Data.Colour.Matrix:inverse from colour-2.3.3, B

Percentage Accurate: 91.2% → 97.0%

Time: 3.1s

Alternatives: 11

Speedup: 0.5×

• 71.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    code = ((x * y) - (z * t)) / a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

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

Initial Program: 91.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    code = ((x * y) - (z * t)) / a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

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

Alternative 1: 97.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \frac{\mathsf{min}\left(z, t\right)}{a} \cdot \left(-\mathsf{max}\left(z, t\right)\right)\\ t_2 := \mathsf{min}\left(x, y\right) \cdot \mathsf{max}\left(x, y\right) - \mathsf{min}\left(z, t\right) \cdot \mathsf{max}\left(z, t\right)\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+304}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{max}\left(x, y\right), \frac{\mathsf{min}\left(x, y\right)}{a}, t\_1\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+168}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{min}\left(x, y\right), \mathsf{max}\left(x, y\right), -\mathsf{max}\left(z, t\right) \cdot \mathsf{min}\left(z, t\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{min}\left(x, y\right), \frac{\mathsf{max}\left(x, y\right)}{a}, t\_1\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* (/ (fmin z t) a) (- (fmax z t))))
       (t_2 (- (* (fmin x y) (fmax x y)) (* (fmin z t) (fmax z t)))))
  (if (<= t_2 -2e+304)
    (fma (fmax x y) (/ (fmin x y) a) t_1)
    (if (<= t_2 2e+168)
      (/ (fma (fmin x y) (fmax x y) (- (* (fmax z t) (fmin z t)))) a)
      (fma (fmin x y) (/ (fmax x y) a) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (fmin(z, t) / a) * -fmax(z, t);
	double t_2 = (fmin(x, y) * fmax(x, y)) - (fmin(z, t) * fmax(z, t));
	double tmp;
	if (t_2 <= -2e+304) {
		tmp = fma(fmax(x, y), (fmin(x, y) / a), t_1);
	} else if (t_2 <= 2e+168) {
		tmp = fma(fmin(x, y), fmax(x, y), -(fmax(z, t) * fmin(z, t))) / a;
	} else {
		tmp = fma(fmin(x, y), (fmax(x, y) / a), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(fmin(z, t) / a) * Float64(-fmax(z, t)))
	t_2 = Float64(Float64(fmin(x, y) * fmax(x, y)) - Float64(fmin(z, t) * fmax(z, t)))
	tmp = 0.0
	if (t_2 <= -2e+304)
		tmp = fma(fmax(x, y), Float64(fmin(x, y) / a), t_1);
	elseif (t_2 <= 2e+168)
		tmp = Float64(fma(fmin(x, y), fmax(x, y), Float64(-Float64(fmax(z, t) * fmin(z, t)))) / a);
	else
		tmp = fma(fmin(x, y), Float64(fmax(x, y) / a), t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[Min[z, t], $MachinePrecision] / a), $MachinePrecision] * (-N[Max[z, t], $MachinePrecision])), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[Min[x, y], $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision] - N[(N[Min[z, t], $MachinePrecision] * N[Max[z, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+304], N[(N[Max[x, y], $MachinePrecision] * N[(N[Min[x, y], $MachinePrecision] / a), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 2e+168], N[(N[(N[Min[x, y], $MachinePrecision] * N[Max[x, y], $MachinePrecision] + (-N[(N[Max[z, t], $MachinePrecision] * N[Min[z, t], $MachinePrecision]), $MachinePrecision])), $MachinePrecision] / a), $MachinePrecision], N[(N[Min[x, y], $MachinePrecision] * N[(N[Max[x, y], $MachinePrecision] / a), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET tmp = IF (z < t) THEN z ELSE t ENDIF IN
	LET tmp_1 = IF (z > t) THEN z ELSE t ENDIF IN
	LET t_1 = ((tmp / a) * (- tmp_1)) IN
		LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
		LET tmp_3 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_4 = IF (z < t) THEN z ELSE t ENDIF IN
		LET tmp_5 = IF (z > t) THEN z ELSE t ENDIF IN
		LET t_2 = ((tmp_2 * tmp_3) - (tmp_4 * tmp_5)) IN
			LET tmp_9 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_10 = IF (x < y) THEN x ELSE y ENDIF IN
			LET tmp_16 = IF (x < y) THEN x ELSE y ENDIF IN
			LET tmp_17 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_18 = IF (z > t) THEN z ELSE t ENDIF IN
			LET tmp_19 = IF (z < t) THEN z ELSE t ENDIF IN
			LET tmp_20 = IF (x < y) THEN x ELSE y ENDIF IN
			LET tmp_21 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_15 = IF (t_2 <= (1999999999999999867720989669485949124743900432860663037223385644615401293399207295251384865191691894341829109199397042951078761626889625586558917010807457234988770000896)) THEN (((tmp_16 * tmp_17) + (- (tmp_18 * tmp_19))) / a) ELSE ((tmp_20 * (tmp_21 / a)) + t_1) ENDIF IN
			LET tmp_8 = IF (t_2 <= (-19999999999999998785071050110729243720080574440234649906381543142646409126026467805686618514881015496873712236112324345157434387485272061060471597681733765549974602883364022082135420506324881811687439605097103198153279365101643665319098224539215899610692069837325144812815208761691919724149808696276287488)) THEN ((tmp_9 * (tmp_10 / a)) + t_1) ELSE tmp_15 ENDIF IN
	tmp_8
END code

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -1.9999999999999999e304

   1. Initial program 91.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Step-by-step derivation

   3. Applied rewrites 87.9%

      \[\leadsto \mathsf{fma}\left(y, \frac{x}{a}, \frac{z}{a} \cdot \left(-t\right)\right) \]

   if -1.9999999999999999e304 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.9999999999999999e168

   1. Initial program 91.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Step-by-step derivation

   3. Applied rewrites 91.4%

      \[\leadsto \frac{\mathsf{fma}\left(x, y, -t \cdot z\right)}{a} \]

   if 1.9999999999999999e168 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 91.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Step-by-step derivation

   3. Applied rewrites 88.1%

      \[\leadsto \mathsf{fma}\left(x, \frac{y}{a}, \frac{z}{a} \cdot \left(-t\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 96.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(x, y\right) \cdot \mathsf{max}\left(x, y\right) - \mathsf{min}\left(z, t\right) \cdot \mathsf{max}\left(z, t\right)\\ t_2 := \frac{\mathsf{min}\left(z, t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+304}:\\ \;\;\;\;\frac{\mathsf{min}\left(x, y\right)}{a} \cdot \mathsf{max}\left(x, y\right) - t\_2 \cdot \mathsf{max}\left(z, t\right)\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+168}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{min}\left(x, y\right), \mathsf{max}\left(x, y\right), -\mathsf{max}\left(z, t\right) \cdot \mathsf{min}\left(z, t\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{min}\left(x, y\right), \frac{\mathsf{max}\left(x, y\right)}{a}, t\_2 \cdot \left(-\mathsf{max}\left(z, t\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (- (* (fmin x y) (fmax x y)) (* (fmin z t) (fmax z t))))
       (t_2 (/ (fmin z t) a)))
  (if (<= t_1 -2e+304)
    (- (* (/ (fmin x y) a) (fmax x y)) (* t_2 (fmax z t)))
    (if (<= t_1 2e+168)
      (/ (fma (fmin x y) (fmax x y) (- (* (fmax z t) (fmin z t)))) a)
      (fma (fmin x y) (/ (fmax x y) a) (* t_2 (- (fmax z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (fmin(x, y) * fmax(x, y)) - (fmin(z, t) * fmax(z, t));
	double t_2 = fmin(z, t) / a;
	double tmp;
	if (t_1 <= -2e+304) {
		tmp = ((fmin(x, y) / a) * fmax(x, y)) - (t_2 * fmax(z, t));
	} else if (t_1 <= 2e+168) {
		tmp = fma(fmin(x, y), fmax(x, y), -(fmax(z, t) * fmin(z, t))) / a;
	} else {
		tmp = fma(fmin(x, y), (fmax(x, y) / a), (t_2 * -fmax(z, t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(fmin(x, y) * fmax(x, y)) - Float64(fmin(z, t) * fmax(z, t)))
	t_2 = Float64(fmin(z, t) / a)
	tmp = 0.0
	if (t_1 <= -2e+304)
		tmp = Float64(Float64(Float64(fmin(x, y) / a) * fmax(x, y)) - Float64(t_2 * fmax(z, t)));
	elseif (t_1 <= 2e+168)
		tmp = Float64(fma(fmin(x, y), fmax(x, y), Float64(-Float64(fmax(z, t) * fmin(z, t)))) / a);
	else
		tmp = fma(fmin(x, y), Float64(fmax(x, y) / a), Float64(t_2 * Float64(-fmax(z, t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[Min[x, y], $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision] - N[(N[Min[z, t], $MachinePrecision] * N[Max[z, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Min[z, t], $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+304], N[(N[(N[(N[Min[x, y], $MachinePrecision] / a), $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision] - N[(t$95$2 * N[Max[z, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+168], N[(N[(N[Min[x, y], $MachinePrecision] * N[Max[x, y], $MachinePrecision] + (-N[(N[Max[z, t], $MachinePrecision] * N[Min[z, t], $MachinePrecision]), $MachinePrecision])), $MachinePrecision] / a), $MachinePrecision], N[(N[Min[x, y], $MachinePrecision] * N[(N[Max[x, y], $MachinePrecision] / a), $MachinePrecision] + N[(t$95$2 * (-N[Max[z, t], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET tmp = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (x > y) THEN x ELSE y ENDIF IN
	LET tmp_2 = IF (z < t) THEN z ELSE t ENDIF IN
	LET tmp_3 = IF (z > t) THEN z ELSE t ENDIF IN
	LET t_1 = ((tmp * tmp_1) - (tmp_2 * tmp_3)) IN
		LET tmp_4 = IF (z < t) THEN z ELSE t ENDIF IN
		LET t_2 = (tmp_4 / a) IN
			LET tmp_9 = IF (x < y) THEN x ELSE y ENDIF IN
			LET tmp_10 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_11 = IF (z > t) THEN z ELSE t ENDIF IN
			LET tmp_17 = IF (x < y) THEN x ELSE y ENDIF IN
			LET tmp_18 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_19 = IF (z > t) THEN z ELSE t ENDIF IN
			LET tmp_20 = IF (z < t) THEN z ELSE t ENDIF IN
			LET tmp_21 = IF (x < y) THEN x ELSE y ENDIF IN
			LET tmp_22 = IF (x > y) THEN x ELSE y ENDIF IN
			LET tmp_23 = IF (z > t) THEN z ELSE t ENDIF IN
			LET tmp_16 = IF (t_1 <= (1999999999999999867720989669485949124743900432860663037223385644615401293399207295251384865191691894341829109199397042951078761626889625586558917010807457234988770000896)) THEN (((tmp_17 * tmp_18) + (- (tmp_19 * tmp_20))) / a) ELSE ((tmp_21 * (tmp_22 / a)) + (t_2 * (- tmp_23))) ENDIF IN
			LET tmp_8 = IF (t_1 <= (-19999999999999998785071050110729243720080574440234649906381543142646409126026467805686618514881015496873712236112324345157434387485272061060471597681733765549974602883364022082135420506324881811687439605097103198153279365101643665319098224539215899610692069837325144812815208761691919724149808696276287488)) THEN (((tmp_9 / a) * tmp_10) - (t_2 * tmp_11)) ELSE tmp_16 ENDIF IN
	tmp_8
END code

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -1.9999999999999999e304

   1. Initial program 91.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Step-by-step derivation

   3. Applied rewrites 88.1%

      \[\leadsto \mathsf{fma}\left(x, \frac{y}{a}, \frac{z}{a} \cdot \left(-t\right)\right) \]
   4. Step-by-step derivation

   5. Applied rewrites 87.3%

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

   if -1.9999999999999999e304 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.9999999999999999e168

   1. Initial program 91.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Step-by-step derivation

   3. Applied rewrites 91.4%

      \[\leadsto \frac{\mathsf{fma}\left(x, y, -t \cdot z\right)}{a} \]

   if 1.9999999999999999e168 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 91.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Step-by-step derivation

   3. Applied rewrites 88.1%

      \[\leadsto \mathsf{fma}\left(x, \frac{y}{a}, \frac{z}{a} \cdot \left(-t\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 95.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := x \cdot \frac{y}{a}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+270}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, -t \cdot z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* x (/ y a))))
  (if (<= (* x y) -2e+304)
    t_1
    (if (<= (* x y) 2e+270) (/ (fma x y (- (* t z))) a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / a);
	double tmp;
	if ((x * y) <= -2e+304) {
		tmp = t_1;
	} else if ((x * y) <= 2e+270) {
		tmp = fma(x, y, -(t * z)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / a))
	tmp = 0.0
	if (Float64(x * y) <= -2e+304)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e+270)
		tmp = Float64(fma(x, y, Float64(-Float64(t * z))) / a);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+304], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e+270], N[(N[(x * y + (-N[(t * z), $MachinePrecision])), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = (x * (y / a)) IN
		LET tmp_1 = IF ((x * y) <= (2000000000000000093507637770912255978379210862660820573682729745488032878789111789220736516360606673878153776268089900578652336369324860662948626554833959632774778559729275871173995040476704622045320156587457342770385866522124606869505276053562755097483935769278566891520)) THEN (((x * y) + (- (t * z))) / a) ELSE t_1 ENDIF IN
		LET tmp = IF ((x * y) <= (-19999999999999998785071050110729243720080574440234649906381543142646409126026467805686618514881015496873712236112324345157434387485272061060471597681733765549974602883364022082135420506324881811687439605097103198153279365101643665319098224539215899610692069837325144812815208761691919724149808696276287488)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.9999999999999999e304 or 2.0000000000000001e270 < (*.f64 x y)

   1. Initial program 91.2%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot y}{a} \]
   3. Step-by-step derivation

   4. Applied rewrites 49.6%

      \[\leadsto \frac{x \cdot y}{a} \]
   5. Step-by-step derivation

   6. Applied rewrites 50.6%

      \[\leadsto x \cdot \frac{y}{a} \]

   if -1.9999999999999999e304 < (*.f64 x y) < 2.0000000000000001e270

   1. Initial program 91.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Step-by-step derivation

   3. Applied rewrites 91.4%

      \[\leadsto \frac{\mathsf{fma}\left(x, y, -t \cdot z\right)}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 95.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := x \cdot \frac{y}{a}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+270}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* x (/ y a))))
  (if (<= (* x y) -2e+304)
    t_1
    (if (<= (* x y) 2e+270) (/ (- (* x y) (* z t)) a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / a);
	double tmp;
	if ((x * y) <= -2e+304) {
		tmp = t_1;
	} else if ((x * y) <= 2e+270) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y / a)
    if ((x * y) <= (-2d+304)) then
        tmp = t_1
    else if ((x * y) <= 2d+270) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / a);
	double tmp;
	if ((x * y) <= -2e+304) {
		tmp = t_1;
	} else if ((x * y) <= 2e+270) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (y / a)
	tmp = 0
	if (x * y) <= -2e+304:
		tmp = t_1
	elif (x * y) <= 2e+270:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / a))
	tmp = 0.0
	if (Float64(x * y) <= -2e+304)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e+270)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / a);
	tmp = 0.0;
	if ((x * y) <= -2e+304)
		tmp = t_1;
	elseif ((x * y) <= 2e+270)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+304], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e+270], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = (x * (y / a)) IN
		LET tmp_1 = IF ((x * y) <= (2000000000000000093507637770912255978379210862660820573682729745488032878789111789220736516360606673878153776268089900578652336369324860662948626554833959632774778559729275871173995040476704622045320156587457342770385866522124606869505276053562755097483935769278566891520)) THEN (((x * y) - (z * t)) / a) ELSE t_1 ENDIF IN
		LET tmp = IF ((x * y) <= (-19999999999999998785071050110729243720080574440234649906381543142646409126026467805686618514881015496873712236112324345157434387485272061060471597681733765549974602883364022082135420506324881811687439605097103198153279365101643665319098224539215899610692069837325144812815208761691919724149808696276287488)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -1.9999999999999999e304 or 2.0000000000000001e270 < (*.f64 x y)

   1. Initial program 91.2%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot y}{a} \]
   3. Step-by-step derivation

   4. Applied rewrites 49.6%

      \[\leadsto \frac{x \cdot y}{a} \]
   5. Step-by-step derivation

   6. Applied rewrites 50.6%

      \[\leadsto x \cdot \frac{y}{a} \]

   if -1.9999999999999999e304 < (*.f64 x y) < 2.0000000000000001e270

   1. Initial program 91.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 94.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\mathsf{min}\left(x, y\right) \cdot \mathsf{max}\left(x, y\right) - z \cdot t \leq -2 \cdot 10^{+304}:\\ \;\;\;\;\frac{\mathsf{min}\left(x, y\right)}{a} \cdot \mathsf{max}\left(x, y\right) - \frac{z}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{min}\left(x, y\right), \mathsf{max}\left(x, y\right), -t \cdot z\right)}{a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= (- (* (fmin x y) (fmax x y)) (* z t)) -2e+304)
  (- (* (/ (fmin x y) a) (fmax x y)) (* (/ z a) t))
  (/ (fma (fmin x y) (fmax x y) (- (* t z))) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((fmin(x, y) * fmax(x, y)) - (z * t)) <= -2e+304) {
		tmp = ((fmin(x, y) / a) * fmax(x, y)) - ((z / a) * t);
	} else {
		tmp = fma(fmin(x, y), fmax(x, y), -(t * z)) / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(fmin(x, y) * fmax(x, y)) - Float64(z * t)) <= -2e+304)
		tmp = Float64(Float64(Float64(fmin(x, y) / a) * fmax(x, y)) - Float64(Float64(z / a) * t));
	else
		tmp = Float64(fma(fmin(x, y), fmax(x, y), Float64(-Float64(t * z))) / a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(N[Min[x, y], $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision], -2e+304], N[(N[(N[(N[Min[x, y], $MachinePrecision] / a), $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision] - N[(N[(z / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(N[Min[x, y], $MachinePrecision] * N[Max[x, y], $MachinePrecision] + (-N[(t * z), $MachinePrecision])), $MachinePrecision] / a), $MachinePrecision]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET tmp_3 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_4 = IF (x > y) THEN x ELSE y ENDIF IN
	LET tmp_5 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
	LET tmp_7 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_8 = IF (x > y) THEN x ELSE y ENDIF IN
	LET tmp_2 = IF (((tmp_3 * tmp_4) - (z * t)) <= (-19999999999999998785071050110729243720080574440234649906381543142646409126026467805686618514881015496873712236112324345157434387485272061060471597681733765549974602883364022082135420506324881811687439605097103198153279365101643665319098224539215899610692069837325144812815208761691919724149808696276287488)) THEN (((tmp_5 / a) * tmp_6) - ((z / a) * t)) ELSE (((tmp_7 * tmp_8) + (- (t * z))) / a) ENDIF IN
	tmp_2
END code

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -1.9999999999999999e304

   1. Initial program 91.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Step-by-step derivation

   3. Applied rewrites 88.1%

      \[\leadsto \mathsf{fma}\left(x, \frac{y}{a}, \frac{z}{a} \cdot \left(-t\right)\right) \]
   4. Step-by-step derivation

   5. Applied rewrites 87.3%

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

   if -1.9999999999999999e304 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 91.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Step-by-step derivation

   3. Applied rewrites 91.4%

      \[\leadsto \frac{\mathsf{fma}\left(x, y, -t \cdot z\right)}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 93.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \cdot y - \mathsf{min}\left(z, t\right) \cdot \mathsf{max}\left(z, t\right) \leq -2 \cdot 10^{+304}:\\ \;\;\;\;\frac{x \cdot \frac{y}{\mathsf{min}\left(z, t\right)} - \mathsf{max}\left(z, t\right)}{a} \cdot \mathsf{min}\left(z, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, -\mathsf{max}\left(z, t\right) \cdot \mathsf{min}\left(z, t\right)\right)}{a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= (- (* x y) (* (fmin z t) (fmax z t))) -2e+304)
  (* (/ (- (* x (/ y (fmin z t))) (fmax z t)) a) (fmin z t))
  (/ (fma x y (- (* (fmax z t) (fmin z t)))) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((x * y) - (fmin(z, t) * fmax(z, t))) <= -2e+304) {
		tmp = (((x * (y / fmin(z, t))) - fmax(z, t)) / a) * fmin(z, t);
	} else {
		tmp = fma(x, y, -(fmax(z, t) * fmin(z, t))) / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(x * y) - Float64(fmin(z, t) * fmax(z, t))) <= -2e+304)
		tmp = Float64(Float64(Float64(Float64(x * Float64(y / fmin(z, t))) - fmax(z, t)) / a) * fmin(z, t));
	else
		tmp = Float64(fma(x, y, Float64(-Float64(fmax(z, t) * fmin(z, t)))) / a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(x * y), $MachinePrecision] - N[(N[Min[z, t], $MachinePrecision] * N[Max[z, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -2e+304], N[(N[(N[(N[(x * N[(y / N[Min[z, t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Max[z, t], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * N[Min[z, t], $MachinePrecision]), $MachinePrecision], N[(N[(x * y + (-N[(N[Max[z, t], $MachinePrecision] * N[Min[z, t], $MachinePrecision]), $MachinePrecision])), $MachinePrecision] / a), $MachinePrecision]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET tmp_4 = IF (z < t) THEN z ELSE t ENDIF IN
	LET tmp_5 = IF (z > t) THEN z ELSE t ENDIF IN
	LET tmp_6 = IF (z < t) THEN z ELSE t ENDIF IN
	LET tmp_7 = IF (z > t) THEN z ELSE t ENDIF IN
	LET tmp_8 = IF (z < t) THEN z ELSE t ENDIF IN
	LET tmp_9 = IF (z > t) THEN z ELSE t ENDIF IN
	LET tmp_10 = IF (z < t) THEN z ELSE t ENDIF IN
	LET tmp_3 = IF (((x * y) - (tmp_4 * tmp_5)) <= (-19999999999999998785071050110729243720080574440234649906381543142646409126026467805686618514881015496873712236112324345157434387485272061060471597681733765549974602883364022082135420506324881811687439605097103198153279365101643665319098224539215899610692069837325144812815208761691919724149808696276287488)) THEN ((((x * (y / tmp_6)) - tmp_7) / a) * tmp_8) ELSE (((x * y) + (- (tmp_9 * tmp_10))) / a) ENDIF IN
	tmp_3
END code

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -1.9999999999999999e304

   1. Initial program 91.2%

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

   2. Taylor expanded in z around inf

      \[\leadsto z \cdot \left(-1 \cdot \frac{t}{a} + \frac{x \cdot y}{a \cdot z}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 79.6%

      \[\leadsto z \cdot \mathsf{fma}\left(-1, \frac{t}{a}, \frac{x \cdot y}{a \cdot z}\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 81.8%

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

   if -1.9999999999999999e304 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 91.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Step-by-step derivation

   3. Applied rewrites 91.4%

      \[\leadsto \frac{\mathsf{fma}\left(x, y, -t \cdot z\right)}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 71.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(x, y\right) \cdot \mathsf{max}\left(x, y\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+42}:\\ \;\;\;\;\frac{\mathsf{min}\left(x, y\right)}{a} \cdot \mathsf{max}\left(x, y\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-150}:\\ \;\;\;\;\frac{\left(-z\right) \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(x, y\right)}{\frac{a}{\mathsf{min}\left(x, y\right)}}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* (fmin x y) (fmax x y))))
  (if (<= t_1 -4e+42)
    (* (/ (fmin x y) a) (fmax x y))
    (if (<= t_1 1e-150)
      (/ (* (- z) t) a)
      (/ (fmax x y) (/ a (fmin x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fmin(x, y) * fmax(x, y);
	double tmp;
	if (t_1 <= -4e+42) {
		tmp = (fmin(x, y) / a) * fmax(x, y);
	} else if (t_1 <= 1e-150) {
		tmp = (-z * t) / a;
	} else {
		tmp = fmax(x, y) / (a / fmin(x, y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = fmin(x, y) * fmax(x, y)
    if (t_1 <= (-4d+42)) then
        tmp = (fmin(x, y) / a) * fmax(x, y)
    else if (t_1 <= 1d-150) then
        tmp = (-z * t) / a
    else
        tmp = fmax(x, y) / (a / fmin(x, y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = fmin(x, y) * fmax(x, y);
	double tmp;
	if (t_1 <= -4e+42) {
		tmp = (fmin(x, y) / a) * fmax(x, y);
	} else if (t_1 <= 1e-150) {
		tmp = (-z * t) / a;
	} else {
		tmp = fmax(x, y) / (a / fmin(x, y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = fmin(x, y) * fmax(x, y)
	tmp = 0
	if t_1 <= -4e+42:
		tmp = (fmin(x, y) / a) * fmax(x, y)
	elif t_1 <= 1e-150:
		tmp = (-z * t) / a
	else:
		tmp = fmax(x, y) / (a / fmin(x, y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(fmin(x, y) * fmax(x, y))
	tmp = 0.0
	if (t_1 <= -4e+42)
		tmp = Float64(Float64(fmin(x, y) / a) * fmax(x, y));
	elseif (t_1 <= 1e-150)
		tmp = Float64(Float64(Float64(-z) * t) / a);
	else
		tmp = Float64(fmax(x, y) / Float64(a / fmin(x, y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = min(x, y) * max(x, y);
	tmp = 0.0;
	if (t_1 <= -4e+42)
		tmp = (min(x, y) / a) * max(x, y);
	elseif (t_1 <= 1e-150)
		tmp = (-z * t) / a;
	else
		tmp = max(x, y) / (a / min(x, y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[Min[x, y], $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+42], N[(N[(N[Min[x, y], $MachinePrecision] / a), $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-150], N[(N[((-z) * t), $MachinePrecision] / a), $MachinePrecision], N[(N[Max[x, y], $MachinePrecision] / N[(a / N[Min[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET tmp = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (x > y) THEN x ELSE y ENDIF IN
	LET t_1 = (tmp * tmp_1) IN
		LET tmp_5 = IF (x < y) THEN x ELSE y ENDIF IN
		LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_8 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_9 = IF (x < y) THEN x ELSE y ENDIF IN
		LET tmp_7 = IF (t_1 <= (100000000000000000629535823217296399721087933638737788046497104705520498254179321138129170532890503704405994963230580103067513751160865633202829165130023467457014156090990295018891776024374768764400416020911642797793722954229019546998397332759107067859731816710377579229973684101427943008113522349948331994414341250592547994858646301304824078966967156534016215353732892623384032049216330051422119140625e-551)) THEN (((- z) * t) / a) ELSE (tmp_8 / (a / tmp_9)) ENDIF IN
		LET tmp_4 = IF (t_1 <= (-4000000000000000179542850712303667142197248)) THEN ((tmp_5 / a) * tmp_6) ELSE tmp_7 ENDIF IN
	tmp_4
END code

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.0000000000000002e42

   1. Initial program 91.2%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot y}{a} \]
   3. Step-by-step derivation

   4. Applied rewrites 49.6%

      \[\leadsto \frac{x \cdot y}{a} \]
   5. Step-by-step derivation

   6. Applied rewrites 50.6%

      \[\leadsto \frac{x}{a} \cdot y \]

   if -4.0000000000000002e42 < (*.f64 x y) < 1e-150

   1. Initial program 91.2%

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

   2. Taylor expanded in x around 0

      \[\leadsto \frac{-1 \cdot \left(t \cdot z\right)}{a} \]
   3. Step-by-step derivation

   4. Applied rewrites 51.3%

      \[\leadsto \frac{-1 \cdot \left(t \cdot z\right)}{a} \]
   5. Step-by-step derivation

   6. Applied rewrites 51.3%

      \[\leadsto \frac{\left(-z\right) \cdot t}{a} \]

   if 1e-150 < (*.f64 x y)

   1. Initial program 91.2%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot y}{a} \]
   3. Step-by-step derivation

   4. Applied rewrites 49.6%

      \[\leadsto \frac{x \cdot y}{a} \]
   5. Step-by-step derivation

   6. Applied rewrites 50.6%

      \[\leadsto \frac{x}{a} \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 50.5%

      \[\leadsto \frac{1}{\frac{a}{x}} \cdot y \]
   9. Step-by-step derivation

   10. Applied rewrites 50.6%

       \[\leadsto \frac{y}{\frac{a}{x}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 70.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(x, y\right) \cdot \mathsf{max}\left(x, y\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+42}:\\ \;\;\;\;\frac{\mathsf{min}\left(x, y\right)}{a} \cdot \mathsf{max}\left(x, y\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-81}:\\ \;\;\;\;\frac{-\mathsf{max}\left(z, t\right)}{a} \cdot \mathsf{min}\left(z, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{max}\left(x, y\right)}{\frac{a}{\mathsf{min}\left(x, y\right)}}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* (fmin x y) (fmax x y))))
  (if (<= t_1 -4e+42)
    (* (/ (fmin x y) a) (fmax x y))
    (if (<= t_1 5e-81)
      (* (/ (- (fmax z t)) a) (fmin z t))
      (/ (fmax x y) (/ a (fmin x y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fmin(x, y) * fmax(x, y);
	double tmp;
	if (t_1 <= -4e+42) {
		tmp = (fmin(x, y) / a) * fmax(x, y);
	} else if (t_1 <= 5e-81) {
		tmp = (-fmax(z, t) / a) * fmin(z, t);
	} else {
		tmp = fmax(x, y) / (a / fmin(x, y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = fmin(x, y) * fmax(x, y)
    if (t_1 <= (-4d+42)) then
        tmp = (fmin(x, y) / a) * fmax(x, y)
    else if (t_1 <= 5d-81) then
        tmp = (-fmax(z, t) / a) * fmin(z, t)
    else
        tmp = fmax(x, y) / (a / fmin(x, y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = fmin(x, y) * fmax(x, y);
	double tmp;
	if (t_1 <= -4e+42) {
		tmp = (fmin(x, y) / a) * fmax(x, y);
	} else if (t_1 <= 5e-81) {
		tmp = (-fmax(z, t) / a) * fmin(z, t);
	} else {
		tmp = fmax(x, y) / (a / fmin(x, y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = fmin(x, y) * fmax(x, y)
	tmp = 0
	if t_1 <= -4e+42:
		tmp = (fmin(x, y) / a) * fmax(x, y)
	elif t_1 <= 5e-81:
		tmp = (-fmax(z, t) / a) * fmin(z, t)
	else:
		tmp = fmax(x, y) / (a / fmin(x, y))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(fmin(x, y) * fmax(x, y))
	tmp = 0.0
	if (t_1 <= -4e+42)
		tmp = Float64(Float64(fmin(x, y) / a) * fmax(x, y));
	elseif (t_1 <= 5e-81)
		tmp = Float64(Float64(Float64(-fmax(z, t)) / a) * fmin(z, t));
	else
		tmp = Float64(fmax(x, y) / Float64(a / fmin(x, y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = min(x, y) * max(x, y);
	tmp = 0.0;
	if (t_1 <= -4e+42)
		tmp = (min(x, y) / a) * max(x, y);
	elseif (t_1 <= 5e-81)
		tmp = (-max(z, t) / a) * min(z, t);
	else
		tmp = max(x, y) / (a / min(x, y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[Min[x, y], $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+42], N[(N[(N[Min[x, y], $MachinePrecision] / a), $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-81], N[(N[((-N[Max[z, t], $MachinePrecision]) / a), $MachinePrecision] * N[Min[z, t], $MachinePrecision]), $MachinePrecision], N[(N[Max[x, y], $MachinePrecision] / N[(a / N[Min[x, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET tmp = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (x > y) THEN x ELSE y ENDIF IN
	LET t_1 = (tmp * tmp_1) IN
		LET tmp_5 = IF (x < y) THEN x ELSE y ENDIF IN
		LET tmp_6 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_10 = IF (z > t) THEN z ELSE t ENDIF IN
		LET tmp_11 = IF (z < t) THEN z ELSE t ENDIF IN
		LET tmp_12 = IF (x > y) THEN x ELSE y ENDIF IN
		LET tmp_13 = IF (x < y) THEN x ELSE y ENDIF IN
		LET tmp_9 = IF (t_1 <= (49999999999999998071265875669377878796566773716936161200192095480366846040605233681099249956642833940716372505901801459595524545533008019196712992904908751668794919697705868294358289954628420535451792383607738656792207621037960052490234375e-319)) THEN (((- tmp_10) / a) * tmp_11) ELSE (tmp_12 / (a / tmp_13)) ENDIF IN
		LET tmp_4 = IF (t_1 <= (-4000000000000000179542850712303667142197248)) THEN ((tmp_5 / a) * tmp_6) ELSE tmp_9 ENDIF IN
	tmp_4
END code

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.0000000000000002e42

   1. Initial program 91.2%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot y}{a} \]
   3. Step-by-step derivation

   4. Applied rewrites 49.6%

      \[\leadsto \frac{x \cdot y}{a} \]
   5. Step-by-step derivation

   6. Applied rewrites 50.6%

      \[\leadsto \frac{x}{a} \cdot y \]

   if -4.0000000000000002e42 < (*.f64 x y) < 4.9999999999999998e-81

   1. Initial program 91.2%

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

   2. Taylor expanded in z around inf

      \[\leadsto z \cdot \left(-1 \cdot \frac{t}{a} + \frac{x \cdot y}{a \cdot z}\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 79.6%

      \[\leadsto z \cdot \mathsf{fma}\left(-1, \frac{t}{a}, \frac{x \cdot y}{a \cdot z}\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto z \cdot \left(-1 \cdot \frac{t}{a}\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 52.1%

      \[\leadsto z \cdot \left(-1 \cdot \frac{t}{a}\right) \]

   9. Applied rewrites 52.1%

      \[\leadsto \frac{-t}{a} \cdot z \]

   if 4.9999999999999998e-81 < (*.f64 x y)

   1. Initial program 91.2%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot y}{a} \]
   3. Step-by-step derivation

   4. Applied rewrites 49.6%

      \[\leadsto \frac{x \cdot y}{a} \]
   5. Step-by-step derivation

   6. Applied rewrites 50.6%

      \[\leadsto \frac{x}{a} \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 50.5%

      \[\leadsto \frac{1}{\frac{a}{x}} \cdot y \]
   9. Step-by-step derivation

   10. Applied rewrites 50.6%

       \[\leadsto \frac{y}{\frac{a}{x}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 53.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{min}\left(x, y\right) \cdot \frac{\mathsf{max}\left(x, y\right)}{a}\\ t_2 := \mathsf{min}\left(x, y\right) \cdot \mathsf{max}\left(x, y\right)\\ t_3 := t\_2 - z \cdot t\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{+222}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+270}:\\ \;\;\;\;\frac{t\_2}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* (fmin x y) (/ (fmax x y) a)))
       (t_2 (* (fmin x y) (fmax x y)))
       (t_3 (- t_2 (* z t))))
  (if (<= t_3 -1e+222) t_1 (if (<= t_3 2e+270) (/ t_2 a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fmin(x, y) * (fmax(x, y) / a);
	double t_2 = fmin(x, y) * fmax(x, y);
	double t_3 = t_2 - (z * t);
	double tmp;
	if (t_3 <= -1e+222) {
		tmp = t_1;
	} else if (t_3 <= 2e+270) {
		tmp = t_2 / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = fmin(x, y) * (fmax(x, y) / a)
    t_2 = fmin(x, y) * fmax(x, y)
    t_3 = t_2 - (z * t)
    if (t_3 <= (-1d+222)) then
        tmp = t_1
    else if (t_3 <= 2d+270) then
        tmp = t_2 / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = fmin(x, y) * (fmax(x, y) / a);
	double t_2 = fmin(x, y) * fmax(x, y);
	double t_3 = t_2 - (z * t);
	double tmp;
	if (t_3 <= -1e+222) {
		tmp = t_1;
	} else if (t_3 <= 2e+270) {
		tmp = t_2 / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = fmin(x, y) * (fmax(x, y) / a)
	t_2 = fmin(x, y) * fmax(x, y)
	t_3 = t_2 - (z * t)
	tmp = 0
	if t_3 <= -1e+222:
		tmp = t_1
	elif t_3 <= 2e+270:
		tmp = t_2 / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(fmin(x, y) * Float64(fmax(x, y) / a))
	t_2 = Float64(fmin(x, y) * fmax(x, y))
	t_3 = Float64(t_2 - Float64(z * t))
	tmp = 0.0
	if (t_3 <= -1e+222)
		tmp = t_1;
	elseif (t_3 <= 2e+270)
		tmp = Float64(t_2 / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = min(x, y) * (max(x, y) / a);
	t_2 = min(x, y) * max(x, y);
	t_3 = t_2 - (z * t);
	tmp = 0.0;
	if (t_3 <= -1e+222)
		tmp = t_1;
	elseif (t_3 <= 2e+270)
		tmp = t_2 / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[Min[x, y], $MachinePrecision] * N[(N[Max[x, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Min[x, y], $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+222], t$95$1, If[LessEqual[t$95$3, 2e+270], N[(t$95$2 / a), $MachinePrecision], t$95$1]]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET tmp = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_1 = IF (x > y) THEN x ELSE y ENDIF IN
	LET t_1 = (tmp * (tmp_1 / a)) IN
		LET tmp_2 = IF (x < y) THEN x ELSE y ENDIF IN
		LET tmp_3 = IF (x > y) THEN x ELSE y ENDIF IN
		LET t_2 = (tmp_2 * tmp_3) IN
			LET t_3 = (t_2 - (z * t)) IN
				LET tmp_5 = IF (t_3 <= (2000000000000000093507637770912255978379210862660820573682729745488032878789111789220736516360606673878153776268089900578652336369324860662948626554833959632774778559729275871173995040476704622045320156587457342770385866522124606869505276053562755097483935769278566891520)) THEN (t_2 / a) ELSE t_1 ENDIF IN
				LET tmp_4 = IF (t_3 <= (-1000000000000000046601807174820697568405085809949376861420980458018682781323086299572767712214195712321033976595985489865317261666006898091360622097492643440587430127367316221899487205895055238326459735771560242784354959360)) THEN t_1 ELSE tmp_5 ENDIF IN
	tmp_4
END code

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -1e222 or 2.0000000000000001e270 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 91.2%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot y}{a} \]
   3. Step-by-step derivation

   4. Applied rewrites 49.6%

      \[\leadsto \frac{x \cdot y}{a} \]
   5. Step-by-step derivation

   6. Applied rewrites 50.6%

      \[\leadsto x \cdot \frac{y}{a} \]

   if -1e222 < (-.f64 (*.f64 x y) (*.f64 z t)) < 2.0000000000000001e270

   1. Initial program 91.2%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot y}{a} \]
   3. Step-by-step derivation

   4. Applied rewrites 49.6%

      \[\leadsto \frac{x \cdot y}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 50.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\mathsf{min}\left(z, t\right) \leq -1.2235104707387102 \cdot 10^{-210}:\\ \;\;\;\;\frac{\mathsf{min}\left(x, y\right)}{a} \cdot \mathsf{max}\left(x, y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{min}\left(x, y\right) \cdot \frac{\mathsf{max}\left(x, y\right)}{a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= (fmin z t) -1.2235104707387102e-210)
  (* (/ (fmin x y) a) (fmax x y))
  (* (fmin x y) (/ (fmax x y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (fmin(z, t) <= -1.2235104707387102e-210) {
		tmp = (fmin(x, y) / a) * fmax(x, y);
	} else {
		tmp = fmin(x, y) * (fmax(x, y) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
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), intent (in) :: a
    real(8) :: tmp
    if (fmin(z, t) <= (-1.2235104707387102d-210)) then
        tmp = (fmin(x, y) / a) * fmax(x, y)
    else
        tmp = fmin(x, y) * (fmax(x, y) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (fmin(z, t) <= -1.2235104707387102e-210) {
		tmp = (fmin(x, y) / a) * fmax(x, y);
	} else {
		tmp = fmin(x, y) * (fmax(x, y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if fmin(z, t) <= -1.2235104707387102e-210:
		tmp = (fmin(x, y) / a) * fmax(x, y)
	else:
		tmp = fmin(x, y) * (fmax(x, y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (fmin(z, t) <= -1.2235104707387102e-210)
		tmp = Float64(Float64(fmin(x, y) / a) * fmax(x, y));
	else
		tmp = Float64(fmin(x, y) * Float64(fmax(x, y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (min(z, t) <= -1.2235104707387102e-210)
		tmp = (min(x, y) / a) * max(x, y);
	else
		tmp = min(x, y) * (max(x, y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[Min[z, t], $MachinePrecision], -1.2235104707387102e-210], N[(N[(N[Min[x, y], $MachinePrecision] / a), $MachinePrecision] * N[Max[x, y], $MachinePrecision]), $MachinePrecision], N[(N[Min[x, y], $MachinePrecision] * N[(N[Max[x, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET tmp_3 = IF (z < t) THEN z ELSE t ENDIF IN
	LET tmp_4 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_5 = IF (x > y) THEN x ELSE y ENDIF IN
	LET tmp_6 = IF (x < y) THEN x ELSE y ENDIF IN
	LET tmp_7 = IF (x > y) THEN x ELSE y ENDIF IN
	LET tmp_2 = IF (tmp_3 <= (-1223510470738710237335215425752450026384389050022156570375992696948433371613196870618918284849804357227865176231039792727356811354597623322157205818206829503267871167040665877559095803499183684743100293266796431964681213353740850242688509890107108630157588811279546267801737443245067419084993323903159017287209003516901869553151809110844687293416199402587440006871932694810354866983830306361199055504827546955858733935087747834909030592048330829131504475506484286356306807648438141087474174257309690073969310475376914837397634983062744140625e-750)) THEN ((tmp_4 / a) * tmp_5) ELSE (tmp_6 * (tmp_7 / a)) ENDIF IN
	tmp_2
END code

Derivation

1. Split input into 2 regimes

2. if z < -1.2235104707387102e-210

   1. Initial program 91.2%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot y}{a} \]
   3. Step-by-step derivation

   4. Applied rewrites 49.6%

      \[\leadsto \frac{x \cdot y}{a} \]
   5. Step-by-step derivation

   6. Applied rewrites 50.6%

      \[\leadsto \frac{x}{a} \cdot y \]

   if -1.2235104707387102e-210 < z

   1. Initial program 91.2%

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

   2. Taylor expanded in x around inf

      \[\leadsto \frac{x \cdot y}{a} \]
   3. Step-by-step derivation

   4. Applied rewrites 49.6%

      \[\leadsto \frac{x \cdot y}{a} \]
   5. Step-by-step derivation

   6. Applied rewrites 50.6%

      \[\leadsto x \cdot \frac{y}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 50.6% accurate, 1.7× speedup

Math

\[x \cdot \frac{y}{a} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

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

Derivation

1. Initial program 91.2%

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

2. Taylor expanded in x around inf

   \[\leadsto \frac{x \cdot y}{a} \]
3. Step-by-step derivation

4. Applied rewrites 49.6%

   \[\leadsto \frac{x \cdot y}{a} \]
5. Step-by-step derivation

6. Applied rewrites 50.6%

   \[\leadsto x \cdot \frac{y}{a} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64
  (/ (- (* x y) (* z t)) a))