z - t) / (y / x);
		} else {
			tmp_2 = t_1;
		}
		tmp_1 = tmp_2 + t;
	} else if (y <= 5e+40) {
		double tmp_3;
		if (t_2 != 0.0) {
			tmp_3 = Math.pow((y / t_2), -1.0);
		} else {
			tmp_3 = t_1;
		}
		tmp_1 = tmp_3 + t;
	} else {
		tmp_1 = (((z - t) / y) * x) + t;
	}
	return tmp_1;
}

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_2 = x * (z - t)
	tmp_1 = 0
	if y <= -2e+114:
		tmp_2 = 0
		if x != 0.0:
			tmp_2 = (z - t) / (y / x)
		else:
			tmp_2 = t_1
		tmp_1 = tmp_2 + t
	elif y <= 5e+40:
		tmp_3 = 0
		if t_2 != 0.0:
			tmp_3 = math.pow((y / t_2), -1.0)
		else:
			tmp_3 = t_1
		tmp_1 = tmp_3 + t
	else:
		tmp_1 = (((z - t) / y) * x) + t
	return tmp_1

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(x / y) * Float64(z - t))
	t_2 = Float64(x * Float64(z - t))
	tmp_1 = 0.0
	if (y <= -2e+114)
		tmp_2 = 0.0
		if (x != 0.0)
			tmp_2 = Float64(Float64(z - t) / Float64(y / x));
		else
			tmp_2 = t_1;
		end
		tmp_1 = Float64(tmp_2 + t);
	elseif (y <= 5e+40)
		tmp_3 = 0.0
		if (t_2 != 0.0)
			tmp_3 = Float64(y / t_2) ^ -1.0;
		else
			tmp_3 = t_1;
		end
		tmp_1 = Float64(tmp_3 + t);
	else
		tmp_1 = Float64(Float64(Float64(Float64(z - t) / y) * x) + t);
	end
	return tmp_1
end

MATLAB

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

↓

function tmp_5 = code(x, y, z, t)
	t_1 = (x / y) * (z - t);
	t_2 = x * (z - t);
	tmp_2 = 0.0;
	if (y <= -2e+114)
		tmp_3 = 0.0;
		if (x ~= 0.0)
			tmp_3 = (z - t) / (y / x);
		else
			tmp_3 = t_1;
		end
		tmp_2 = tmp_3 + t;
	elseif (y <= 5e+40)
		tmp_4 = 0.0;
		if (t_2 ~= 0.0)
			tmp_4 = (y / t_2) ^ -1.0;
		else
			tmp_4 = t_1;
		end
		tmp_2 = tmp_4 + t;
	else
		tmp_2 = (((z - t) / y) * x) + t;
	end
	tmp_5 = tmp_2;
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[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2e+114], N[(If[Unequal[x, 0.0], N[(N[(z - t), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], t$95$1] + t), $MachinePrecision], If[LessEqual[y, 5e+40], N[(If[Unequal[t$95$2, 0.0], N[Power[N[(y / t$95$2), $MachinePrecision], -1.0], $MachinePrecision], t$95$1] + t), $MachinePrecision], N[(N[(N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision] * x), $MachinePrecision] + t), $MachinePrecision]]]]]

Target

Original	1.9
Target	2.2
Herbie	1.4

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

Derivation

1. Split input into 3 regimes

2. if y < -2e114

   1. Initial program 1.0

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

   2. Applied egg-rr 1.2

      \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;x \ne 0:\\ \;\;\;\;\frac{z - t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ } \end{array}} + t \]

   if -2e114 < y < 5.00000000000000003e40

   1. Initial program 2.4

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

   2. Applied egg-rr 1.6

      \[\leadsto \color{blue}{\begin{array}{l} \color{blue}{\mathbf{if}\;x \cdot \left(z - t\right) \ne 0:\\ \;\;\;\;{\left(\frac{y}{x \cdot \left(z - t\right)}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ } \end{array}} + t \]

   if 5.00000000000000003e40 < y

   1. Initial program 1.3

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

   2. Applied egg-rr 1.1

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

Alternatives

Alternative 1
Error	31.1
Cost	1440

\[\begin{array}{l} t_1 := t \cdot \frac{-x}{y}\\ t_2 := \frac{z \cdot x}{y}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+133}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -7 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-57}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-260}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.86 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 0.000115:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 2
Error	31.2
Cost	1440

\[\begin{array}{l} t_1 := \frac{z \cdot x}{y}\\ t_2 := t \cdot \frac{-x}{y}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+133}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-57}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-169}:\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 10^{-174}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.00012:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3
Error	30.8
Cost	1440

\[\begin{array}{l} t_1 := \frac{z \cdot x}{y}\\ t_2 := t \cdot \frac{-x}{y}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+133}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.55 \cdot 10^{-59}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-156}:\\ \;\;\;\;\frac{-t \cdot x}{y}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-259}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-181}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.00013:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4
Error	21.9
Cost	976

\[\begin{array}{l} t_1 := \frac{z \cdot x}{y}\\ t_2 := t \cdot \frac{y - x}{y}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -76000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+205}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	12.1
Cost	968

\[\begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -0.04:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 100000000:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	2.9
Cost	968

\[\begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -5:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{y} \cdot z + t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	1.8
Cost	708

\[\begin{array}{l} \mathbf{if}\;x \ne 0:\\ \;\;\;\;\frac{z - t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \end{array} + t \]

Alternative 8
Error	25.9
Cost	584

\[\begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-68}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-64}:\\ \;\;\;\;\frac{z \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9
Error	1.9
Cost	576

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

Alternative 10
Error	30.7
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023033 
(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))