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

Percentage Accurate: 85.6% → 98.1%

Time: 4.0s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.6%

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

3. Applied rewrites 95.8%

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

Alternative 2: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.6%

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

3. Applied rewrites 98.1%

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

Alternative 3: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -5.4571549521241516 \cdot 10^{-14}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{t}, x\right)\\ \mathbf{elif}\;t \leq 3.260484372634548 \cdot 10^{-40}:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{t - a}, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= t -5.4571549521241516e-14)
  (fma y (- 1.0 (/ z t)) x)
  (if (<= t 3.260484372634548e-40)
    (+ x (/ (* y z) (- a t)))
    (fma y (/ t (- t a)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -5.4571549521241516e-14) {
		tmp = fma(y, (1.0 - (z / t)), x);
	} else if (t <= 3.260484372634548e-40) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = fma(y, (t / (t - a)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -5.4571549521241516e-14)
		tmp = fma(y, Float64(1.0 - Float64(z / t)), x);
	elseif (t <= 3.260484372634548e-40)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = fma(y, Float64(t / Float64(t - a)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -5.4571549521241516e-14], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 3.260484372634548e-40], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(t / N[(t - a), $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 =
	LET tmp_1 = IF (t <= (326048437263454803195331966268701919940038645673851321628990153669150920666324305786086649677313169248815682976783136837184429168701171875e-177)) THEN (x + ((y * z) / (a - t))) ELSE ((y * (t / (t - a))) + x) ENDIF IN
	LET tmp = IF (t <= (-54571549521241515535920819635449088562287149606344627272846992127597332000732421875e-96)) THEN ((y * ((1) - (z / t))) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if t < -5.4571549521241516e-14

   1. Initial program 85.6%

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

   3. Applied rewrites 98.1%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 67.0%

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

   8. Applied rewrites 67.0%

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

   if -5.4571549521241516e-14 < t < 3.260484372634548e-40

   1. Initial program 85.6%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 73.9%

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

   if 3.260484372634548e-40 < t

   1. Initial program 85.6%

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

   3. Applied rewrites 98.1%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 72.0%

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

Alternative 4: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -2.677882717229924 \cdot 10^{-15}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{t}, x\right)\\ \mathbf{elif}\;t \leq 2.0275327203029445 \cdot 10^{-52}:\\ \;\;\;\;\mathsf{fma}\left(z - t, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{t - a}, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= t -2.677882717229924e-15)
  (fma y (- 1.0 (/ z t)) x)
  (if (<= t 2.0275327203029445e-52)
    (fma (- z t) (/ y a) x)
    (fma y (/ t (- t a)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.677882717229924e-15) {
		tmp = fma(y, (1.0 - (z / t)), x);
	} else if (t <= 2.0275327203029445e-52) {
		tmp = fma((z - t), (y / a), x);
	} else {
		tmp = fma(y, (t / (t - a)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.677882717229924e-15)
		tmp = fma(y, Float64(1.0 - Float64(z / t)), x);
	elseif (t <= 2.0275327203029445e-52)
		tmp = fma(Float64(z - t), Float64(y / a), x);
	else
		tmp = fma(y, Float64(t / Float64(t - a)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.677882717229924e-15], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 2.0275327203029445e-52], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(t / N[(t - a), $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 =
	LET tmp_1 = IF (t <= (2027532720302944540217881058725914008137919835616601502313229083201171874413302625428451282710804074817306513566255398441255729073684488383833013358525931835174560546875e-220)) THEN (((z - t) * (y / a)) + x) ELSE ((y * (t / (t - a))) + x) ENDIF IN
	LET tmp = IF (t <= (-26778827172299239476305609360241898358304698905818508336551531101576983928680419921875e-100)) THEN ((y * ((1) - (z / t))) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if t < -2.6778827172299239e-15

   1. Initial program 85.6%

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

   3. Applied rewrites 98.1%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 67.0%

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

   8. Applied rewrites 67.0%

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

   if -2.6778827172299239e-15 < t < 2.0275327203029445e-52

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 57.4%

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

   6. Applied rewrites 61.1%

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

   if 2.0275327203029445e-52 < t

   1. Initial program 85.6%

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

   3. Applied rewrites 98.1%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 72.0%

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

Alternative 5: 82.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -2.8391169769943698 \cdot 10^{-15}:\\ \;\;\;\;\mathsf{fma}\left(y, 1 - \frac{z}{t}, x\right)\\ \mathbf{elif}\;t \leq 2.8638456223567507 \cdot 10^{-121}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{t - a}, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= t -2.8391169769943698e-15)
  (fma y (- 1.0 (/ z t)) x)
  (if (<= t 2.8638456223567507e-121)
    (+ x (* z (/ y a)))
    (fma t (/ y (- t a)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8391169769943698e-15) {
		tmp = fma(y, (1.0 - (z / t)), x);
	} else if (t <= 2.8638456223567507e-121) {
		tmp = x + (z * (y / a));
	} else {
		tmp = fma(t, (y / (t - a)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8391169769943698e-15)
		tmp = fma(y, Float64(1.0 - Float64(z / t)), x);
	elseif (t <= 2.8638456223567507e-121)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = fma(t, Float64(y / Float64(t - a)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8391169769943698e-15], N[(y * N[(1.0 - N[(z / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 2.8638456223567507e-121], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(t - a), $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 =
	LET tmp_1 = IF (t <= (286384562235675071580504820202616686807309994331158217926948394783820180384218896537029689973027625062122225152814927656394975676578400974255165222693263127968096319600328883893458430223736203563812228072756324791133831472285030586526340700078912304022621663526679646372620939634979679179319946025206178319422178901731967926025390625e-453)) THEN (x + (z * (y / a))) ELSE ((t * (y / (t - a))) + x) ENDIF IN
	LET tmp = IF (t <= (-28391169769943697668438335491106141511284438778972560868396612931974232196807861328125e-100)) THEN ((y * ((1) - (z / t))) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if t < -2.8391169769943698e-15

   1. Initial program 85.6%

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

   3. Applied rewrites 98.1%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 67.0%

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

   8. Applied rewrites 67.0%

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

   if -2.8391169769943698e-15 < t < 2.8638456223567507e-121

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 60.5%

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

   6. Applied rewrites 62.1%

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

   if 2.8638456223567507e-121 < t

   1. Initial program 85.6%

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 70.8%

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

Alternative 6: 82.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -2.8391169769943698 \cdot 10^{-15}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - z}{t}, x\right)\\ \mathbf{elif}\;t \leq 2.8638456223567507 \cdot 10^{-121}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{t - a}, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= t -2.8391169769943698e-15)
  (fma y (/ (- t z) t) x)
  (if (<= t 2.8638456223567507e-121)
    (+ x (* z (/ y a)))
    (fma t (/ y (- t a)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8391169769943698e-15) {
		tmp = fma(y, ((t - z) / t), x);
	} else if (t <= 2.8638456223567507e-121) {
		tmp = x + (z * (y / a));
	} else {
		tmp = fma(t, (y / (t - a)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8391169769943698e-15)
		tmp = fma(y, Float64(Float64(t - z) / t), x);
	elseif (t <= 2.8638456223567507e-121)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = fma(t, Float64(y / Float64(t - a)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8391169769943698e-15], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 2.8638456223567507e-121], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(t - a), $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 =
	LET tmp_1 = IF (t <= (286384562235675071580504820202616686807309994331158217926948394783820180384218896537029689973027625062122225152814927656394975676578400974255165222693263127968096319600328883893458430223736203563812228072756324791133831472285030586526340700078912304022621663526679646372620939634979679179319946025206178319422178901731967926025390625e-453)) THEN (x + (z * (y / a))) ELSE ((t * (y / (t - a))) + x) ENDIF IN
	LET tmp = IF (t <= (-28391169769943697668438335491106141511284438778972560868396612931974232196807861328125e-100)) THEN ((y * ((t - z) / t)) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if t < -2.8391169769943698e-15

   1. Initial program 85.6%

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

   3. Applied rewrites 98.1%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 67.0%

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

   if -2.8391169769943698e-15 < t < 2.8638456223567507e-121

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 60.5%

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

   6. Applied rewrites 62.1%

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

   if 2.8638456223567507e-121 < t

   1. Initial program 85.6%

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 70.8%

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

Alternative 7: 81.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -2.8391169769943698 \cdot 10^{-15}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - z}{t}, x\right)\\ \mathbf{elif}\;t \leq 2.4961977514465657 \cdot 10^{-52}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{t - a}, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= t -2.8391169769943698e-15)
  (fma y (/ (- t z) t) x)
  (if (<= t 2.4961977514465657e-52)
    (+ x (* z (/ y a)))
    (fma y (/ t (- t a)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.8391169769943698e-15) {
		tmp = fma(y, ((t - z) / t), x);
	} else if (t <= 2.4961977514465657e-52) {
		tmp = x + (z * (y / a));
	} else {
		tmp = fma(y, (t / (t - a)), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.8391169769943698e-15)
		tmp = fma(y, Float64(Float64(t - z) / t), x);
	elseif (t <= 2.4961977514465657e-52)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = fma(y, Float64(t / Float64(t - a)), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.8391169769943698e-15], N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t, 2.4961977514465657e-52], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(t / N[(t - a), $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 =
	LET tmp_1 = IF (t <= (249619775144656569669740825459633311902825249617630238395163005329547159697583457937845930714331145659362726404163422856530879143620305082862387280329130589962005615234375e-222)) THEN (x + (z * (y / a))) ELSE ((y * (t / (t - a))) + x) ENDIF IN
	LET tmp = IF (t <= (-28391169769943697668438335491106141511284438778972560868396612931974232196807861328125e-100)) THEN ((y * ((t - z) / t)) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if t < -2.8391169769943698e-15

   1. Initial program 85.6%

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

   3. Applied rewrites 98.1%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 67.0%

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

   if -2.8391169769943698e-15 < t < 2.4961977514465657e-52

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 60.5%

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

   6. Applied rewrites 62.1%

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

   if 2.4961977514465657e-52 < t

   1. Initial program 85.6%

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

   3. Applied rewrites 98.1%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 72.0%

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

Alternative 8: 81.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(y, \frac{t - z}{t}, x\right)\\ \mathbf{if}\;t \leq -2.8391169769943698 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.830958487977724 \cdot 10^{-52}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma y (/ (- t z) t) x)))
  (if (<= t -2.8391169769943698e-15)
    t_1
    (if (<= t 2.830958487977724e-52) (+ x (* z (/ y a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(y, ((t - z) / t), x);
	double tmp;
	if (t <= -2.8391169769943698e-15) {
		tmp = t_1;
	} else if (t <= 2.830958487977724e-52) {
		tmp = x + (z * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(y, Float64(Float64(t - z) / t), x)
	tmp = 0.0
	if (t <= -2.8391169769943698e-15)
		tmp = t_1;
	elseif (t <= 2.830958487977724e-52)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(t - z), $MachinePrecision] / t), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t, -2.8391169769943698e-15], t$95$1, If[LessEqual[t, 2.830958487977724e-52], N[(x + N[(z * N[(y / a), $MachinePrecision]), $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 * ((t - z) / t)) + x) IN
		LET tmp_1 = IF (t <= (28309584879777238245773341382504061581671441771892107294461212644110143610793170715248081858363606863186599168044092873541575132380516965913130889020976610481739044189453125e-224)) THEN (x + (z * (y / a))) ELSE t_1 ENDIF IN
		LET tmp = IF (t <= (-28391169769943697668438335491106141511284438778972560868396612931974232196807861328125e-100)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if t < -2.8391169769943698e-15 or 2.8309584879777238e-52 < t

   1. Initial program 85.6%

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

   3. Applied rewrites 98.1%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 67.0%

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

   if -2.8391169769943698e-15 < t < 2.8309584879777238e-52

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 60.5%

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

   6. Applied rewrites 62.1%

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

Alternative 9: 77.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -4.7662824425608525 \cdot 10^{-14}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 2.4961977514465657 \cdot 10^{-52}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= t -4.7662824425608525e-14)
  (+ x y)
  (if (<= t 2.4961977514465657e-52) (+ x (* z (/ y a))) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.7662824425608525e-14) {
		tmp = x + y;
	} else if (t <= 2.4961977514465657e-52) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.7662824425608525d-14)) then
        tmp = x + y
    else if (t <= 2.4961977514465657d-52) then
        tmp = x + (z * (y / a))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.7662824425608525e-14) {
		tmp = x + y;
	} else if (t <= 2.4961977514465657e-52) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.7662824425608525e-14:
		tmp = x + y
	elif t <= 2.4961977514465657e-52:
		tmp = x + (z * (y / a))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.7662824425608525e-14)
		tmp = Float64(x + y);
	elseif (t <= 2.4961977514465657e-52)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.7662824425608525e-14)
		tmp = x + y;
	elseif (t <= 2.4961977514465657e-52)
		tmp = x + (z * (y / a));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.7662824425608525e-14], N[(x + y), $MachinePrecision], If[LessEqual[t, 2.4961977514465657e-52], N[(x + N[(z * N[(y / a), $MachinePrecision]), $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 (t <= (249619775144656569669740825459633311902825249617630238395163005329547159697583457937845930714331145659362726404163422856530879143620305082862387280329130589962005615234375e-222)) THEN (x + (z * (y / a))) ELSE (x + y) ENDIF IN
	LET tmp = IF (t <= (-4766282442560852502077537738280695218950899771925833192653954029083251953125e-89)) THEN (x + y) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if t < -4.7662824425608525e-14 or 2.4961977514465657e-52 < t

   1. Initial program 85.6%

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

   2. Taylor expanded in t around inf

      \[\leadsto x + y \]
   3. Step-by-step derivation

   4. Applied rewrites 61.3%

      \[\leadsto x + y \]

   if -4.7662824425608525e-14 < t < 2.4961977514465657e-52

   1. Initial program 85.6%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 60.5%

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

   6. Applied rewrites 62.1%

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

Alternative 10: 64.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t, \frac{y}{t}, x\right)\\ \mathbf{if}\;a \leq -2.803375420246256 \cdot 10^{+161}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;a \leq -1.316894047366868 \cdot 10^{-268}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.6050336491349997 \cdot 10^{-278}:\\ \;\;\;\;\frac{y \cdot \left(t - z\right)}{t}\\ \mathbf{elif}\;a \leq 1.9720017373547914 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma t (/ y t) x)))
  (if (<= a -2.803375420246256e+161)
    (* x 1.0)
    (if (<= a -1.316894047366868e-268)
      t_1
      (if (<= a 1.6050336491349997e-278)
        (/ (* y (- t z)) t)
        (if (<= a 1.9720017373547914e+106) t_1 (* x 1.0)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(t, (y / t), x);
	double tmp;
	if (a <= -2.803375420246256e+161) {
		tmp = x * 1.0;
	} else if (a <= -1.316894047366868e-268) {
		tmp = t_1;
	} else if (a <= 1.6050336491349997e-278) {
		tmp = (y * (t - z)) / t;
	} else if (a <= 1.9720017373547914e+106) {
		tmp = t_1;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(t, Float64(y / t), x)
	tmp = 0.0
	if (a <= -2.803375420246256e+161)
		tmp = Float64(x * 1.0);
	elseif (a <= -1.316894047366868e-268)
		tmp = t_1;
	elseif (a <= 1.6050336491349997e-278)
		tmp = Float64(Float64(y * Float64(t - z)) / t);
	elseif (a <= 1.9720017373547914e+106)
		tmp = t_1;
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / t), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -2.803375420246256e+161], N[(x * 1.0), $MachinePrecision], If[LessEqual[a, -1.316894047366868e-268], t$95$1, If[LessEqual[a, 1.6050336491349997e-278], N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 1.9720017373547914e+106], t$95$1, 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 =
	LET t_1 = ((t * (y / t)) + x) IN
		LET tmp_3 = IF (a <= (19720017373547913738974786793130590873398222113986135146369594783732800465675538875672716716696974309457920)) THEN t_1 ELSE (x * (1)) ENDIF IN
		LET tmp_2 = IF (a <= (1605033649134999737813388523917831301769786873361452095428425072607556141745548770684512854450685413552610192990149106179745006342256291837868647616743877355045313553197242073343074865726454111312146364048364206706241059674706362021461666922178110491963402205481376713971307233788425979764336697458053209844939400534349716989472585206018872693953155898158954779967934131816871062890472894112361601140896608787876656530776241406712910091162988312197328767892925874990752121436697520809607664968153624473428127621288563919325874975463455618243439128202640859074049235928894750897953193385952154497493953207937910571457434039685646899938035919577273042223980979714692551851840107701718807220458984375e-974)) THEN ((y * (t - z)) / t) ELSE tmp_3 ENDIF IN
		LET tmp_1 = IF (a <= (-131689404736686795539013537409198416331873781586321037554247048437898289917443321392924031133313155113045413882240520504750292313687977180357856200219071336891428591710421307917025523890568825396542460871365842764854791910004763441194124536160002667256094448032663198901490030025430479989277341100488188418883082666551496816231126014563661129983007750720220546956436736155227987413199606171366914355604089038863512293651509610779453032458764528845312280990623687281540375184570806132222252958521470304332660974388828883542150046501241967315446195271819965680503307444710261771084652840678306579303090171302879525909648595534428595910103609867292107082903385162353515625e-936)) THEN t_1 ELSE tmp_2 ENDIF IN
		LET tmp = IF (a <= (-280337542024625624693651066497335093453761970279776419790132214526074812119086978961118586694716000330608302937522322130839813562701241903729275664649615013052416)) THEN (x * (1)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if a < -2.8033754202462562e161 or 1.9720017373547914e106 < a

   1. Initial program 85.6%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 79.3%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 51.3%

      \[\leadsto x \cdot 1 \]

   if -2.8033754202462562e161 < a < -1.316894047366868e-268 or 1.6050336491349997e-278 < a < 1.9720017373547914e106

   1. Initial program 85.6%

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in t around inf

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

   6. Applied rewrites 65.4%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 60.2%

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

   if -1.316894047366868e-268 < a < 1.6050336491349997e-278

   1. Initial program 85.6%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 48.8%

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

   6. Applied rewrites 48.7%

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

   7. Taylor expanded in a around 0

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

   9. Applied rewrites 24.1%

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

Alternative 11: 64.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := z \cdot \frac{y}{a - t}\\ \mathbf{if}\;z \leq -2.5041685250512675 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8793295931340427 \cdot 10^{+90}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* z (/ y (- a t)))))
  (if (<= z -2.5041685250512675e+119)
    t_1
    (if (<= z 1.8793295931340427e+90) (+ x y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / (a - t));
	double tmp;
	if (z <= -2.5041685250512675e+119) {
		tmp = t_1;
	} else if (z <= 1.8793295931340427e+90) {
		tmp = x + y;
	} 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 = z * (y / (a - t))
    if (z <= (-2.5041685250512675d+119)) then
        tmp = t_1
    else if (z <= 1.8793295931340427d+90) then
        tmp = x + 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 a) {
	double t_1 = z * (y / (a - t));
	double tmp;
	if (z <= -2.5041685250512675e+119) {
		tmp = t_1;
	} else if (z <= 1.8793295931340427e+90) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / (a - t))
	tmp = 0
	if z <= -2.5041685250512675e+119:
		tmp = t_1
	elif z <= 1.8793295931340427e+90:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(a - t)))
	tmp = 0.0
	if (z <= -2.5041685250512675e+119)
		tmp = t_1;
	elseif (z <= 1.8793295931340427e+90)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / (a - t));
	tmp = 0.0;
	if (z <= -2.5041685250512675e+119)
		tmp = t_1;
	elseif (z <= 1.8793295931340427e+90)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5041685250512675e+119], t$95$1, If[LessEqual[z, 1.8793295931340427e+90], N[(x + y), $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 = (z * (y / (a - t))) IN
		LET tmp_1 = IF (z <= (1879329593134042723717887216607391831273627632221002891386801269637503640284666951117045760)) THEN (x + y) ELSE t_1 ENDIF IN
		LET tmp = IF (z <= (-250416852505126753522150493918095262396822526547809660521366021611686595593662031864695868179652100189992839617510899712)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -2.5041685250512675e119 or 1.8793295931340427e90 < z

   1. Initial program 85.6%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 39.1%

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

   5. Taylor expanded in z around inf

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

   7. Applied rewrites 26.2%

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

   9. Applied rewrites 28.3%

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

   if -2.5041685250512675e119 < z < 1.8793295931340427e90

   1. Initial program 85.6%

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

   2. Taylor expanded in t around inf

      \[\leadsto x + y \]
   3. Step-by-step derivation

   4. Applied rewrites 61.3%

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

Alternative 12: 63.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -2.803375420246256 \cdot 10^{+161}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;a \leq 1.9720017373547914 \cdot 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{t}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= a -2.803375420246256e+161)
  (* x 1.0)
  (if (<= a 1.9720017373547914e+106) (fma t (/ y t) x) (* x 1.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.803375420246256e+161) {
		tmp = x * 1.0;
	} else if (a <= 1.9720017373547914e+106) {
		tmp = fma(t, (y / t), x);
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.803375420246256e+161)
		tmp = Float64(x * 1.0);
	elseif (a <= 1.9720017373547914e+106)
		tmp = fma(t, Float64(y / t), x);
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.803375420246256e+161], N[(x * 1.0), $MachinePrecision], If[LessEqual[a, 1.9720017373547914e+106], N[(t * N[(y / t), $MachinePrecision] + x), $MachinePrecision], 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 =
	LET tmp_1 = IF (a <= (19720017373547913738974786793130590873398222113986135146369594783732800465675538875672716716696974309457920)) THEN ((t * (y / t)) + x) ELSE (x * (1)) ENDIF IN
	LET tmp = IF (a <= (-280337542024625624693651066497335093453761970279776419790132214526074812119086978961118586694716000330608302937522322130839813562701241903729275664649615013052416)) THEN (x * (1)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if a < -2.8033754202462562e161 or 1.9720017373547914e106 < a

   1. Initial program 85.6%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 79.3%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 51.3%

      \[\leadsto x \cdot 1 \]

   if -2.8033754202462562e161 < a < 1.9720017373547914e106

   1. Initial program 85.6%

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in t around inf

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

   6. Applied rewrites 65.4%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 60.2%

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

Alternative 13: 62.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -2.7643020932137052 \cdot 10^{-27}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 6.243433878926949 \cdot 10^{-93}:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= t -2.7643020932137052e-27)
  (+ x y)
  (if (<= t 6.243433878926949e-93) (* x 1.0) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7643020932137052e-27) {
		tmp = x + y;
	} else if (t <= 6.243433878926949e-93) {
		tmp = x * 1.0;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.7643020932137052d-27)) then
        tmp = x + y
    else if (t <= 6.243433878926949d-93) then
        tmp = x * 1.0d0
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.7643020932137052e-27) {
		tmp = x + y;
	} else if (t <= 6.243433878926949e-93) {
		tmp = x * 1.0;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.7643020932137052e-27:
		tmp = x + y
	elif t <= 6.243433878926949e-93:
		tmp = x * 1.0
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.7643020932137052e-27)
		tmp = Float64(x + y);
	elseif (t <= 6.243433878926949e-93)
		tmp = Float64(x * 1.0);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.7643020932137052e-27)
		tmp = x + y;
	elseif (t <= 6.243433878926949e-93)
		tmp = x * 1.0;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.7643020932137052e-27], N[(x + y), $MachinePrecision], If[LessEqual[t, 6.243433878926949e-93], N[(x * 1.0), $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 (t <= (62434338789269486655428326929253601212393091949463781487715916825132628870879348982251113950616459077413656525594774240749660902303432713359573261837980573003883533447189525816162902145627152428413858067211718465836521572173527239169033009602571837604045867919921875e-358)) THEN (x * (1)) ELSE (x + y) ENDIF IN
	LET tmp = IF (t <= (-2764302093213705231947701562323418861007341667710571802926353310155007888572475938104844317422248423099517822265625e-141)) THEN (x + y) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if t < -2.7643020932137052e-27 or 6.2434338789269487e-93 < t

   1. Initial program 85.6%

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

   2. Taylor expanded in t around inf

      \[\leadsto x + y \]
   3. Step-by-step derivation

   4. Applied rewrites 61.3%

      \[\leadsto x + y \]

   if -2.7643020932137052e-27 < t < 6.2434338789269487e-93

   1. Initial program 85.6%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 79.3%

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

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 51.3%

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

Alternative 14: 61.3% accurate, 4.3× speedup

Math

\[x + y \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := 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 =
	x + y
END code

Derivation

1. Initial program 85.6%

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

2. Taylor expanded in t around inf

   \[\leadsto x + y \]
3. Step-by-step derivation

4. Applied rewrites 61.3%

   \[\leadsto x + y \]
5. Add Preprocessing

Alternative 15: 18.7% accurate, 15.6× speedup

Math

\[y \]

FPCore

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

C

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

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 = y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := y

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
END code

Derivation

1. Initial program 85.6%

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

2. Taylor expanded in t around inf

   \[\leadsto x + y \]
3. Step-by-step derivation

4. Applied rewrites 61.3%

   \[\leadsto x + y \]

5. Taylor expanded in x around 0

   \[\leadsto y \]
6. Step-by-step derivation

7. Applied rewrites 18.7%

   \[\leadsto y \]
8. Add Preprocessing

Reproduce

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