Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Average Error: 6.8 → 0.4

Time: 5.3s

Precision: binary64

\[ \begin{array}{c}[y, t] = \mathsf{sort}([y, t])\\ \end{array} \]

Math

\[\left(x \cdot y - z \cdot y\right) \cdot t \]

↓

\[\begin{array}{l} t_1 := x \cdot y - y \cdot z\\ t_2 := t_1 \cdot t\\ t_3 := y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-200}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+269}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

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) (* y z))) (t_2 (* t_1 t)) (t_3 (* y (* t (- x z)))))
   (if (<= t_1 (- INFINITY))
     t_3
     (if (<= t_1 -5e-180)
       t_2
       (if (<= t_1 2e-200) t_3 (if (<= t_1 2e+269) t_2 t_3))))))

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) - (y * z);
	double t_2 = t_1 * t;
	double t_3 = y * (t * (x - z));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_1 <= -5e-180) {
		tmp = t_2;
	} else if (t_1 <= 2e-200) {
		tmp = t_3;
	} else if (t_1 <= 2e+269) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

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) - (y * z);
	double t_2 = t_1 * t;
	double t_3 = y * (t * (x - z));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_1 <= -5e-180) {
		tmp = t_2;
	} else if (t_1 <= 2e-200) {
		tmp = t_3;
	} else if (t_1 <= 2e+269) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) - (y * z)
	t_2 = t_1 * t
	t_3 = y * (t * (x - z))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_3
	elif t_1 <= -5e-180:
		tmp = t_2
	elif t_1 <= 2e-200:
		tmp = t_3
	elif t_1 <= 2e+269:
		tmp = t_2
	else:
		tmp = t_3
	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(y * z))
	t_2 = Float64(t_1 * t)
	t_3 = Float64(y * Float64(t * Float64(x - z)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_1 <= -5e-180)
		tmp = t_2;
	elseif (t_1 <= 2e-200)
		tmp = t_3;
	elseif (t_1 <= 2e+269)
		tmp = t_2;
	else
		tmp = t_3;
	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) - (y * z);
	t_2 = t_1 * t;
	t_3 = y * (t * (x - z));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_3;
	elseif (t_1 <= -5e-180)
		tmp = t_2;
	elseif (t_1 <= 2e-200)
		tmp = t_3;
	elseif (t_1 <= 2e+269)
		tmp = t_2;
	else
		tmp = t_3;
	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[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * t), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(t * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$3, If[LessEqual[t$95$1, -5e-180], t$95$2, If[LessEqual[t$95$1, 2e-200], t$95$3, If[LessEqual[t$95$1, 2e+269], t$95$2, t$95$3]]]]]]]

Target

Original	6.8
Target	3.4
Herbie	0.4

\[\begin{array}{l} \mathbf{if}\;t < -9.231879582886777 \cdot 10^{-80}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(x - z\right)\\ \mathbf{elif}\;t < 2.543067051564877 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z y)) < -inf.0 or -5.0000000000000001e-180 < (-.f64 (*.f64 x y) (*.f64 z y)) < 2e-200 or 2.0000000000000001e269 < (-.f64 (*.f64 x y) (*.f64 z y))

   1. Initial program 26.0

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]

   2. Simplified 0.8

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z y)) < -5.0000000000000001e-180 or 2e-200 < (-.f64 (*.f64 x y) (*.f64 z y)) < 2.0000000000000001e269

   1. Initial program 0.2

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - y \cdot z \leq -\infty:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq -5 \cdot 10^{-180}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 2 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{elif}\;x \cdot y - y \cdot z \leq 2 \cdot 10^{+269}:\\ \;\;\;\;\left(x \cdot y - y \cdot z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array} \]

Reproduce

herbie shell --seed 2022210 
(FPCore (x y z t)
  :name "Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -9.231879582886777e-80) (* (* y t) (- x z)) (if (< t 2.543067051564877e+83) (* y (* t (- x z))) (* (* y (- x z)) t)))

  (* (- (* x y) (* z y)) t))