Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3

Percentage Accurate: 90.5% → 99.5%

Time: 2.3s

Alternatives: 6

Speedup: 0.9×

• 75.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (* (- (* x y) (* z y)) t))

C

double code(double x, double y, double z, double t) {
	return ((x * y) - (z * y)) * t;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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

Java

public static double code(double x, double y, double z, double t) {
	return ((x * y) - (z * y)) * t;
}

Python

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

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x * y) - Float64(z * y)) * t)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x * y), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	((x * y) - (z * y)) * t
END code

Initial Program: 90.5% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (* (- (* x y) (* z y)) t))

C

double code(double x, double y, double z, double t) {
	return ((x * y) - (z * y)) * t;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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

Java

public static double code(double x, double y, double z, double t) {
	return ((x * y) - (z * y)) * t;
}

Python

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

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x * y) - Float64(z * y)) * t)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x * y), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	((x * y) - (z * y)) * t
END code

Alternative 1: 99.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\left|y\right|, \left|t\right|\right)\\ t_2 := \mathsf{max}\left(\left|y\right|, \left|t\right|\right)\\ t_3 := \left(t\_1 \cdot \left(x - z\right)\right) \cdot t\_2\\ t_4 := \left(x \cdot t\_1 - z \cdot t\_1\right) \cdot t\_2\\ \mathsf{copysign}\left(1, y\right) \cdot \left(\mathsf{copysign}\left(1, t\right) \cdot \begin{array}{l} \mathbf{if}\;t\_4 \leq -1 \cdot 10^{-13}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 10^{+34}:\\ \;\;\;\;t\_1 \cdot \left(\left(x - z\right) \cdot t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmin (fabs y) (fabs t)))
       (t_2 (fmax (fabs y) (fabs t)))
       (t_3 (* (* t_1 (- x z)) t_2))
       (t_4 (* (- (* x t_1) (* z t_1)) t_2)))
  (*
   (copysign 1.0 y)
   (*
    (copysign 1.0 t)
    (if (<= t_4 -1e-13)
      t_3
      (if (<= t_4 1e+34) (* t_1 (* (- x z) t_2)) t_3))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmin(fabs(y), fabs(t));
	double t_2 = fmax(fabs(y), fabs(t));
	double t_3 = (t_1 * (x - z)) * t_2;
	double t_4 = ((x * t_1) - (z * t_1)) * t_2;
	double tmp;
	if (t_4 <= -1e-13) {
		tmp = t_3;
	} else if (t_4 <= 1e+34) {
		tmp = t_1 * ((x - z) * t_2);
	} else {
		tmp = t_3;
	}
	return copysign(1.0, y) * (copysign(1.0, t) * tmp);
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmin(Math.abs(y), Math.abs(t));
	double t_2 = fmax(Math.abs(y), Math.abs(t));
	double t_3 = (t_1 * (x - z)) * t_2;
	double t_4 = ((x * t_1) - (z * t_1)) * t_2;
	double tmp;
	if (t_4 <= -1e-13) {
		tmp = t_3;
	} else if (t_4 <= 1e+34) {
		tmp = t_1 * ((x - z) * t_2);
	} else {
		tmp = t_3;
	}
	return Math.copySign(1.0, y) * (Math.copySign(1.0, t) * tmp);
}

Python

def code(x, y, z, t):
	t_1 = fmin(math.fabs(y), math.fabs(t))
	t_2 = fmax(math.fabs(y), math.fabs(t))
	t_3 = (t_1 * (x - z)) * t_2
	t_4 = ((x * t_1) - (z * t_1)) * t_2
	tmp = 0
	if t_4 <= -1e-13:
		tmp = t_3
	elif t_4 <= 1e+34:
		tmp = t_1 * ((x - z) * t_2)
	else:
		tmp = t_3
	return math.copysign(1.0, y) * (math.copysign(1.0, t) * tmp)

Julia

function code(x, y, z, t)
	t_1 = fmin(abs(y), abs(t))
	t_2 = fmax(abs(y), abs(t))
	t_3 = Float64(Float64(t_1 * Float64(x - z)) * t_2)
	t_4 = Float64(Float64(Float64(x * t_1) - Float64(z * t_1)) * t_2)
	tmp = 0.0
	if (t_4 <= -1e-13)
		tmp = t_3;
	elseif (t_4 <= 1e+34)
		tmp = Float64(t_1 * Float64(Float64(x - z) * t_2));
	else
		tmp = t_3;
	end
	return Float64(copysign(1.0, y) * Float64(copysign(1.0, t) * tmp))
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = min(abs(y), abs(t));
	t_2 = max(abs(y), abs(t));
	t_3 = (t_1 * (x - z)) * t_2;
	t_4 = ((x * t_1) - (z * t_1)) * t_2;
	tmp = 0.0;
	if (t_4 <= -1e-13)
		tmp = t_3;
	elseif (t_4 <= 1e+34)
		tmp = t_1 * ((x - z) * t_2);
	else
		tmp = t_3;
	end
	tmp_2 = (sign(y) * abs(1.0)) * ((sign(t) * abs(1.0)) * tmp);
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Min[N[Abs[y], $MachinePrecision], N[Abs[t], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Abs[y], $MachinePrecision], N[Abs[t], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$1 * N[(x - z), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(x * t$95$1), $MachinePrecision] - N[(z * t$95$1), $MachinePrecision]), $MachinePrecision] * t$95$2), $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$4, -1e-13], t$95$3, If[LessEqual[t$95$4, 1e+34], N[(t$95$1 * N[(N[(x - z), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision], t$95$3]]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t) < -1e-13 or 9.9999999999999995e33 < (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t)

   1. Initial program 90.5%

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

   2. Taylor expanded in y around 0

      \[\leadsto \left(y \cdot \left(x - z\right)\right) \cdot t \]
   3. Step-by-step derivation

   4. Applied rewrites 92.0%

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

   if -1e-13 < (*.f64 (-.f64 (*.f64 x y) (*.f64 z y)) t) < 9.9999999999999995e33

   1. Initial program 90.5%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

   3. Applied rewrites 92.1%

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

Alternative 2: 98.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\left|y\right|, \left|t\right|\right)\\ t_2 := \mathsf{max}\left(\left|y\right|, \left|t\right|\right)\\ \mathsf{copysign}\left(1, y\right) \cdot \left(\mathsf{copysign}\left(1, t\right) \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq 7.825399874758337 \cdot 10^{-21}:\\ \;\;\;\;t\_1 \cdot \left(\left(x - z\right) \cdot t\_2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t\_2 \cdot t\_1\right) \cdot \left(x - z\right)\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmin (fabs y) (fabs t))) (t_2 (fmax (fabs y) (fabs t))))
  (*
   (copysign 1.0 y)
   (*
    (copysign 1.0 t)
    (if (<= t_2 7.825399874758337e-21)
      (* t_1 (* (- x z) t_2))
      (* (* t_2 t_1) (- x z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmin(fabs(y), fabs(t));
	double t_2 = fmax(fabs(y), fabs(t));
	double tmp;
	if (t_2 <= 7.825399874758337e-21) {
		tmp = t_1 * ((x - z) * t_2);
	} else {
		tmp = (t_2 * t_1) * (x - z);
	}
	return copysign(1.0, y) * (copysign(1.0, t) * tmp);
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmin(Math.abs(y), Math.abs(t));
	double t_2 = fmax(Math.abs(y), Math.abs(t));
	double tmp;
	if (t_2 <= 7.825399874758337e-21) {
		tmp = t_1 * ((x - z) * t_2);
	} else {
		tmp = (t_2 * t_1) * (x - z);
	}
	return Math.copySign(1.0, y) * (Math.copySign(1.0, t) * tmp);
}

Python

def code(x, y, z, t):
	t_1 = fmin(math.fabs(y), math.fabs(t))
	t_2 = fmax(math.fabs(y), math.fabs(t))
	tmp = 0
	if t_2 <= 7.825399874758337e-21:
		tmp = t_1 * ((x - z) * t_2)
	else:
		tmp = (t_2 * t_1) * (x - z)
	return math.copysign(1.0, y) * (math.copysign(1.0, t) * tmp)

Julia

function code(x, y, z, t)
	t_1 = fmin(abs(y), abs(t))
	t_2 = fmax(abs(y), abs(t))
	tmp = 0.0
	if (t_2 <= 7.825399874758337e-21)
		tmp = Float64(t_1 * Float64(Float64(x - z) * t_2));
	else
		tmp = Float64(Float64(t_2 * t_1) * Float64(x - z));
	end
	return Float64(copysign(1.0, y) * Float64(copysign(1.0, t) * tmp))
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = min(abs(y), abs(t));
	t_2 = max(abs(y), abs(t));
	tmp = 0.0;
	if (t_2 <= 7.825399874758337e-21)
		tmp = t_1 * ((x - z) * t_2);
	else
		tmp = (t_2 * t_1) * (x - z);
	end
	tmp_2 = (sign(y) * abs(1.0)) * ((sign(t) * abs(1.0)) * tmp);
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Min[N[Abs[y], $MachinePrecision], N[Abs[t], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Abs[y], $MachinePrecision], N[Abs[t], $MachinePrecision]], $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$2, 7.825399874758337e-21], N[(t$95$1 * N[(N[(x - z), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$2 * t$95$1), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < 7.825399874758337e-21

   1. Initial program 90.5%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

   3. Applied rewrites 92.1%

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

   if 7.825399874758337e-21 < t

   1. Initial program 90.5%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

   3. Applied rewrites 92.0%

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

Alternative 3: 91.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq 2.7611275205280107 \cdot 10^{+180}:\\ \;\;\;\;y \cdot \left(\left(x - z\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= x 2.7611275205280107e+180) (* y (* (- x z) t)) (* t (* x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 2.7611275205280107e+180) {
		tmp = y * ((x - z) * t);
	} else {
		tmp = t * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= 2.7611275205280107d+180) then
        tmp = y * ((x - z) * t)
    else
        tmp = t * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= 2.7611275205280107e+180) {
		tmp = y * ((x - z) * t);
	} else {
		tmp = t * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= 2.7611275205280107e+180:
		tmp = y * ((x - z) * t)
	else:
		tmp = t * (x * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= 2.7611275205280107e+180)
		tmp = Float64(y * Float64(Float64(x - z) * t));
	else
		tmp = Float64(t * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= 2.7611275205280107e+180)
		tmp = y * ((x - z) * t);
	else
		tmp = t * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, 2.7611275205280107e+180], N[(y * N[(N[(x - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET tmp = IF (x <= (2761127520528010725143187158635350542126058317478749032429697251553016806515811491581073856237179998103849536393422360095080879370993818931168039324562157286764221760023357204463616)) THEN (y * ((x - z) * t)) ELSE (t * (x * y)) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < 2.7611275205280107e180

   1. Initial program 90.5%

      \[\left(x \cdot y - z \cdot y\right) \cdot t \]
   2. Step-by-step derivation

   3. Applied rewrites 92.1%

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

   if 2.7611275205280107e180 < x

   1. Initial program 90.5%

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

   2. Taylor expanded in x around inf

      \[\leadsto t \cdot \left(x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 53.4%

      \[\leadsto t \cdot \left(x \cdot y\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 57.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\left|y\right|, \left|t\right|\right)\\ t_2 := \mathsf{max}\left(\left|y\right|, \left|t\right|\right)\\ \mathsf{copysign}\left(1, y\right) \cdot \left(\mathsf{copysign}\left(1, t\right) \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq 1.650261910233758 \cdot 10^{+70}:\\ \;\;\;\;t\_1 \cdot \left(t\_2 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t\_2 \cdot t\_1\right)\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmin (fabs y) (fabs t))) (t_2 (fmax (fabs y) (fabs t))))
  (*
   (copysign 1.0 y)
   (*
    (copysign 1.0 t)
    (if (<= t_2 1.650261910233758e+70)
      (* t_1 (* t_2 x))
      (* x (* t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmin(fabs(y), fabs(t));
	double t_2 = fmax(fabs(y), fabs(t));
	double tmp;
	if (t_2 <= 1.650261910233758e+70) {
		tmp = t_1 * (t_2 * x);
	} else {
		tmp = x * (t_2 * t_1);
	}
	return copysign(1.0, y) * (copysign(1.0, t) * tmp);
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmin(Math.abs(y), Math.abs(t));
	double t_2 = fmax(Math.abs(y), Math.abs(t));
	double tmp;
	if (t_2 <= 1.650261910233758e+70) {
		tmp = t_1 * (t_2 * x);
	} else {
		tmp = x * (t_2 * t_1);
	}
	return Math.copySign(1.0, y) * (Math.copySign(1.0, t) * tmp);
}

Python

def code(x, y, z, t):
	t_1 = fmin(math.fabs(y), math.fabs(t))
	t_2 = fmax(math.fabs(y), math.fabs(t))
	tmp = 0
	if t_2 <= 1.650261910233758e+70:
		tmp = t_1 * (t_2 * x)
	else:
		tmp = x * (t_2 * t_1)
	return math.copysign(1.0, y) * (math.copysign(1.0, t) * tmp)

Julia

function code(x, y, z, t)
	t_1 = fmin(abs(y), abs(t))
	t_2 = fmax(abs(y), abs(t))
	tmp = 0.0
	if (t_2 <= 1.650261910233758e+70)
		tmp = Float64(t_1 * Float64(t_2 * x));
	else
		tmp = Float64(x * Float64(t_2 * t_1));
	end
	return Float64(copysign(1.0, y) * Float64(copysign(1.0, t) * tmp))
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = min(abs(y), abs(t));
	t_2 = max(abs(y), abs(t));
	tmp = 0.0;
	if (t_2 <= 1.650261910233758e+70)
		tmp = t_1 * (t_2 * x);
	else
		tmp = x * (t_2 * t_1);
	end
	tmp_2 = (sign(y) * abs(1.0)) * ((sign(t) * abs(1.0)) * tmp);
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Min[N[Abs[y], $MachinePrecision], N[Abs[t], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Abs[y], $MachinePrecision], N[Abs[t], $MachinePrecision]], $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$2, 1.650261910233758e+70], N[(t$95$1 * N[(t$95$2 * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(t$95$2 * t$95$1), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < 1.6502619102337581e70

   1. Initial program 90.5%

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

   2. Taylor expanded in x around inf

      \[\leadsto t \cdot \left(x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 53.4%

      \[\leadsto t \cdot \left(x \cdot y\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 53.3%

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

   if 1.6502619102337581e70 < t

   1. Initial program 90.5%

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

   2. Taylor expanded in x around inf

      \[\leadsto t \cdot \left(x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 53.4%

      \[\leadsto t \cdot \left(x \cdot y\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 54.5%

      \[\leadsto x \cdot \left(t \cdot y\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 57.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(\left|y\right|, \left|t\right|\right)\\ t_2 := \mathsf{max}\left(\left|y\right|, \left|t\right|\right)\\ \mathsf{copysign}\left(1, y\right) \cdot \left(\mathsf{copysign}\left(1, t\right) \cdot \begin{array}{l} \mathbf{if}\;t\_2 \leq 1.4055685462936228 \cdot 10^{-52}:\\ \;\;\;\;t\_2 \cdot \left(x \cdot t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t\_2 \cdot t\_1\right)\\ \end{array}\right) \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fmin (fabs y) (fabs t))) (t_2 (fmax (fabs y) (fabs t))))
  (*
   (copysign 1.0 y)
   (*
    (copysign 1.0 t)
    (if (<= t_2 1.4055685462936228e-52)
      (* t_2 (* x t_1))
      (* x (* t_2 t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fmin(fabs(y), fabs(t));
	double t_2 = fmax(fabs(y), fabs(t));
	double tmp;
	if (t_2 <= 1.4055685462936228e-52) {
		tmp = t_2 * (x * t_1);
	} else {
		tmp = x * (t_2 * t_1);
	}
	return copysign(1.0, y) * (copysign(1.0, t) * tmp);
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = fmin(Math.abs(y), Math.abs(t));
	double t_2 = fmax(Math.abs(y), Math.abs(t));
	double tmp;
	if (t_2 <= 1.4055685462936228e-52) {
		tmp = t_2 * (x * t_1);
	} else {
		tmp = x * (t_2 * t_1);
	}
	return Math.copySign(1.0, y) * (Math.copySign(1.0, t) * tmp);
}

Python

def code(x, y, z, t):
	t_1 = fmin(math.fabs(y), math.fabs(t))
	t_2 = fmax(math.fabs(y), math.fabs(t))
	tmp = 0
	if t_2 <= 1.4055685462936228e-52:
		tmp = t_2 * (x * t_1)
	else:
		tmp = x * (t_2 * t_1)
	return math.copysign(1.0, y) * (math.copysign(1.0, t) * tmp)

Julia

function code(x, y, z, t)
	t_1 = fmin(abs(y), abs(t))
	t_2 = fmax(abs(y), abs(t))
	tmp = 0.0
	if (t_2 <= 1.4055685462936228e-52)
		tmp = Float64(t_2 * Float64(x * t_1));
	else
		tmp = Float64(x * Float64(t_2 * t_1));
	end
	return Float64(copysign(1.0, y) * Float64(copysign(1.0, t) * tmp))
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = min(abs(y), abs(t));
	t_2 = max(abs(y), abs(t));
	tmp = 0.0;
	if (t_2 <= 1.4055685462936228e-52)
		tmp = t_2 * (x * t_1);
	else
		tmp = x * (t_2 * t_1);
	end
	tmp_2 = (sign(y) * abs(1.0)) * ((sign(t) * abs(1.0)) * tmp);
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[Min[N[Abs[y], $MachinePrecision], N[Abs[t], $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Max[N[Abs[y], $MachinePrecision], N[Abs[t], $MachinePrecision]], $MachinePrecision]}, N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[t$95$2, 1.4055685462936228e-52], N[(t$95$2 * N[(x * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x * N[(t$95$2 * t$95$1), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < 1.4055685462936228e-52

   1. Initial program 90.5%

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

   2. Taylor expanded in x around inf

      \[\leadsto t \cdot \left(x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 53.4%

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

   if 1.4055685462936228e-52 < t

   1. Initial program 90.5%

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

   2. Taylor expanded in x around inf

      \[\leadsto t \cdot \left(x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 53.4%

      \[\leadsto t \cdot \left(x \cdot y\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 54.5%

      \[\leadsto x \cdot \left(t \cdot y\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 53.4% accurate, 1.8× speedup

Math

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

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (* t (* x y)))

C

double code(double x, double y, double z, double t) {
	return t * (x * y);
}

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t * (x * y)
end function

Java

public static double code(double x, double y, double z, double t) {
	return t * (x * y);
}

Python

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

Julia

function code(x, y, z, t)
	return Float64(t * Float64(x * y))
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(t * N[(x * y), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	t * (x * y)
END code

Derivation

1. Initial program 90.5%

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

2. Taylor expanded in x around inf

   \[\leadsto t \cdot \left(x \cdot y\right) \]
3. Step-by-step derivation

4. Applied rewrites 53.4%

   \[\leadsto t \cdot \left(x \cdot y\right) \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z t)
  :name "Linear.Projection:inverseInfinitePerspective from linear-1.19.1.3"
  :precision binary64
  (* (- (* x y) (* z y)) t))