Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, H

Percentage Accurate: 95.8% → 97.5%

Time: 4.5s

Alternatives: 18

Speedup: 0.9×

• 71.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * 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 = (x - (y / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $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 =
	(x - (y / (z * (3)))) + (t / ((z * (3)) * y))
END code

Initial Program: 95.8% accurate, 1.0× speedup

Math

\[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * 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 = (x - (y / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $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 =
	(x - (y / (z * (3)))) + (t / ((z * (3)) * y))
END code

Alternative 1: 97.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -2.462434139390015 \cdot 10^{+30}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{3 \cdot z}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= t -2.462434139390015e+30)
  (+ (- x (/ (/ y z) 3.0)) (/ t (* (* z 3.0) y)))
  (+ x (/ (- (/ t y) y) (* 3.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.462434139390015e+30) {
		tmp = (x - ((y / z) / 3.0)) + (t / ((z * 3.0) * y));
	} else {
		tmp = x + (((t / y) - y) / (3.0 * z));
	}
	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 (t <= (-2.462434139390015d+30)) then
        tmp = (x - ((y / z) / 3.0d0)) + (t / ((z * 3.0d0) * y))
    else
        tmp = x + (((t / y) - y) / (3.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.462434139390015e+30) {
		tmp = (x - ((y / z) / 3.0)) + (t / ((z * 3.0) * y));
	} else {
		tmp = x + (((t / y) - y) / (3.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.462434139390015e+30:
		tmp = (x - ((y / z) / 3.0)) + (t / ((z * 3.0) * y))
	else:
		tmp = x + (((t / y) - y) / (3.0 * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.462434139390015e+30)
		tmp = Float64(Float64(x - Float64(Float64(y / z) / 3.0)) + Float64(t / Float64(Float64(z * 3.0) * y)));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(3.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.462434139390015e+30)
		tmp = (x - ((y / z) / 3.0)) + (t / ((z * 3.0) * y));
	else
		tmp = x + (((t / y) - y) / (3.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.462434139390015e+30], N[(N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(3.0 * z), $MachinePrecision]), $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 (t <= (-2462434139390015088894333157376)) THEN ((x - ((y / z) / (3))) + (t / ((z * (3)) * y))) ELSE (x + (((t / y) - y) / ((3) * z))) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if t < -2.4624341393900151e30

   1. Initial program 95.8%

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

   3. Applied rewrites 95.7%

      \[\leadsto \left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   if -2.4624341393900151e30 < t

   1. Initial program 95.8%

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

   3. Applied rewrites 95.7%

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

Alternative 2: 97.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -4.713208571323078 \cdot 10^{+25}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{-0.3333333333333333}{z}, x\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{3 \cdot z}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= t -4.713208571323078e+25)
  (+ (fma y (/ -0.3333333333333333 z) x) (/ t (* (* z 3.0) y)))
  (+ x (/ (- (/ t y) y) (* 3.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.713208571323078e+25) {
		tmp = fma(y, (-0.3333333333333333 / z), x) + (t / ((z * 3.0) * y));
	} else {
		tmp = x + (((t / y) - y) / (3.0 * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.713208571323078e+25)
		tmp = Float64(fma(y, Float64(-0.3333333333333333 / z), x) + Float64(t / Float64(Float64(z * 3.0) * y)));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(3.0 * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.713208571323078e+25], N[(N[(y * N[(-0.3333333333333333 / z), $MachinePrecision] + x), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(3.0 * z), $MachinePrecision]), $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 (t <= (-47132085713230782105911296)) THEN (((y * ((-333333333333333314829616256247390992939472198486328125e-54) / z)) + x) + (t / ((z * (3)) * y))) ELSE (x + (((t / y) - y) / ((3) * z))) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if t < -4.7132085713230782e25

   1. Initial program 95.8%

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

   3. Applied rewrites 95.8%

      \[\leadsto \mathsf{fma}\left(y, \frac{-0.3333333333333333}{z}, x\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   if -4.7132085713230782e25 < t

   1. Initial program 95.8%

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

   3. Applied rewrites 95.7%

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

Alternative 3: 97.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -4.469137424736664 \cdot 10^{+45}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{y \cdot z}, 0.3333333333333333, \mathsf{fma}\left(\frac{y}{z}, -0.3333333333333333, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{3 \cdot z}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= t -4.469137424736664e+45)
  (fma
   (/ t (* y z))
   0.3333333333333333
   (fma (/ y z) -0.3333333333333333 x))
  (+ x (/ (- (/ t y) y) (* 3.0 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.469137424736664e+45) {
		tmp = fma((t / (y * z)), 0.3333333333333333, fma((y / z), -0.3333333333333333, x));
	} else {
		tmp = x + (((t / y) - y) / (3.0 * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.469137424736664e+45)
		tmp = fma(Float64(t / Float64(y * z)), 0.3333333333333333, fma(Float64(y / z), -0.3333333333333333, x));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(3.0 * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.469137424736664e+45], N[(N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision] * 0.3333333333333333 + N[(N[(y / z), $MachinePrecision] * -0.3333333333333333 + x), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(3.0 * z), $MachinePrecision]), $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 (t <= (-4469137424736664278128761670947944305004642304)) THEN (((t / (y * z)) * (333333333333333314829616256247390992939472198486328125e-54)) + (((y / z) * (-333333333333333314829616256247390992939472198486328125e-54)) + x)) ELSE (x + (((t / y) - y) / ((3) * z))) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if t < -4.4691374247366643e45

   1. Initial program 95.8%

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

   3. Applied rewrites 95.6%

      \[\leadsto \mathsf{fma}\left(\frac{t}{y \cdot z}, 0.3333333333333333, \mathsf{fma}\left(\frac{y}{z}, -0.3333333333333333, x\right)\right) \]

   if -4.4691374247366643e45 < t

   1. Initial program 95.8%

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

   3. Applied rewrites 95.7%

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

Alternative 4: 95.7% accurate, 1.4× speedup

Math

\[x + \frac{\frac{t}{y} - y}{3 \cdot z} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (+ x (/ (- (/ t y) y) (* 3.0 z))))

C

double code(double x, double y, double z, double t) {
	return x + (((t / y) - y) / (3.0 * z));
}

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 + (((t / y) - y) / (3.0d0 * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + (((t / y) - y) / (3.0 * z));
}

Python

def code(x, y, z, t):
	return x + (((t / y) - y) / (3.0 * z))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(3.0 * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + (((t / y) - y) / (3.0 * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(3.0 * z), $MachinePrecision]), $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 =
	x + (((t / y) - y) / ((3) * z))
END code

Derivation

1. Initial program 95.8%

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

3. Applied rewrites 95.7%

   \[\leadsto x + \frac{\frac{t}{y} - y}{3 \cdot z} \]
4. Add Preprocessing

Alternative 5: 95.6% accurate, 1.4× speedup

Math

\[\mathsf{fma}\left(y - \frac{t}{y}, \frac{-0.3333333333333333}{z}, x\right) \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (fma (- y (/ t y)) (/ -0.3333333333333333 z) x))

C

double code(double x, double y, double z, double t) {
	return fma((y - (t / y)), (-0.3333333333333333 / z), x);
}

Julia

function code(x, y, z, t)
	return fma(Float64(y - Float64(t / y)), Float64(-0.3333333333333333 / z), x)
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] * N[(-0.3333333333333333 / z), $MachinePrecision] + x), $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 =
	((y - (t / y)) * ((-333333333333333314829616256247390992939472198486328125e-54) / z)) + x
END code

Derivation

1. Initial program 95.8%

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

3. Applied rewrites 95.7%

   \[\leadsto \mathsf{fma}\left(\frac{y}{z}, -0.3333333333333333, x\right) - \frac{t}{\left(-3 \cdot y\right) \cdot z} \]

5. Applied rewrites 95.6%

   \[\leadsto \mathsf{fma}\left(y - \frac{t}{y}, \frac{-0.3333333333333333}{z}, x\right) \]
6. Add Preprocessing

Alternative 6: 91.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{z}, -0.3333333333333333, x\right)\\ \mathbf{if}\;y \leq -6.09362789177678 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.309806978246206 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(\frac{0.3333333333333333}{y}, \frac{t}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma (/ y z) -0.3333333333333333 x)))
  (if (<= y -6.09362789177678e-33)
    t_1
    (if (<= y 4.309806978246206e+32)
      (fma (/ 0.3333333333333333 y) (/ t z) x)
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((y / z), -0.3333333333333333, x);
	double tmp;
	if (y <= -6.09362789177678e-33) {
		tmp = t_1;
	} else if (y <= 4.309806978246206e+32) {
		tmp = fma((0.3333333333333333 / y), (t / z), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(y / z), -0.3333333333333333, x)
	tmp = 0.0
	if (y <= -6.09362789177678e-33)
		tmp = t_1;
	elseif (y <= 4.309806978246206e+32)
		tmp = fma(Float64(0.3333333333333333 / y), Float64(t / z), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * -0.3333333333333333 + x), $MachinePrecision]}, If[LessEqual[y, -6.09362789177678e-33], t$95$1, If[LessEqual[y, 4.309806978246206e+32], N[(N[(0.3333333333333333 / y), $MachinePrecision] * N[(t / z), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

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 t_1 = (((y / z) * (-333333333333333314829616256247390992939472198486328125e-54)) + x) IN
		LET tmp_1 = IF (y <= (430980697824620576377632033079296)) THEN ((((333333333333333314829616256247390992939472198486328125e-54) / y) * (t / z)) + x) ELSE t_1 ENDIF IN
		LET tmp = IF (y <= (-6093627891776779958655424844567020329681569360501345202102719116828236287862557310035342694742865887747029773890972137451171875e-159)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -6.09362789177678e-33 or 4.3098069782462058e32 < y

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 68.0%

      \[\leadsto 0.3333333333333333 \cdot \frac{t}{y \cdot z} - 0.3333333333333333 \cdot \frac{y}{z} \]

   6. Applied rewrites 68.2%

      \[\leadsto \frac{\frac{t}{y} - y}{3 \cdot z} \]

   7. Taylor expanded in t around 0

      \[\leadsto x - \frac{1}{3} \cdot \frac{y}{z} \]
   8. Step-by-step derivation

   9. Applied rewrites 64.1%

      \[\leadsto x - 0.3333333333333333 \cdot \frac{y}{z} \]

   11. Applied rewrites 64.1%

       \[\leadsto \mathsf{fma}\left(\frac{y}{z}, -0.3333333333333333, x\right) \]

   if -6.09362789177678e-33 < y < 4.3098069782462058e32

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 61.0%

      \[\leadsto \frac{\mathsf{fma}\left(0.3333333333333333, \frac{t}{z}, x \cdot y\right)}{y} \]

   6. Applied rewrites 66.3%

      \[\leadsto \mathsf{fma}\left(\frac{0.3333333333333333}{y}, \frac{t}{z}, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 89.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{z}, -0.3333333333333333, x\right)\\ \mathbf{if}\;y \leq -6.09362789177678 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.296860608809366 \cdot 10^{+32}:\\ \;\;\;\;x - \frac{t}{\left(-3 \cdot z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma (/ y z) -0.3333333333333333 x)))
  (if (<= y -6.09362789177678e-33)
    t_1
    (if (<= y 2.296860608809366e+32)
      (- x (/ t (* (* -3.0 z) y)))
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((y / z), -0.3333333333333333, x);
	double tmp;
	if (y <= -6.09362789177678e-33) {
		tmp = t_1;
	} else if (y <= 2.296860608809366e+32) {
		tmp = x - (t / ((-3.0 * z) * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(y / z), -0.3333333333333333, x)
	tmp = 0.0
	if (y <= -6.09362789177678e-33)
		tmp = t_1;
	elseif (y <= 2.296860608809366e+32)
		tmp = Float64(x - Float64(t / Float64(Float64(-3.0 * z) * y)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * -0.3333333333333333 + x), $MachinePrecision]}, If[LessEqual[y, -6.09362789177678e-33], t$95$1, If[LessEqual[y, 2.296860608809366e+32], N[(x - N[(t / N[(N[(-3.0 * z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

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 t_1 = (((y / z) * (-333333333333333314829616256247390992939472198486328125e-54)) + x) IN
		LET tmp_1 = IF (y <= (229686060880936600713247353470976)) THEN (x - (t / (((-3) * z) * y))) ELSE t_1 ENDIF IN
		LET tmp = IF (y <= (-6093627891776779958655424844567020329681569360501345202102719116828236287862557310035342694742865887747029773890972137451171875e-159)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -6.09362789177678e-33 or 2.296860608809366e32 < y

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 68.0%

      \[\leadsto 0.3333333333333333 \cdot \frac{t}{y \cdot z} - 0.3333333333333333 \cdot \frac{y}{z} \]

   6. Applied rewrites 68.2%

      \[\leadsto \frac{\frac{t}{y} - y}{3 \cdot z} \]

   7. Taylor expanded in t around 0

      \[\leadsto x - \frac{1}{3} \cdot \frac{y}{z} \]
   8. Step-by-step derivation

   9. Applied rewrites 64.1%

      \[\leadsto x - 0.3333333333333333 \cdot \frac{y}{z} \]

   11. Applied rewrites 64.1%

       \[\leadsto \mathsf{fma}\left(\frac{y}{z}, -0.3333333333333333, x\right) \]

   if -6.09362789177678e-33 < y < 2.296860608809366e32

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 61.0%

      \[\leadsto \frac{\mathsf{fma}\left(0.3333333333333333, \frac{t}{z}, x \cdot y\right)}{y} \]

   6. Applied rewrites 62.2%

      \[\leadsto \mathsf{fma}\left(\frac{0.3333333333333333}{z \cdot y}, t, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 62.5%

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

Alternative 8: 89.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{z}, -0.3333333333333333, x\right)\\ \mathbf{if}\;y \leq -6.09362789177678 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.296860608809366 \cdot 10^{+32}:\\ \;\;\;\;x - \frac{t}{z \cdot \left(-3 \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma (/ y z) -0.3333333333333333 x)))
  (if (<= y -6.09362789177678e-33)
    t_1
    (if (<= y 2.296860608809366e+32)
      (- x (/ t (* z (* -3.0 y))))
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((y / z), -0.3333333333333333, x);
	double tmp;
	if (y <= -6.09362789177678e-33) {
		tmp = t_1;
	} else if (y <= 2.296860608809366e+32) {
		tmp = x - (t / (z * (-3.0 * y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(y / z), -0.3333333333333333, x)
	tmp = 0.0
	if (y <= -6.09362789177678e-33)
		tmp = t_1;
	elseif (y <= 2.296860608809366e+32)
		tmp = Float64(x - Float64(t / Float64(z * Float64(-3.0 * y))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * -0.3333333333333333 + x), $MachinePrecision]}, If[LessEqual[y, -6.09362789177678e-33], t$95$1, If[LessEqual[y, 2.296860608809366e+32], N[(x - N[(t / N[(z * N[(-3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

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 t_1 = (((y / z) * (-333333333333333314829616256247390992939472198486328125e-54)) + x) IN
		LET tmp_1 = IF (y <= (229686060880936600713247353470976)) THEN (x - (t / (z * ((-3) * y)))) ELSE t_1 ENDIF IN
		LET tmp = IF (y <= (-6093627891776779958655424844567020329681569360501345202102719116828236287862557310035342694742865887747029773890972137451171875e-159)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -6.09362789177678e-33 or 2.296860608809366e32 < y

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 68.0%

      \[\leadsto 0.3333333333333333 \cdot \frac{t}{y \cdot z} - 0.3333333333333333 \cdot \frac{y}{z} \]

   6. Applied rewrites 68.2%

      \[\leadsto \frac{\frac{t}{y} - y}{3 \cdot z} \]

   7. Taylor expanded in t around 0

      \[\leadsto x - \frac{1}{3} \cdot \frac{y}{z} \]
   8. Step-by-step derivation

   9. Applied rewrites 64.1%

      \[\leadsto x - 0.3333333333333333 \cdot \frac{y}{z} \]

   11. Applied rewrites 64.1%

       \[\leadsto \mathsf{fma}\left(\frac{y}{z}, -0.3333333333333333, x\right) \]

   if -6.09362789177678e-33 < y < 2.296860608809366e32

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 61.0%

      \[\leadsto \frac{\mathsf{fma}\left(0.3333333333333333, \frac{t}{z}, x \cdot y\right)}{y} \]

   6. Applied rewrites 62.2%

      \[\leadsto \mathsf{fma}\left(\frac{0.3333333333333333}{z \cdot y}, t, x\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 62.5%

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

   10. Applied rewrites 62.5%

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

Alternative 9: 88.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{z}, -0.3333333333333333, x\right)\\ \mathbf{if}\;y \leq -6.09362789177678 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.296860608809366 \cdot 10^{+32}:\\ \;\;\;\;\mathsf{fma}\left(\frac{0.3333333333333333}{z \cdot y}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma (/ y z) -0.3333333333333333 x)))
  (if (<= y -6.09362789177678e-33)
    t_1
    (if (<= y 2.296860608809366e+32)
      (fma (/ 0.3333333333333333 (* z y)) t x)
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((y / z), -0.3333333333333333, x);
	double tmp;
	if (y <= -6.09362789177678e-33) {
		tmp = t_1;
	} else if (y <= 2.296860608809366e+32) {
		tmp = fma((0.3333333333333333 / (z * y)), t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(y / z), -0.3333333333333333, x)
	tmp = 0.0
	if (y <= -6.09362789177678e-33)
		tmp = t_1;
	elseif (y <= 2.296860608809366e+32)
		tmp = fma(Float64(0.3333333333333333 / Float64(z * y)), t, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * -0.3333333333333333 + x), $MachinePrecision]}, If[LessEqual[y, -6.09362789177678e-33], t$95$1, If[LessEqual[y, 2.296860608809366e+32], N[(N[(0.3333333333333333 / N[(z * y), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], t$95$1]]]

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 t_1 = (((y / z) * (-333333333333333314829616256247390992939472198486328125e-54)) + x) IN
		LET tmp_1 = IF (y <= (229686060880936600713247353470976)) THEN ((((333333333333333314829616256247390992939472198486328125e-54) / (z * y)) * t) + x) ELSE t_1 ENDIF IN
		LET tmp = IF (y <= (-6093627891776779958655424844567020329681569360501345202102719116828236287862557310035342694742865887747029773890972137451171875e-159)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -6.09362789177678e-33 or 2.296860608809366e32 < y

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 68.0%

      \[\leadsto 0.3333333333333333 \cdot \frac{t}{y \cdot z} - 0.3333333333333333 \cdot \frac{y}{z} \]

   6. Applied rewrites 68.2%

      \[\leadsto \frac{\frac{t}{y} - y}{3 \cdot z} \]

   7. Taylor expanded in t around 0

      \[\leadsto x - \frac{1}{3} \cdot \frac{y}{z} \]
   8. Step-by-step derivation

   9. Applied rewrites 64.1%

      \[\leadsto x - 0.3333333333333333 \cdot \frac{y}{z} \]

   11. Applied rewrites 64.1%

       \[\leadsto \mathsf{fma}\left(\frac{y}{z}, -0.3333333333333333, x\right) \]

   if -6.09362789177678e-33 < y < 2.296860608809366e32

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 61.0%

      \[\leadsto \frac{\mathsf{fma}\left(0.3333333333333333, \frac{t}{z}, x \cdot y\right)}{y} \]

   6. Applied rewrites 62.2%

      \[\leadsto \mathsf{fma}\left(\frac{0.3333333333333333}{z \cdot y}, t, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 77.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{z}, -0.3333333333333333, x\right)\\ \mathbf{if}\;y \leq -2.7870391605929528 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.890449633550395 \cdot 10^{-139}:\\ \;\;\;\;\frac{0.3333333333333333}{y} \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma (/ y z) -0.3333333333333333 x)))
  (if (<= y -2.7870391605929528e-114)
    t_1
    (if (<= y 1.890449633550395e-139)
      (* (/ 0.3333333333333333 y) (/ t z))
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((y / z), -0.3333333333333333, x);
	double tmp;
	if (y <= -2.7870391605929528e-114) {
		tmp = t_1;
	} else if (y <= 1.890449633550395e-139) {
		tmp = (0.3333333333333333 / y) * (t / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(y / z), -0.3333333333333333, x)
	tmp = 0.0
	if (y <= -2.7870391605929528e-114)
		tmp = t_1;
	elseif (y <= 1.890449633550395e-139)
		tmp = Float64(Float64(0.3333333333333333 / y) * Float64(t / z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * -0.3333333333333333 + x), $MachinePrecision]}, If[LessEqual[y, -2.7870391605929528e-114], t$95$1, If[LessEqual[y, 1.890449633550395e-139], N[(N[(0.3333333333333333 / y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

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 t_1 = (((y / z) * (-333333333333333314829616256247390992939472198486328125e-54)) + x) IN
		LET tmp_1 = IF (y <= (189044963355039516083484157312367417220408659850691830863947258404760595140518856352587421623116905810455482383883468409453443870463283861175076581285548803009097968237193456342937560435960504469766504487214129453650897158805003173217742332024466402601966814723999701341414809200261815892130263108316468776788379600659167672496450474974027944341514739790000021457672119140625e-513)) THEN (((333333333333333314829616256247390992939472198486328125e-54) / y) * (t / z)) ELSE t_1 ENDIF IN
		LET tmp = IF (y <= (-27870391605929527843619951474517218586746835377694357826558167765144730996185682089431723273910324346259029055975475442404589015291090933046532527430602748062714930846766840260490092180869212328039196419837502646994768163476900674649925679164982045933684704570313217856958212630125171216377566452138125896453857421875e-430)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -2.7870391605929528e-114 or 1.8904496335503952e-139 < y

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 68.0%

      \[\leadsto 0.3333333333333333 \cdot \frac{t}{y \cdot z} - 0.3333333333333333 \cdot \frac{y}{z} \]

   6. Applied rewrites 68.2%

      \[\leadsto \frac{\frac{t}{y} - y}{3 \cdot z} \]

   7. Taylor expanded in t around 0

      \[\leadsto x - \frac{1}{3} \cdot \frac{y}{z} \]
   8. Step-by-step derivation

   9. Applied rewrites 64.1%

      \[\leadsto x - 0.3333333333333333 \cdot \frac{y}{z} \]

   11. Applied rewrites 64.1%

       \[\leadsto \mathsf{fma}\left(\frac{y}{z}, -0.3333333333333333, x\right) \]

   if -2.7870391605929528e-114 < y < 1.8904496335503952e-139

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 61.0%

      \[\leadsto \frac{\mathsf{fma}\left(0.3333333333333333, \frac{t}{z}, x \cdot y\right)}{y} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{1}{3} \cdot \frac{t}{y \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 35.3%

      \[\leadsto 0.3333333333333333 \cdot \frac{t}{y \cdot z} \]
   8. Step-by-step derivation

   9. Applied rewrites 38.7%

      \[\leadsto \frac{0.3333333333333333}{y} \cdot \frac{t}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 76.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{z}, -0.3333333333333333, x\right)\\ \mathbf{if}\;y \leq -3.30264017361586 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.890449633550395 \cdot 10^{-139}:\\ \;\;\;\;\frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma (/ y z) -0.3333333333333333 x)))
  (if (<= y -3.30264017361586e-114)
    t_1
    (if (<= y 1.890449633550395e-139) (/ t (* z (* 3.0 y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((y / z), -0.3333333333333333, x);
	double tmp;
	if (y <= -3.30264017361586e-114) {
		tmp = t_1;
	} else if (y <= 1.890449633550395e-139) {
		tmp = t / (z * (3.0 * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(y / z), -0.3333333333333333, x)
	tmp = 0.0
	if (y <= -3.30264017361586e-114)
		tmp = t_1;
	elseif (y <= 1.890449633550395e-139)
		tmp = Float64(t / Float64(z * Float64(3.0 * y)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * -0.3333333333333333 + x), $MachinePrecision]}, If[LessEqual[y, -3.30264017361586e-114], t$95$1, If[LessEqual[y, 1.890449633550395e-139], N[(t / N[(z * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

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 t_1 = (((y / z) * (-333333333333333314829616256247390992939472198486328125e-54)) + x) IN
		LET tmp_1 = IF (y <= (189044963355039516083484157312367417220408659850691830863947258404760595140518856352587421623116905810455482383883468409453443870463283861175076581285548803009097968237193456342937560435960504469766504487214129453650897158805003173217742332024466402601966814723999701341414809200261815892130263108316468776788379600659167672496450474974027944341514739790000021457672119140625e-513)) THEN (t / (z * ((3) * y))) ELSE t_1 ENDIF IN
		LET tmp = IF (y <= (-3302640173615860206097297360763973489498339623300453317341318844379272987034111406549918125572461682567938817635244947683214339751400988984282445920980103918709728644172324705943764372105477153349611899107193386161372344950696702677875489344821838296573701805889243025591097725757183667383287684060633182525634765625e-429)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -3.3026401736158602e-114 or 1.8904496335503952e-139 < y

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 68.0%

      \[\leadsto 0.3333333333333333 \cdot \frac{t}{y \cdot z} - 0.3333333333333333 \cdot \frac{y}{z} \]

   6. Applied rewrites 68.2%

      \[\leadsto \frac{\frac{t}{y} - y}{3 \cdot z} \]

   7. Taylor expanded in t around 0

      \[\leadsto x - \frac{1}{3} \cdot \frac{y}{z} \]
   8. Step-by-step derivation

   9. Applied rewrites 64.1%

      \[\leadsto x - 0.3333333333333333 \cdot \frac{y}{z} \]

   11. Applied rewrites 64.1%

       \[\leadsto \mathsf{fma}\left(\frac{y}{z}, -0.3333333333333333, x\right) \]

   if -3.3026401736158602e-114 < y < 1.8904496335503952e-139

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 61.0%

      \[\leadsto \frac{\mathsf{fma}\left(0.3333333333333333, \frac{t}{z}, x \cdot y\right)}{y} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{1}{3} \cdot \frac{t}{y \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 35.3%

      \[\leadsto 0.3333333333333333 \cdot \frac{t}{y \cdot z} \]
   8. Step-by-step derivation

   9. Applied rewrites 35.4%

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

   11. Applied rewrites 35.4%

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

Alternative 12: 76.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{z}, -0.3333333333333333, x\right)\\ \mathbf{if}\;y \leq -3.30264017361586 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.890449633550395 \cdot 10^{-139}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma (/ y z) -0.3333333333333333 x)))
  (if (<= y -3.30264017361586e-114)
    t_1
    (if (<= y 1.890449633550395e-139)
      (* 0.3333333333333333 (/ t (* y z)))
      t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((y / z), -0.3333333333333333, x);
	double tmp;
	if (y <= -3.30264017361586e-114) {
		tmp = t_1;
	} else if (y <= 1.890449633550395e-139) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(y / z), -0.3333333333333333, x)
	tmp = 0.0
	if (y <= -3.30264017361586e-114)
		tmp = t_1;
	elseif (y <= 1.890449633550395e-139)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * -0.3333333333333333 + x), $MachinePrecision]}, If[LessEqual[y, -3.30264017361586e-114], t$95$1, If[LessEqual[y, 1.890449633550395e-139], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

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 t_1 = (((y / z) * (-333333333333333314829616256247390992939472198486328125e-54)) + x) IN
		LET tmp_1 = IF (y <= (189044963355039516083484157312367417220408659850691830863947258404760595140518856352587421623116905810455482383883468409453443870463283861175076581285548803009097968237193456342937560435960504469766504487214129453650897158805003173217742332024466402601966814723999701341414809200261815892130263108316468776788379600659167672496450474974027944341514739790000021457672119140625e-513)) THEN ((333333333333333314829616256247390992939472198486328125e-54) * (t / (y * z))) ELSE t_1 ENDIF IN
		LET tmp = IF (y <= (-3302640173615860206097297360763973489498339623300453317341318844379272987034111406549918125572461682567938817635244947683214339751400988984282445920980103918709728644172324705943764372105477153349611899107193386161372344950696702677875489344821838296573701805889243025591097725757183667383287684060633182525634765625e-429)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -3.3026401736158602e-114 or 1.8904496335503952e-139 < y

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 68.0%

      \[\leadsto 0.3333333333333333 \cdot \frac{t}{y \cdot z} - 0.3333333333333333 \cdot \frac{y}{z} \]

   6. Applied rewrites 68.2%

      \[\leadsto \frac{\frac{t}{y} - y}{3 \cdot z} \]

   7. Taylor expanded in t around 0

      \[\leadsto x - \frac{1}{3} \cdot \frac{y}{z} \]
   8. Step-by-step derivation

   9. Applied rewrites 64.1%

      \[\leadsto x - 0.3333333333333333 \cdot \frac{y}{z} \]

   11. Applied rewrites 64.1%

       \[\leadsto \mathsf{fma}\left(\frac{y}{z}, -0.3333333333333333, x\right) \]

   if -3.3026401736158602e-114 < y < 1.8904496335503952e-139

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 61.0%

      \[\leadsto \frac{\mathsf{fma}\left(0.3333333333333333, \frac{t}{z}, x \cdot y\right)}{y} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{1}{3} \cdot \frac{t}{y \cdot z} \]
   6. Step-by-step derivation

   7. Applied rewrites 35.3%

      \[\leadsto 0.3333333333333333 \cdot \frac{t}{y \cdot z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 64.1% accurate, 2.3× speedup

Math

\[\mathsf{fma}\left(\frac{y}{z}, -0.3333333333333333, x\right) \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (fma (/ y z) -0.3333333333333333 x))

C

double code(double x, double y, double z, double t) {
	return fma((y / z), -0.3333333333333333, x);
}

Julia

function code(x, y, z, t)
	return fma(Float64(y / z), -0.3333333333333333, x)
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(y / z), $MachinePrecision] * -0.3333333333333333 + x), $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 =
	((y / z) * (-333333333333333314829616256247390992939472198486328125e-54)) + x
END code

Derivation

1. Initial program 95.8%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

2. Taylor expanded in x around 0

   \[\leadsto \frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z} \]
3. Step-by-step derivation

4. Applied rewrites 68.0%

   \[\leadsto 0.3333333333333333 \cdot \frac{t}{y \cdot z} - 0.3333333333333333 \cdot \frac{y}{z} \]

6. Applied rewrites 68.2%

   \[\leadsto \frac{\frac{t}{y} - y}{3 \cdot z} \]

7. Taylor expanded in t around 0

   \[\leadsto x - \frac{1}{3} \cdot \frac{y}{z} \]
8. Step-by-step derivation

9. Applied rewrites 64.1%

   \[\leadsto x - 0.3333333333333333 \cdot \frac{y}{z} \]

11. Applied rewrites 64.1%

    \[\leadsto \mathsf{fma}\left(\frac{y}{z}, -0.3333333333333333, x\right) \]
12. Add Preprocessing

Alternative 14: 46.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -2.0681494829383775 \cdot 10^{-33}:\\ \;\;\;\;\frac{y}{-3 \cdot z}\\ \mathbf{elif}\;y \leq 3.5513325988060555 \cdot 10^{+76}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{z}}{-3}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= y -2.0681494829383775e-33)
  (/ y (* -3.0 z))
  (if (<= y 3.5513325988060555e+76) (/ (* x y) y) (/ (/ y z) -3.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.0681494829383775e-33) {
		tmp = y / (-3.0 * z);
	} else if (y <= 3.5513325988060555e+76) {
		tmp = (x * y) / y;
	} else {
		tmp = (y / z) / -3.0;
	}
	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 (y <= (-2.0681494829383775d-33)) then
        tmp = y / ((-3.0d0) * z)
    else if (y <= 3.5513325988060555d+76) then
        tmp = (x * y) / y
    else
        tmp = (y / z) / (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.0681494829383775e-33) {
		tmp = y / (-3.0 * z);
	} else if (y <= 3.5513325988060555e+76) {
		tmp = (x * y) / y;
	} else {
		tmp = (y / z) / -3.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.0681494829383775e-33:
		tmp = y / (-3.0 * z)
	elif y <= 3.5513325988060555e+76:
		tmp = (x * y) / y
	else:
		tmp = (y / z) / -3.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.0681494829383775e-33)
		tmp = Float64(y / Float64(-3.0 * z));
	elseif (y <= 3.5513325988060555e+76)
		tmp = Float64(Float64(x * y) / y);
	else
		tmp = Float64(Float64(y / z) / -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.0681494829383775e-33)
		tmp = y / (-3.0 * z);
	elseif (y <= 3.5513325988060555e+76)
		tmp = (x * y) / y;
	else
		tmp = (y / z) / -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.0681494829383775e-33], N[(y / N[(-3.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5513325988060555e+76], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision], N[(N[(y / z), $MachinePrecision] / -3.0), $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_1 = IF (y <= (35513325988060555074912100087773517708281933258246215593194965378161910480896)) THEN ((x * y) / y) ELSE ((y / z) / (-3)) ENDIF IN
	LET tmp = IF (y <= (-20681494829383775098804415409152343062282864338188075106929606524247191745307422993250916209984069382699090056121349334716796875e-160)) THEN (y / ((-3) * z)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if y < -2.0681494829383775e-33

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 68.0%

      \[\leadsto 0.3333333333333333 \cdot \frac{t}{y \cdot z} - 0.3333333333333333 \cdot \frac{y}{z} \]

   6. Applied rewrites 68.2%

      \[\leadsto \frac{\frac{t}{y} - y}{3 \cdot z} \]

   7. Taylor expanded in y around inf

      \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} \]
   8. Step-by-step derivation

   9. Applied rewrites 36.3%

      \[\leadsto -0.3333333333333333 \cdot \frac{y}{z} \]
   10. Step-by-step derivation

   11. Applied rewrites 36.4%

       \[\leadsto \frac{y}{-3 \cdot z} \]

   if -2.0681494829383775e-33 < y < 3.5513325988060555e76

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 61.0%

      \[\leadsto \frac{\mathsf{fma}\left(0.3333333333333333, \frac{t}{z}, x \cdot y\right)}{y} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{z}}{y} \]
   6. Step-by-step derivation

   7. Applied rewrites 38.7%

      \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{z}}{y} \]

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 25.5%

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

   if 3.5513325988060555e76 < y

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 68.0%

      \[\leadsto 0.3333333333333333 \cdot \frac{t}{y \cdot z} - 0.3333333333333333 \cdot \frac{y}{z} \]

   6. Applied rewrites 68.2%

      \[\leadsto \frac{\frac{t}{y} - y}{3 \cdot z} \]

   7. Taylor expanded in y around inf

      \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} \]
   8. Step-by-step derivation

   9. Applied rewrites 36.3%

      \[\leadsto -0.3333333333333333 \cdot \frac{y}{z} \]
   10. Step-by-step derivation

   11. Applied rewrites 36.3%

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

Alternative 15: 46.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} t_1 := \frac{y}{-3 \cdot z}\\ \mathbf{if}\;y \leq -2.0681494829383775 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5513325988060555 \cdot 10^{+76}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ y (* -3.0 z))))
  (if (<= y -2.0681494829383775e-33)
    t_1
    (if (<= y 3.5513325988060555e+76) (/ (* x y) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (-3.0 * z);
	double tmp;
	if (y <= -2.0681494829383775e-33) {
		tmp = t_1;
	} else if (y <= 3.5513325988060555e+76) {
		tmp = (x * y) / y;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = y / ((-3.0d0) * z)
    if (y <= (-2.0681494829383775d-33)) then
        tmp = t_1
    else if (y <= 3.5513325988060555d+76) then
        tmp = (x * y) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / (-3.0 * z);
	double tmp;
	if (y <= -2.0681494829383775e-33) {
		tmp = t_1;
	} else if (y <= 3.5513325988060555e+76) {
		tmp = (x * y) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (-3.0 * z)
	tmp = 0
	if y <= -2.0681494829383775e-33:
		tmp = t_1
	elif y <= 3.5513325988060555e+76:
		tmp = (x * y) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(-3.0 * z))
	tmp = 0.0
	if (y <= -2.0681494829383775e-33)
		tmp = t_1;
	elseif (y <= 3.5513325988060555e+76)
		tmp = Float64(Float64(x * y) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (-3.0 * z);
	tmp = 0.0;
	if (y <= -2.0681494829383775e-33)
		tmp = t_1;
	elseif (y <= 3.5513325988060555e+76)
		tmp = (x * y) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(-3.0 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.0681494829383775e-33], t$95$1, If[LessEqual[y, 3.5513325988060555e+76], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

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 t_1 = (y / ((-3) * z)) IN
		LET tmp_1 = IF (y <= (35513325988060555074912100087773517708281933258246215593194965378161910480896)) THEN ((x * y) / y) ELSE t_1 ENDIF IN
		LET tmp = IF (y <= (-20681494829383775098804415409152343062282864338188075106929606524247191745307422993250916209984069382699090056121349334716796875e-160)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -2.0681494829383775e-33 or 3.5513325988060555e76 < y

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 68.0%

      \[\leadsto 0.3333333333333333 \cdot \frac{t}{y \cdot z} - 0.3333333333333333 \cdot \frac{y}{z} \]

   6. Applied rewrites 68.2%

      \[\leadsto \frac{\frac{t}{y} - y}{3 \cdot z} \]

   7. Taylor expanded in y around inf

      \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} \]
   8. Step-by-step derivation

   9. Applied rewrites 36.3%

      \[\leadsto -0.3333333333333333 \cdot \frac{y}{z} \]
   10. Step-by-step derivation

   11. Applied rewrites 36.4%

       \[\leadsto \frac{y}{-3 \cdot z} \]

   if -2.0681494829383775e-33 < y < 3.5513325988060555e76

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 61.0%

      \[\leadsto \frac{\mathsf{fma}\left(0.3333333333333333, \frac{t}{z}, x \cdot y\right)}{y} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{z}}{y} \]
   6. Step-by-step derivation

   7. Applied rewrites 38.7%

      \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{z}}{y} \]

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 25.5%

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

Alternative 16: 46.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} t_1 := -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -2.0681494829383775 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5513325988060555 \cdot 10^{+76}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* -0.3333333333333333 (/ y z))))
  (if (<= y -2.0681494829383775e-33)
    t_1
    (if (<= y 3.5513325988060555e+76) (/ (* x y) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -0.3333333333333333 * (y / z);
	double tmp;
	if (y <= -2.0681494829383775e-33) {
		tmp = t_1;
	} else if (y <= 3.5513325988060555e+76) {
		tmp = (x * y) / y;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (-0.3333333333333333d0) * (y / z)
    if (y <= (-2.0681494829383775d-33)) then
        tmp = t_1
    else if (y <= 3.5513325988060555d+76) then
        tmp = (x * y) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -0.3333333333333333 * (y / z);
	double tmp;
	if (y <= -2.0681494829383775e-33) {
		tmp = t_1;
	} else if (y <= 3.5513325988060555e+76) {
		tmp = (x * y) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -0.3333333333333333 * (y / z)
	tmp = 0
	if y <= -2.0681494829383775e-33:
		tmp = t_1
	elif y <= 3.5513325988060555e+76:
		tmp = (x * y) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-0.3333333333333333 * Float64(y / z))
	tmp = 0.0
	if (y <= -2.0681494829383775e-33)
		tmp = t_1;
	elseif (y <= 3.5513325988060555e+76)
		tmp = Float64(Float64(x * y) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -0.3333333333333333 * (y / z);
	tmp = 0.0;
	if (y <= -2.0681494829383775e-33)
		tmp = t_1;
	elseif (y <= 3.5513325988060555e+76)
		tmp = (x * y) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.0681494829383775e-33], t$95$1, If[LessEqual[y, 3.5513325988060555e+76], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

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 t_1 = ((-333333333333333314829616256247390992939472198486328125e-54) * (y / z)) IN
		LET tmp_1 = IF (y <= (35513325988060555074912100087773517708281933258246215593194965378161910480896)) THEN ((x * y) / y) ELSE t_1 ENDIF IN
		LET tmp = IF (y <= (-20681494829383775098804415409152343062282864338188075106929606524247191745307422993250916209984069382699090056121349334716796875e-160)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -2.0681494829383775e-33 or 3.5513325988060555e76 < y

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 68.0%

      \[\leadsto 0.3333333333333333 \cdot \frac{t}{y \cdot z} - 0.3333333333333333 \cdot \frac{y}{z} \]

   6. Applied rewrites 68.2%

      \[\leadsto \frac{\frac{t}{y} - y}{3 \cdot z} \]

   7. Taylor expanded in y around inf

      \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} \]
   8. Step-by-step derivation

   9. Applied rewrites 36.3%

      \[\leadsto -0.3333333333333333 \cdot \frac{y}{z} \]

   if -2.0681494829383775e-33 < y < 3.5513325988060555e76

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 61.0%

      \[\leadsto \frac{\mathsf{fma}\left(0.3333333333333333, \frac{t}{z}, x \cdot y\right)}{y} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{z}}{y} \]
   6. Step-by-step derivation

   7. Applied rewrites 38.7%

      \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{z}}{y} \]

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 25.5%

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

Alternative 17: 46.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} t_1 := \frac{-0.3333333333333333 \cdot y}{z}\\ \mathbf{if}\;y \leq -2.0681494829383775 \cdot 10^{-33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5513325988060555 \cdot 10^{+76}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (* -0.3333333333333333 y) z)))
  (if (<= y -2.0681494829383775e-33)
    t_1
    (if (<= y 3.5513325988060555e+76) (/ (* x y) y) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-0.3333333333333333 * y) / z;
	double tmp;
	if (y <= -2.0681494829383775e-33) {
		tmp = t_1;
	} else if (y <= 3.5513325988060555e+76) {
		tmp = (x * y) / y;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = ((-0.3333333333333333d0) * y) / z
    if (y <= (-2.0681494829383775d-33)) then
        tmp = t_1
    else if (y <= 3.5513325988060555d+76) then
        tmp = (x * y) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (-0.3333333333333333 * y) / z;
	double tmp;
	if (y <= -2.0681494829383775e-33) {
		tmp = t_1;
	} else if (y <= 3.5513325988060555e+76) {
		tmp = (x * y) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (-0.3333333333333333 * y) / z
	tmp = 0
	if y <= -2.0681494829383775e-33:
		tmp = t_1
	elif y <= 3.5513325988060555e+76:
		tmp = (x * y) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-0.3333333333333333 * y) / z)
	tmp = 0.0
	if (y <= -2.0681494829383775e-33)
		tmp = t_1;
	elseif (y <= 3.5513325988060555e+76)
		tmp = Float64(Float64(x * y) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (-0.3333333333333333 * y) / z;
	tmp = 0.0;
	if (y <= -2.0681494829383775e-33)
		tmp = t_1;
	elseif (y <= 3.5513325988060555e+76)
		tmp = (x * y) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(-0.3333333333333333 * y), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -2.0681494829383775e-33], t$95$1, If[LessEqual[y, 3.5513325988060555e+76], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

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 t_1 = (((-333333333333333314829616256247390992939472198486328125e-54) * y) / z) IN
		LET tmp_1 = IF (y <= (35513325988060555074912100087773517708281933258246215593194965378161910480896)) THEN ((x * y) / y) ELSE t_1 ENDIF IN
		LET tmp = IF (y <= (-20681494829383775098804415409152343062282864338188075106929606524247191745307422993250916209984069382699090056121349334716796875e-160)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -2.0681494829383775e-33 or 3.5513325988060555e76 < y

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in z around 0

      \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{y} - \frac{1}{3} \cdot y}{z} \]
   3. Step-by-step derivation

   4. Applied rewrites 68.1%

      \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} - 0.3333333333333333 \cdot y}{z} \]
   5. Step-by-step derivation

   6. Applied rewrites 68.2%

      \[\leadsto \frac{\frac{y - \frac{t}{y}}{-3}}{z} \]

   7. Taylor expanded in y around inf

      \[\leadsto \frac{\frac{-1}{3} \cdot y}{z} \]
   8. Step-by-step derivation

   9. Applied rewrites 36.4%

      \[\leadsto \frac{-0.3333333333333333 \cdot y}{z} \]

   if -2.0681494829383775e-33 < y < 3.5513325988060555e76

   1. Initial program 95.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 61.0%

      \[\leadsto \frac{\mathsf{fma}\left(0.3333333333333333, \frac{t}{z}, x \cdot y\right)}{y} \]

   5. Taylor expanded in x around 0

      \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{z}}{y} \]
   6. Step-by-step derivation

   7. Applied rewrites 38.7%

      \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{z}}{y} \]

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 25.5%

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

Alternative 18: 25.5% accurate, 2.9× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return (x * y) / 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 = (x * y) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.8%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

2. Taylor expanded in y around 0

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

4. Applied rewrites 61.0%

   \[\leadsto \frac{\mathsf{fma}\left(0.3333333333333333, \frac{t}{z}, x \cdot y\right)}{y} \]

5. Taylor expanded in x around 0

   \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{z}}{y} \]
6. Step-by-step derivation

7. Applied rewrites 38.7%

   \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{z}}{y} \]

8. Taylor expanded in x around inf

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

10. Applied rewrites 25.5%

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

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64
  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))