Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Average Error: 7.0 → 1.5

Time: 10.8s

Precision: binary64

Cost: 1736

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

Math

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

↓

\[\begin{array}{l} t_1 := x \cdot y - z \cdot y\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+188}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+199}:\\ \;\;\;\;\left(y \cdot x\right) \cdot t - t \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array} \]

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))))
   (if (<= t_1 -5e+188)
     (* (- x z) (* y t))
     (if (<= t_1 5e+199)
       (- (* (* y x) t) (* t (* y z)))
       (* y (* t (- x z)))))))

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);
	double tmp;
	if (t_1 <= -5e+188) {
		tmp = (x - z) * (y * t);
	} else if (t_1 <= 5e+199) {
		tmp = ((y * x) * t) - (t * (y * z));
	} else {
		tmp = y * (t * (x - z));
	}
	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)
    if (t_1 <= (-5d+188)) then
        tmp = (x - z) * (y * t)
    else if (t_1 <= 5d+199) then
        tmp = ((y * x) * t) - (t * (y * z))
    else
        tmp = y * (t * (x - z))
    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);
	double tmp;
	if (t_1 <= -5e+188) {
		tmp = (x - z) * (y * t);
	} else if (t_1 <= 5e+199) {
		tmp = ((y * x) * t) - (t * (y * z));
	} else {
		tmp = y * (t * (x - z));
	}
	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)
	tmp = 0
	if t_1 <= -5e+188:
		tmp = (x - z) * (y * t)
	elif t_1 <= 5e+199:
		tmp = ((y * x) * t) - (t * (y * z))
	else:
		tmp = y * (t * (x - z))
	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(z * y))
	tmp = 0.0
	if (t_1 <= -5e+188)
		tmp = Float64(Float64(x - z) * Float64(y * t));
	elseif (t_1 <= 5e+199)
		tmp = Float64(Float64(Float64(y * x) * t) - Float64(t * Float64(y * z)));
	else
		tmp = Float64(y * Float64(t * Float64(x - z)));
	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);
	tmp = 0.0;
	if (t_1 <= -5e+188)
		tmp = (x - z) * (y * t);
	elseif (t_1 <= 5e+199)
		tmp = ((y * x) * t) - (t * (y * z));
	else
		tmp = y * (t * (x - z));
	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[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+188], N[(N[(x - z), $MachinePrecision] * N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+199], N[(N[(N[(y * x), $MachinePrecision] * t), $MachinePrecision] - N[(t * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(t * N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	7.0
Target	3.4
Herbie	1.5

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

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z y)) < -5.0000000000000001e188

   1. Initial program 24.3

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

   2. Simplified 1.4

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

      [Start] 24.3	\[ \left(x \cdot y - z \cdot y\right) \cdot t \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 24.3	\[ \color{blue}{t \cdot \left(x \cdot y - z \cdot y\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 24.3	\[ t \cdot \left(x \cdot y - \color{blue}{y \cdot z}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-102 [=>] 24.3	\[ t \cdot \color{blue}{\left(y \cdot \left(x - z\right)\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-7 [=>] 1.4	\[ \color{blue}{y \cdot \left(t \cdot \left(x - z\right)\right)} \]

   3. Applied egg-rr 1.1

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

   4. Applied egg-rr 1.1

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

   if -5.0000000000000001e188 < (-.f64 (*.f64 x y) (*.f64 z y)) < 4.9999999999999998e199

   1. Initial program 1.6

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

   2. Applied egg-rr 4.6

      \[\leadsto \color{blue}{\left(\left(\left(y \cdot \left(x - z\right)\right) \cdot \frac{1}{y \cdot \left(x - z\right)}\right) \cdot \left(y \cdot \left(x - z\right)\right)\right)} \cdot t \]

   3. Applied egg-rr 1.6

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

   if 4.9999999999999998e199 < (-.f64 (*.f64 x y) (*.f64 z y))

   1. Initial program 29.0

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

   2. Simplified 1.3

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

      [Start] 29.0	\[ \left(x \cdot y - z \cdot y\right) \cdot t \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 29.0	\[ \color{blue}{t \cdot \left(x \cdot y - z \cdot y\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 29.0	\[ t \cdot \left(x \cdot y - \color{blue}{y \cdot z}\right) \]
      rational_best_oopsla_all_46_json_45_simplify-102 [=>] 29.0	\[ t \cdot \color{blue}{\left(y \cdot \left(x - z\right)\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-7 [=>] 1.3	\[ \color{blue}{y \cdot \left(t \cdot \left(x - z\right)\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 1.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot y \leq -5 \cdot 10^{+188}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;x \cdot y - z \cdot y \leq 5 \cdot 10^{+199}:\\ \;\;\;\;\left(y \cdot x\right) \cdot t - t \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	1.5
Cost	1480

\[\begin{array}{l} t_1 := x \cdot y - z \cdot y\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+188}:\\ \;\;\;\;\left(x - z\right) \cdot \left(y \cdot t\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+199}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \end{array} \]

Alternative 2
Error	20.3
Cost	912

\[\begin{array}{l} t_1 := \left(-z\right) \cdot \left(t \cdot y\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-18}:\\ \;\;\;\;\left(y \cdot x\right) \cdot t\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	20.8
Cost	912

\[\begin{array}{l} t_1 := \left(y \cdot \left(-z\right)\right) \cdot t\\ \mathbf{if}\;z \leq -2 \cdot 10^{-118}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-18}:\\ \;\;\;\;\left(y \cdot x\right) \cdot t\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+21}:\\ \;\;\;\;\left(-z\right) \cdot \left(t \cdot y\right)\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	7.4
Cost	712

\[\begin{array}{l} t_1 := y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-234}:\\ \;\;\;\;\left(-z\right) \cdot \left(t \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	19.9
Cost	648

\[\begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot t\\ \end{array} \]

Alternative 6
Error	2.6
Cost	580

\[\begin{array}{l} \mathbf{if}\;t \leq 9 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \left(t \cdot \left(x - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(x - z\right)\right) \cdot t\\ \end{array} \]

Alternative 7
Error	29.3
Cost	452

\[\begin{array}{l} \mathbf{if}\;t \leq 6600000000000:\\ \;\;\;\;y \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot t\right)\\ \end{array} \]

Alternative 8
Error	29.7
Cost	452

\[\begin{array}{l} \mathbf{if}\;t \leq 10^{-149}:\\ \;\;\;\;y \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot t\\ \end{array} \]

Alternative 9
Error	31.4
Cost	320

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

Reproduce

herbie shell --seed 2023090 
(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))