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

Average Error: 2.1 → 1.5

Time: 1.6min

Precision: binary64

Cost: 2508

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x - y}{z - y} \cdot t\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-283}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+294}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - y} \cdot \left(x - y\right)\\ \end{array} \]

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)) t)))
   (if (<= t_1 -1e-295)
     t_1
     (if (<= t_1 5e-283)
       (/ (* (- x y) t) z)
       (if (<= t_1 4e+294) t_1 (* (/ t (- z y)) (- x 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)) * t;
	double tmp;
	if (t_1 <= -1e-295) {
		tmp = t_1;
	} else if (t_1 <= 5e-283) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 4e+294) {
		tmp = t_1;
	} else {
		tmp = (t / (z - y)) * (x - 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)) * t
    if (t_1 <= (-1d-295)) then
        tmp = t_1
    else if (t_1 <= 5d-283) then
        tmp = ((x - y) * t) / z
    else if (t_1 <= 4d+294) then
        tmp = t_1
    else
        tmp = (t / (z - y)) * (x - 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)) * t;
	double tmp;
	if (t_1 <= -1e-295) {
		tmp = t_1;
	} else if (t_1 <= 5e-283) {
		tmp = ((x - y) * t) / z;
	} else if (t_1 <= 4e+294) {
		tmp = t_1;
	} else {
		tmp = (t / (z - y)) * (x - 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)) * t
	tmp = 0
	if t_1 <= -1e-295:
		tmp = t_1
	elif t_1 <= 5e-283:
		tmp = ((x - y) * t) / z
	elif t_1 <= 4e+294:
		tmp = t_1
	else:
		tmp = (t / (z - y)) * (x - 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(Float64(x - y) / Float64(z - y)) * t)
	tmp = 0.0
	if (t_1 <= -1e-295)
		tmp = t_1;
	elseif (t_1 <= 5e-283)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (t_1 <= 4e+294)
		tmp = t_1;
	else
		tmp = Float64(Float64(t / Float64(z - y)) * Float64(x - 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)) * t;
	tmp = 0.0;
	if (t_1 <= -1e-295)
		tmp = t_1;
	elseif (t_1 <= 5e-283)
		tmp = ((x - y) * t) / z;
	elseif (t_1 <= 4e+294)
		tmp = t_1;
	else
		tmp = (t / (z - y)) * (x - 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[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-295], t$95$1, If[LessEqual[t$95$1, 5e-283], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 4e+294], t$95$1, N[(N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	2.1
Target	2.1
Herbie	1.5

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

Derivation

1. Split input into 3 regimes

2. if (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t) < -1.00000000000000006e-295 or 5.0000000000000001e-283 < (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t) < 4.00000000000000027e294

   1. Initial program 0.6

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

   if -1.00000000000000006e-295 < (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t) < 5.0000000000000001e-283

   1. Initial program 7.7

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

   2. Taylor expanded in z around inf 6.9

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

   3. Simplified 6.9

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

   if 4.00000000000000027e294 < (*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

   1. Initial program 31.6

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

   2. Applied egg-rr 2.9

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

Alternatives

Alternative 1
Error	1.9
Cost	1996

\[\begin{array}{l} t_1 := \frac{x - y}{z - y} \cdot t\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-295}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;y - x \ne 0:\\ \;\;\;\;\frac{t}{\frac{z - y}{x - y}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-59}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot t}{y - z}\\ \mathbf{elif}\;t \ne 0:\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	1.9
Cost	1996

\[\begin{array}{l} t_1 := \frac{x - y}{z - y} \cdot t\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-59}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot t}{y - z}\\ \mathbf{elif}\;t \ne 0:\\ \;\;\;\;\frac{x - y}{\frac{z - y}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	1.7
Cost	1864

\[\begin{array}{l} t_1 := \frac{x - y}{z - y} \cdot t\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-28}:\\ \;\;\;\;\frac{\left(y - x\right) \cdot t}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z - y} \cdot \left(x - y\right)\\ \end{array} \]

Alternative 4
Error	18.4
Cost	976

\[\begin{array}{l} t_1 := \left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-45}:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+162}:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	20.4
Cost	844

\[\begin{array}{l} t_1 := \left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-212}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-46}:\\ \;\;\;\;\frac{t}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	7.8
Cost	840

\[\begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+195}:\\ \;\;\;\;\left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+242}:\\ \;\;\;\;\frac{t}{z - y} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7
Error	25.8
Cost	716

\[\begin{array}{l} \mathbf{if}\;y \leq -280000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-212}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{t}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8
Error	18.2
Cost	712

\[\begin{array}{l} t_1 := \left(1 - \frac{x}{y}\right) \cdot t\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{t}{z} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	26.1
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -22000000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-45}:\\ \;\;\;\;\frac{t}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10
Error	39.3
Cost	64

\[t \]

Reproduce

herbie shell --seed 2023033 
(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))