Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B

Percentage Accurate: 77.0% → 98.1%

Time: 4.6s

Alternatives: 12

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

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) * y) / (a - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) * y) / (a - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 77.0%

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

3. Applied rewrites 93.9%

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

4. Taylor expanded in t around 0

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

6. Applied rewrites 98.1%

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

Alternative 2: 86.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -7.767293747409786 \cdot 10^{-87}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{a}{a - t}, x\right)\\ \mathbf{elif}\;a \leq 6.238359636049081 \cdot 10^{-18}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - z \cdot \frac{y}{a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= a -7.767293747409786e-87)
  (fma y (/ a (- a t)) x)
  (if (<= a 6.238359636049081e-18)
    (fma z (/ y (- t a)) x)
    (- (+ x y) (* z (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.767293747409786e-87) {
		tmp = fma(y, (a / (a - t)), x);
	} else if (a <= 6.238359636049081e-18) {
		tmp = fma(z, (y / (t - a)), x);
	} else {
		tmp = (x + y) - (z * (y / a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.767293747409786e-87)
		tmp = fma(y, Float64(a / Float64(a - t)), x);
	elseif (a <= 6.238359636049081e-18)
		tmp = fma(z, Float64(y / Float64(t - a)), x);
	else
		tmp = Float64(Float64(x + y) - Float64(z * Float64(y / a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.767293747409786e-87], N[(y * N[(a / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 6.238359636049081e-18], N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(z * N[(y / a), $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_1 = IF (a <= (6238359636049080634043266411720840101667096935550600733666470887328614480793476104736328125e-108)) THEN ((z * (y / (t - a))) + x) ELSE ((x + y) - (z * (y / a))) ENDIF IN
	LET tmp = IF (a <= (-7767293747409786068860004718053809514319862217966251197644451806220388392778359204458858685011090803370413084866929821613201903964891940446760468621856013708268980104612414688340717808333809105499388671915936559371484992908563071978278458118438720703125e-339)) THEN ((y * (a / (a - t))) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if a < -7.7672937474097861e-87

   1. Initial program 77.0%

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

   3. Applied rewrites 93.9%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 72.4%

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

   if -7.7672937474097861e-87 < a < 6.2383596360490806e-18

   1. Initial program 77.0%

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

   3. Applied rewrites 87.0%

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

   4. Taylor expanded in t around inf

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

   6. Applied rewrites 77.2%

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

   8. Applied rewrites 77.2%

      \[\leadsto \mathsf{fma}\left(z, \frac{y}{t - a}, x - 0\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 77.2%

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

   if 6.2383596360490806e-18 < a

   1. Initial program 77.0%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 64.7%

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

   6. Applied rewrites 66.6%

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

Alternative 3: 86.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -7.767293747409786 \cdot 10^{-87}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{a}{a - t}, x\right)\\ \mathbf{elif}\;a \leq 6.238359636049081 \cdot 10^{-18}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{y}{t - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{a - z}{a}, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= a -7.767293747409786e-87)
  (fma y (/ a (- a t)) x)
  (if (<= a 6.238359636049081e-18)
    (fma z (/ y (- t a)) x)
    (fma y (/ (- a z) a) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -7.767293747409786e-87) {
		tmp = fma(y, (a / (a - t)), x);
	} else if (a <= 6.238359636049081e-18) {
		tmp = fma(z, (y / (t - a)), x);
	} else {
		tmp = fma(y, ((a - z) / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -7.767293747409786e-87)
		tmp = fma(y, Float64(a / Float64(a - t)), x);
	elseif (a <= 6.238359636049081e-18)
		tmp = fma(z, Float64(y / Float64(t - a)), x);
	else
		tmp = fma(y, Float64(Float64(a - z) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -7.767293747409786e-87], N[(y * N[(a / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 6.238359636049081e-18], N[(z * N[(y / N[(t - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(N[(a - z), $MachinePrecision] / a), $MachinePrecision] + x), $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_1 = IF (a <= (6238359636049080634043266411720840101667096935550600733666470887328614480793476104736328125e-108)) THEN ((z * (y / (t - a))) + x) ELSE ((y * ((a - z) / a)) + x) ENDIF IN
	LET tmp = IF (a <= (-7767293747409786068860004718053809514319862217966251197644451806220388392778359204458858685011090803370413084866929821613201903964891940446760468621856013708268980104612414688340717808333809105499388671915936559371484992908563071978278458118438720703125e-339)) THEN ((y * (a / (a - t))) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if a < -7.7672937474097861e-87

   1. Initial program 77.0%

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

   3. Applied rewrites 93.9%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 72.4%

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

   if -7.7672937474097861e-87 < a < 6.2383596360490806e-18

   1. Initial program 77.0%

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

   3. Applied rewrites 87.0%

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

   4. Taylor expanded in t around inf

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

   6. Applied rewrites 77.2%

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

   8. Applied rewrites 77.2%

      \[\leadsto \mathsf{fma}\left(z, \frac{y}{t - a}, x - 0\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 77.2%

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

   if 6.2383596360490806e-18 < a

   1. Initial program 77.0%

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

   3. Applied rewrites 93.9%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 66.6%

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

Alternative 4: 81.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -6.38665791065844 \cdot 10^{-98}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{a}{a - t}, x\right)\\ \mathbf{elif}\;a \leq 1.99087747824985 \cdot 10^{-46}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{a - z}{a}, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= a -6.38665791065844e-98)
  (fma y (/ a (- a t)) x)
  (if (<= a 1.99087747824985e-46)
    (+ x (/ (* y z) t))
    (fma y (/ (- a z) a) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.38665791065844e-98) {
		tmp = fma(y, (a / (a - t)), x);
	} else if (a <= 1.99087747824985e-46) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = fma(y, ((a - z) / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.38665791065844e-98)
		tmp = fma(y, Float64(a / Float64(a - t)), x);
	elseif (a <= 1.99087747824985e-46)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	else
		tmp = fma(y, Float64(Float64(a - z) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.38665791065844e-98], N[(y * N[(a / N[(a - t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 1.99087747824985e-46], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(a - z), $MachinePrecision] / a), $MachinePrecision] + x), $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_1 = IF (a <= (199087747824984997886936872567856876854385410234444426897562071506677284933182711521177846255462710731655466742830835023825297724897609441541135311126708984375e-204)) THEN (x + ((y * z) / t)) ELSE ((y * ((a - z) / a)) + x) ENDIF IN
	LET tmp = IF (a <= (-63866579106584405506981906040670426465631804627889179778673726773923104937353692653962337658245320279703048988352080320914247659761099343849866450533491356225701021626109490901859264695964462277401532530499587101613399551057338899908723782450348238626247621141374111175537109375e-375)) THEN ((y * (a / (a - t))) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if a < -6.3866579106584406e-98

   1. Initial program 77.0%

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

   3. Applied rewrites 93.9%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 72.4%

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

   if -6.3866579106584406e-98 < a < 1.99087747824985e-46

   1. Initial program 77.0%

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

   2. Taylor expanded in t around -inf

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

   4. Applied rewrites 58.1%

      \[\leadsto x + -1 \cdot \frac{a \cdot y - y \cdot z}{t} \]

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 61.0%

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

   if 1.99087747824985e-46 < a

   1. Initial program 77.0%

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

   3. Applied rewrites 93.9%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 66.6%

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

Alternative 5: 81.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{a - z}{a}, x\right)\\ \mathbf{if}\;a \leq -4.636794655788244 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.99087747824985 \cdot 10^{-46}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma y (/ (- a z) a) x)))
  (if (<= a -4.636794655788244e-97)
    t_1
    (if (<= a 1.99087747824985e-46) (+ x (/ (* y z) t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, ((a - z) / a), x);
	double tmp;
	if (a <= -4.636794655788244e-97) {
		tmp = t_1;
	} else if (a <= 1.99087747824985e-46) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(Float64(a - z) / a), x)
	tmp = 0.0
	if (a <= -4.636794655788244e-97)
		tmp = t_1;
	elseif (a <= 1.99087747824985e-46)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(a - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -4.636794655788244e-97], t$95$1, If[LessEqual[a, 1.99087747824985e-46], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $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 = ((y * ((a - z) / a)) + x) IN
		LET tmp_1 = IF (a <= (199087747824984997886936872567856876854385410234444426897562071506677284933182711521177846255462710731655466742830835023825297724897609441541135311126708984375e-204)) THEN (x + ((y * z) / t)) ELSE t_1 ENDIF IN
		LET tmp = IF (a <= (-4636794655788244106205890780400092776968265779497900829864312184489138126709900652532247695786012145183880387530159310844688074697528154710961678879739479776583348965041979855810706223203959339235709257233776220354908983746422201517567961148724720032987534068524837493896484375e-373)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if a < -4.6367946557882441e-97 or 1.99087747824985e-46 < a

   1. Initial program 77.0%

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

   3. Applied rewrites 93.9%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 66.6%

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

   if -4.6367946557882441e-97 < a < 1.99087747824985e-46

   1. Initial program 77.0%

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

   2. Taylor expanded in t around -inf

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

   4. Applied rewrites 58.1%

      \[\leadsto x + -1 \cdot \frac{a \cdot y - y \cdot z}{t} \]

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 61.0%

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

Alternative 6: 76.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -2.8197968432687736 \cdot 10^{-44}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{y}{a}, x\right)\\ \mathbf{elif}\;a \leq 1.7299952040874803 \cdot 10^{-44}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \left(-y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= a -2.8197968432687736e-44)
  (fma a (/ y a) x)
  (if (<= a 1.7299952040874803e-44) (+ x (/ (* y z) t)) (- x (- y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.8197968432687736e-44) {
		tmp = fma(a, (y / a), x);
	} else if (a <= 1.7299952040874803e-44) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = x - -y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.8197968432687736e-44)
		tmp = fma(a, Float64(y / a), x);
	elseif (a <= 1.7299952040874803e-44)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	else
		tmp = Float64(x - Float64(-y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.8197968432687736e-44], N[(a * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 1.7299952040874803e-44], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x - (-y)), $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_1 = IF (a <= (17299952040874803418414247971230233205871008441999637021103833758252304860327992232766502972757785728140875823708073888429481712591950781643390655517578125e-198)) THEN (x + ((y * z) / t)) ELSE (x - (- y)) ENDIF IN
	LET tmp = IF (a <= (-2819796843268773614640655943967757972125580407807420717691756877242900831520732692518096284692827848864992446313755547482315932938945479691028594970703125e-197)) THEN ((a * (y / a)) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if a < -2.8197968432687736e-44

   1. Initial program 77.0%

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

   3. Applied rewrites 93.9%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 58.3%

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

   8. Applied rewrites 65.5%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 59.6%

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

   if -2.8197968432687736e-44 < a < 1.7299952040874803e-44

   1. Initial program 77.0%

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

   2. Taylor expanded in t around -inf

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

   4. Applied rewrites 58.1%

      \[\leadsto x + -1 \cdot \frac{a \cdot y - y \cdot z}{t} \]

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 61.0%

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

   if 1.7299952040874803e-44 < a

   1. Initial program 77.0%

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

   3. Applied rewrites 80.3%

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

   4. Taylor expanded in a around inf

      \[\leadsto x - -1 \cdot y \]
   5. Step-by-step derivation

   6. Applied rewrites 60.8%

      \[\leadsto x - -1 \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 60.8%

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

Alternative 7: 75.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -5.649431352281286 \cdot 10^{-46}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{y}{a}, x\right)\\ \mathbf{elif}\;a \leq 1.4695601448716176 \cdot 10^{-41}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(-y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= a -5.649431352281286e-46)
  (fma a (/ y a) x)
  (if (<= a 1.4695601448716176e-41) (fma y (/ z t) x) (- x (- y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.649431352281286e-46) {
		tmp = fma(a, (y / a), x);
	} else if (a <= 1.4695601448716176e-41) {
		tmp = fma(y, (z / t), x);
	} else {
		tmp = x - -y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.649431352281286e-46)
		tmp = fma(a, Float64(y / a), x);
	elseif (a <= 1.4695601448716176e-41)
		tmp = fma(y, Float64(z / t), x);
	else
		tmp = Float64(x - Float64(-y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.649431352281286e-46], N[(a * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 1.4695601448716176e-41], N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision], N[(x - (-y)), $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_1 = IF (a <= (146956014487161759545361415833330398912754032598929048665339341158869906267905470159666315090122358735943118579481136976028210483491420745849609375e-187)) THEN ((y * (z / t)) + x) ELSE (x - (- y)) ENDIF IN
	LET tmp = IF (a <= (-5649431352281286034085126318945065878873864764640056167622648579870085906491504741951659109966815981418844940965405705679547310182897490449249744415283203125e-202)) THEN ((a * (y / a)) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if a < -5.649431352281286e-46

   1. Initial program 77.0%

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

   3. Applied rewrites 93.9%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 58.3%

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

   8. Applied rewrites 65.5%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 59.6%

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

   if -5.649431352281286e-46 < a < 1.4695601448716176e-41

   1. Initial program 77.0%

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

   2. Taylor expanded in t around -inf

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

   4. Applied rewrites 58.1%

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

   6. Applied rewrites 58.5%

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

   8. Applied rewrites 60.6%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 62.1%

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

   if 1.4695601448716176e-41 < a

   1. Initial program 77.0%

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

   3. Applied rewrites 80.3%

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

   4. Taylor expanded in a around inf

      \[\leadsto x - -1 \cdot y \]
   5. Step-by-step derivation

   6. Applied rewrites 60.8%

      \[\leadsto x - -1 \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 60.8%

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

Alternative 8: 64.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -6.484516363435089 \cdot 10^{-221}:\\ \;\;\;\;\mathsf{fma}\left(a, \frac{y}{a}, x\right)\\ \mathbf{elif}\;a \leq 1.1437049085958378 \cdot 10^{-141}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x - \left(-y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= a -6.484516363435089e-221)
  (fma a (/ y a) x)
  (if (<= a 1.1437049085958378e-141) (/ (* y z) t) (- x (- y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.484516363435089e-221) {
		tmp = fma(a, (y / a), x);
	} else if (a <= 1.1437049085958378e-141) {
		tmp = (y * z) / t;
	} else {
		tmp = x - -y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.484516363435089e-221)
		tmp = fma(a, Float64(y / a), x);
	elseif (a <= 1.1437049085958378e-141)
		tmp = Float64(Float64(y * z) / t);
	else
		tmp = Float64(x - Float64(-y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.484516363435089e-221], N[(a * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 1.1437049085958378e-141], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], N[(x - (-y)), $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_1 = IF (a <= (114370490859583777271374036729465620805172096937795052943677469182271019900591827520730328083914053097537391008004524757140382858662677664461573204580447671393737482385891980537269100108984238330795851089737739279275282826958458553828576250880428745901248441937054516857168802072728745268439250969788984492428766607666172702666036381578644476331163559734704904258251190185546875e-518)) THEN ((y * z) / t) ELSE (x - (- y)) ENDIF IN
	LET tmp = IF (a <= (-64845163634350893305161489319631960443392902123726436481453975237944805185575063166056120803718912265584694039716055291619812239443383167009808873683128931121477221902018764882023680076618772329835736224009857527721434962456203072720475450928231719974625665332956061501085417580924278641871820923579778616827856948597457808636045555058322098009533646702383920066212905671800637220103002524385734977723890017423958021172852685917220397555399323677886970653244957413031622884334230996362610134333925514357912184444194676996402193491775278744171373546123504638671875e-783)) THEN ((a * (y / a)) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if a < -6.4845163634350893e-221

   1. Initial program 77.0%

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

   3. Applied rewrites 93.9%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 58.3%

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

   8. Applied rewrites 65.5%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 59.6%

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

   if -6.4845163634350893e-221 < a < 1.1437049085958378e-141

   1. Initial program 77.0%

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

   2. Taylor expanded in t around -inf

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

   4. Applied rewrites 58.1%

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

   6. Applied rewrites 58.5%

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

   8. Applied rewrites 60.6%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 18.3%

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

   if 1.1437049085958378e-141 < a

   1. Initial program 77.0%

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

   3. Applied rewrites 80.3%

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

   4. Taylor expanded in a around inf

      \[\leadsto x - -1 \cdot y \]
   5. Step-by-step derivation

   6. Applied rewrites 60.8%

      \[\leadsto x - -1 \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 60.8%

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

Alternative 9: 60.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := x - \left(-y\right)\\ \mathbf{if}\;a \leq -6.484516363435089 \cdot 10^{-221}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.1437049085958378 \cdot 10^{-141}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (- x (- y))))
  (if (<= a -6.484516363435089e-221)
    t_1
    (if (<= a 1.1437049085958378e-141) (/ (* y z) t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - -y;
	double tmp;
	if (a <= -6.484516363435089e-221) {
		tmp = t_1;
	} else if (a <= 1.1437049085958378e-141) {
		tmp = (y * z) / t;
	} 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
    if (a <= (-6.484516363435089d-221)) then
        tmp = t_1
    else if (a <= 1.1437049085958378d-141) then
        tmp = (y * z) / t
    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;
	double tmp;
	if (a <= -6.484516363435089e-221) {
		tmp = t_1;
	} else if (a <= 1.1437049085958378e-141) {
		tmp = (y * z) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - -y
	tmp = 0
	if a <= -6.484516363435089e-221:
		tmp = t_1
	elif a <= 1.1437049085958378e-141:
		tmp = (y * z) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(-y))
	tmp = 0.0
	if (a <= -6.484516363435089e-221)
		tmp = t_1;
	elseif (a <= 1.1437049085958378e-141)
		tmp = Float64(Float64(y * z) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - -y;
	tmp = 0.0;
	if (a <= -6.484516363435089e-221)
		tmp = t_1;
	elseif (a <= 1.1437049085958378e-141)
		tmp = (y * z) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - (-y)), $MachinePrecision]}, If[LessEqual[a, -6.484516363435089e-221], t$95$1, If[LessEqual[a, 1.1437049085958378e-141], N[(N[(y * z), $MachinePrecision] / t), $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)) IN
		LET tmp_1 = IF (a <= (114370490859583777271374036729465620805172096937795052943677469182271019900591827520730328083914053097537391008004524757140382858662677664461573204580447671393737482385891980537269100108984238330795851089737739279275282826958458553828576250880428745901248441937054516857168802072728745268439250969788984492428766607666172702666036381578644476331163559734704904258251190185546875e-518)) THEN ((y * z) / t) ELSE t_1 ENDIF IN
		LET tmp = IF (a <= (-64845163634350893305161489319631960443392902123726436481453975237944805185575063166056120803718912265584694039716055291619812239443383167009808873683128931121477221902018764882023680076618772329835736224009857527721434962456203072720475450928231719974625665332956061501085417580924278641871820923579778616827856948597457808636045555058322098009533646702383920066212905671800637220103002524385734977723890017423958021172852685917220397555399323677886970653244957413031622884334230996362610134333925514357912184444194676996402193491775278744171373546123504638671875e-783)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if a < -6.4845163634350893e-221 or 1.1437049085958378e-141 < a

   1. Initial program 77.0%

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

   3. Applied rewrites 80.3%

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

   4. Taylor expanded in a around inf

      \[\leadsto x - -1 \cdot y \]
   5. Step-by-step derivation

   6. Applied rewrites 60.8%

      \[\leadsto x - -1 \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 60.8%

      \[\leadsto x - \left(-y\right) \]

   if -6.4845163634350893e-221 < a < 1.1437049085958378e-141

   1. Initial program 77.0%

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

   2. Taylor expanded in t around -inf

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

   4. Applied rewrites 58.1%

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

   6. Applied rewrites 58.5%

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

   8. Applied rewrites 60.6%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 18.3%

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

Alternative 10: 60.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := x - \left(-y\right)\\ \mathbf{if}\;a \leq -6.484516363435089 \cdot 10^{-221}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.1437049085958378 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (- x (- y))))
  (if (<= a -6.484516363435089e-221)
    t_1
    (if (<= a 1.1437049085958378e-141) (* y (/ z t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - -y;
	double tmp;
	if (a <= -6.484516363435089e-221) {
		tmp = t_1;
	} else if (a <= 1.1437049085958378e-141) {
		tmp = y * (z / t);
	} 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
    if (a <= (-6.484516363435089d-221)) then
        tmp = t_1
    else if (a <= 1.1437049085958378d-141) then
        tmp = y * (z / t)
    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;
	double tmp;
	if (a <= -6.484516363435089e-221) {
		tmp = t_1;
	} else if (a <= 1.1437049085958378e-141) {
		tmp = y * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - -y
	tmp = 0
	if a <= -6.484516363435089e-221:
		tmp = t_1
	elif a <= 1.1437049085958378e-141:
		tmp = y * (z / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(-y))
	tmp = 0.0
	if (a <= -6.484516363435089e-221)
		tmp = t_1;
	elseif (a <= 1.1437049085958378e-141)
		tmp = Float64(y * Float64(z / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - -y;
	tmp = 0.0;
	if (a <= -6.484516363435089e-221)
		tmp = t_1;
	elseif (a <= 1.1437049085958378e-141)
		tmp = y * (z / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - (-y)), $MachinePrecision]}, If[LessEqual[a, -6.484516363435089e-221], t$95$1, If[LessEqual[a, 1.1437049085958378e-141], N[(y * N[(z / t), $MachinePrecision]), $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)) IN
		LET tmp_1 = IF (a <= (114370490859583777271374036729465620805172096937795052943677469182271019900591827520730328083914053097537391008004524757140382858662677664461573204580447671393737482385891980537269100108984238330795851089737739279275282826958458553828576250880428745901248441937054516857168802072728745268439250969788984492428766607666172702666036381578644476331163559734704904258251190185546875e-518)) THEN (y * (z / t)) ELSE t_1 ENDIF IN
		LET tmp = IF (a <= (-64845163634350893305161489319631960443392902123726436481453975237944805185575063166056120803718912265584694039716055291619812239443383167009808873683128931121477221902018764882023680076618772329835736224009857527721434962456203072720475450928231719974625665332956061501085417580924278641871820923579778616827856948597457808636045555058322098009533646702383920066212905671800637220103002524385734977723890017423958021172852685917220397555399323677886970653244957413031622884334230996362610134333925514357912184444194676996402193491775278744171373546123504638671875e-783)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if a < -6.4845163634350893e-221 or 1.1437049085958378e-141 < a

   1. Initial program 77.0%

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

   3. Applied rewrites 80.3%

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

   4. Taylor expanded in a around inf

      \[\leadsto x - -1 \cdot y \]
   5. Step-by-step derivation

   6. Applied rewrites 60.8%

      \[\leadsto x - -1 \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 60.8%

      \[\leadsto x - \left(-y\right) \]

   if -6.4845163634350893e-221 < a < 1.1437049085958378e-141

   1. Initial program 77.0%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 43.8%

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

   5. Taylor expanded in a around 0

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

   7. Applied rewrites 19.7%

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

Alternative 11: 59.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} t_1 := x - \left(-y\right)\\ \mathbf{if}\;a \leq -5.524266933419271 \cdot 10^{-46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.501123753950062 \cdot 10^{-83}:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (- x (- y))))
  (if (<= a -5.524266933419271e-46)
    t_1
    (if (<= a 5.501123753950062e-83) (* x 1.0) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - -y;
	double tmp;
	if (a <= -5.524266933419271e-46) {
		tmp = t_1;
	} else if (a <= 5.501123753950062e-83) {
		tmp = x * 1.0;
	} 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
    if (a <= (-5.524266933419271d-46)) then
        tmp = t_1
    else if (a <= 5.501123753950062d-83) then
        tmp = x * 1.0d0
    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;
	double tmp;
	if (a <= -5.524266933419271e-46) {
		tmp = t_1;
	} else if (a <= 5.501123753950062e-83) {
		tmp = x * 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - -y
	tmp = 0
	if a <= -5.524266933419271e-46:
		tmp = t_1
	elif a <= 5.501123753950062e-83:
		tmp = x * 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(-y))
	tmp = 0.0
	if (a <= -5.524266933419271e-46)
		tmp = t_1;
	elseif (a <= 5.501123753950062e-83)
		tmp = Float64(x * 1.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - -y;
	tmp = 0.0;
	if (a <= -5.524266933419271e-46)
		tmp = t_1;
	elseif (a <= 5.501123753950062e-83)
		tmp = x * 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - (-y)), $MachinePrecision]}, If[LessEqual[a, -5.524266933419271e-46], t$95$1, If[LessEqual[a, 5.501123753950062e-83], N[(x * 1.0), $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)) IN
		LET tmp_1 = IF (a <= (550112375395006215264065830248421423148279323137760169791012310228656434031263840549532241924139425239018088415733531205046607855016932308142045621145153195141818214024160484891394296818750703726441935066671096166146526229567825794219970703125e-325)) THEN (x * (1)) ELSE t_1 ENDIF IN
		LET tmp = IF (a <= (-5524266933419270696379376482145355092983230355190068415953939097793202543076501506689501139211518258463466868045149867072485250218960572965443134307861328125e-202)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if a < -5.5242669334192707e-46 or 5.5011237539500622e-83 < a

   1. Initial program 77.0%

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

   3. Applied rewrites 80.3%

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

   4. Taylor expanded in a around inf

      \[\leadsto x - -1 \cdot y \]
   5. Step-by-step derivation

   6. Applied rewrites 60.8%

      \[\leadsto x - -1 \cdot y \]
   7. Step-by-step derivation

   8. Applied rewrites 60.8%

      \[\leadsto x - \left(-y\right) \]

   if -5.5242669334192707e-46 < a < 5.5011237539500622e-83

   1. Initial program 77.0%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 68.6%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 21.7%

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

   8. Taylor expanded in x around inf

      \[\leadsto x \cdot 1 \]
   9. Step-by-step derivation

   10. Applied rewrites 51.9%

       \[\leadsto x \cdot 1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 51.9% accurate, 4.6× speedup

Math

\[x \cdot 1 \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (* x 1.0))

C

double code(double x, double y, double z, double t, double a) {
	return x * 1.0;
}

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 * 1.0d0
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x * 1.0;
}

Python

def code(x, y, z, t, a):
	return x * 1.0

Julia

function code(x, y, z, t, a)
	return Float64(x * 1.0)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x * 1.0;
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x * 1.0), $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 * (1)
END code

Derivation

1. Initial program 77.0%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 68.6%

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

5. Taylor expanded in z around inf

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

7. Applied rewrites 21.7%

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

8. Taylor expanded in x around inf

   \[\leadsto x \cdot 1 \]
9. Step-by-step derivation

10. Applied rewrites 51.9%

    \[\leadsto x \cdot 1 \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64
  (- (+ x y) (/ (* (- z t) y) (- a t))))