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

Average Error: 2.0 → 0.7

Time: 9.8s

Precision: binary64

Cost: 1356

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -\infty:\\ \;\;\;\;t + \frac{x}{\frac{y}{z - t}}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-254}:\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 0:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z - t}{\frac{y}{x}}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) (- INFINITY))
   (+ t (/ x (/ y (- z t))))
   (if (<= (/ x y) -1e-254)
     (+ t (* (/ x y) (- z t)))
     (if (<= (/ x y) 0.0) (+ t (/ (* x z) y)) (+ t (/ (- z t) (/ y x)))))))

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 tmp;
	if ((x / y) <= -((double) INFINITY)) {
		tmp = t + (x / (y / (z - t)));
	} else if ((x / y) <= -1e-254) {
		tmp = t + ((x / y) * (z - t));
	} else if ((x / y) <= 0.0) {
		tmp = t + ((x * z) / y);
	} else {
		tmp = t + ((z - t) / (y / x));
	}
	return tmp;
}

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 tmp;
	if ((x / y) <= -Double.POSITIVE_INFINITY) {
		tmp = t + (x / (y / (z - t)));
	} else if ((x / y) <= -1e-254) {
		tmp = t + ((x / y) * (z - t));
	} else if ((x / y) <= 0.0) {
		tmp = t + ((x * z) / y);
	} else {
		tmp = t + ((z - t) / (y / x));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -math.inf:
		tmp = t + (x / (y / (z - t)))
	elif (x / y) <= -1e-254:
		tmp = t + ((x / y) * (z - t))
	elif (x / y) <= 0.0:
		tmp = t + ((x * z) / y)
	else:
		tmp = t + ((z - t) / (y / x))
	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)
	tmp = 0.0
	if (Float64(x / y) <= Float64(-Inf))
		tmp = Float64(t + Float64(x / Float64(y / Float64(z - t))));
	elseif (Float64(x / y) <= -1e-254)
		tmp = Float64(t + Float64(Float64(x / y) * Float64(z - t)));
	elseif (Float64(x / y) <= 0.0)
		tmp = Float64(t + Float64(Float64(x * z) / y));
	else
		tmp = Float64(t + Float64(Float64(z - t) / Float64(y / x)));
	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)
	tmp = 0.0;
	if ((x / y) <= -Inf)
		tmp = t + (x / (y / (z - t)));
	elseif ((x / y) <= -1e-254)
		tmp = t + ((x / y) * (z - t));
	elseif ((x / y) <= 0.0)
		tmp = t + ((x * z) / y);
	else
		tmp = t + ((z - t) / (y / x));
	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_] := If[LessEqual[N[(x / y), $MachinePrecision], (-Infinity)], N[(t + N[(x / N[(y / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -1e-254], N[(t + N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 0.0], N[(t + N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(z - t), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	2.0
Target	2.1
Herbie	0.7

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

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -inf.0

   1. Initial program 64.0

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

   2. Applied egg-rr 0.3

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

   if -inf.0 < (/.f64 x y) < -9.9999999999999991e-255

   1. Initial program 0.2

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

   if -9.9999999999999991e-255 < (/.f64 x y) < 0.0

   1. Initial program 3.2

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

   2. Taylor expanded in z around inf 0.0

      \[\leadsto \color{blue}{\frac{z \cdot x}{y}} + t \]

   if 0.0 < (/.f64 x y)

   1. Initial program 1.7

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

   2. Applied egg-rr 1.6

      \[\leadsto \color{blue}{\frac{z - t}{\frac{y}{x}}} + t \]
3. Recombined 4 regimes into one program.

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -\infty:\\ \;\;\;\;t + \frac{x}{\frac{y}{z - t}}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-254}:\\ \;\;\;\;t + \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 0:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{z - t}{\frac{y}{x}}\\ \end{array} \]

Alternatives

Alternative 1
Error	22.3
Cost	1944

\[\begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ t_2 := \frac{x}{y} \cdot \left(-t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-84}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-110}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-15}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	22.1
Cost	1944

\[\begin{array}{l} t_1 := \frac{x}{y} \cdot z\\ t_2 := x \cdot \left(-\frac{t}{y}\right)\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-84}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-110}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-15}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	15.0
Cost	1488

\[\begin{array}{l} t_1 := t - \frac{t}{\frac{y}{x}}\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-110}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;\frac{x}{y} \leq 1000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \end{array} \]

Alternative 4
Error	23.0
Cost	1360

\[\begin{array}{l} t_1 := \frac{x}{\frac{y}{z}}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-84}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-15}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	23.1
Cost	1360

\[\begin{array}{l} t_1 := \frac{x}{\frac{y}{z}}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-84}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-15}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	22.1
Cost	1360

\[\begin{array}{l} t_1 := \frac{z}{\frac{y}{x}}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-84}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-110}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-15}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	22.1
Cost	1360

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-84}:\\ \;\;\;\;t\\ \mathbf{elif}\;\frac{x}{y} \leq -4 \cdot 10^{-110}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-15}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 8
Error	1.2
Cost	1356

\[\begin{array}{l} t_1 := t + \frac{z - t}{\frac{y}{x}}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+97}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -1 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 0:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	18.4
Cost	976

\[\begin{array}{l} t_1 := t - \frac{t}{\frac{y}{x}}\\ \mathbf{if}\;t \leq -7.149389740861886 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.923713598184971 \cdot 10^{-188}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \mathbf{elif}\;t \leq -7.485168110957467 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.7568564525764289 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{\frac{y}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	14.0
Cost	968

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1000000:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \end{array} \]

Alternative 11
Error	5.3
Cost	968

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1000000:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-15}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \end{array} \]

Alternative 12
Error	16.2
Cost	712

\[\begin{array}{l} t_1 := t - \frac{t}{\frac{y}{x}}\\ \mathbf{if}\;t \leq -5.7156593846115204 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.4346150061238826 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	16.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -5.7156593846115204 \cdot 10^{-80}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 2.4346150061238826 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]

Alternative 14
Error	31.4
Cost	64

\[t \]

Reproduce

herbie shell --seed 2022300 
(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))