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

Percentage Accurate: 85.4% → 98.0%

Time: 3.0s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.4%

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

3. Applied rewrites 98.0%

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

Alternative 2: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -3.591333072792645 \cdot 10^{+119}:\\ \;\;\;\;x + \left(y - \frac{t}{z} \cdot y\right)\\ \mathbf{elif}\;z \leq 6.160770138968741 \cdot 10^{-44}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= z -3.591333072792645e+119)
  (+ x (- y (* (/ t z) y)))
  (if (<= z 6.160770138968741e-44)
    (fma t (/ y (- a z)) x)
    (+ x (* y (/ (- z t) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.591333072792645e+119) {
		tmp = x + (y - ((t / z) * y));
	} else if (z <= 6.160770138968741e-44) {
		tmp = fma(t, (y / (a - z)), x);
	} else {
		tmp = x + (y * ((z - t) / z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.591333072792645e+119)
		tmp = Float64(x + Float64(y - Float64(Float64(t / z) * y)));
	elseif (z <= 6.160770138968741e-44)
		tmp = fma(t, Float64(y / Float64(a - z)), x);
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.591333072792645e+119], N[(x + N[(y - N[(N[(t / z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.160770138968741e-44], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $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 (z <= (6160770138968740753864306258720029515741723332288246234688933099762526271665158209876938712959280219646923952743489127925613502156920731067657470703125e-194)) THEN ((t * (y / (a - z))) + x) ELSE (x + (y * ((z - t) / z))) ENDIF IN
	LET tmp = IF (z <= (-359133307279264471181423639226018461358023480459202427092018584051089105935211859604956351549633280856114360094507925504)) THEN (x + (y - ((t / z) * y))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if z < -3.5913330727926447e119

   1. Initial program 85.4%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 58.8%

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

   6. Applied rewrites 66.9%

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

   8. Applied rewrites 66.9%

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

   if -3.5913330727926447e119 < z < 6.1607701389687408e-44

   1. Initial program 85.4%

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 76.6%

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

   if 6.1607701389687408e-44 < z

   1. Initial program 85.4%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 58.8%

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

   6. Applied rewrites 66.9%

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

Alternative 3: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := x + y \cdot \frac{z - t}{z}\\ \mathbf{if}\;z \leq -3.591333072792645 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.160770138968741 \cdot 10^{-44}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (+ x (* y (/ (- z t) z)))))
  (if (<= z -3.591333072792645e+119)
    t_1
    (if (<= z 6.160770138968741e-44) (fma t (/ y (- a z)) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * ((z - t) / z));
	double tmp;
	if (z <= -3.591333072792645e+119) {
		tmp = t_1;
	} else if (z <= 6.160770138968741e-44) {
		tmp = fma(t, (y / (a - z)), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(Float64(z - t) / z)))
	tmp = 0.0
	if (z <= -3.591333072792645e+119)
		tmp = t_1;
	elseif (z <= 6.160770138968741e-44)
		tmp = fma(t, Float64(y / Float64(a - z)), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.591333072792645e+119], t$95$1, If[LessEqual[z, 6.160770138968741e-44], N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $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 * ((z - t) / z))) IN
		LET tmp_1 = IF (z <= (6160770138968740753864306258720029515741723332288246234688933099762526271665158209876938712959280219646923952743489127925613502156920731067657470703125e-194)) THEN ((t * (y / (a - z))) + x) ELSE t_1 ENDIF IN
		LET tmp = IF (z <= (-359133307279264471181423639226018461358023480459202427092018584051089105935211859604956351549633280856114360094507925504)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -3.5913330727926447e119 or 6.1607701389687408e-44 < z

   1. Initial program 85.4%

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

   2. Taylor expanded in a around 0

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

   4. Applied rewrites 58.8%

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

   6. Applied rewrites 66.9%

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

   if -3.5913330727926447e119 < z < 6.1607701389687408e-44

   1. Initial program 85.4%

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 76.6%

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

Alternative 4: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -3.2006332828584774 \cdot 10^{+119}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.0860344461208277 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= z -3.2006332828584774e+119)
  (+ x y)
  (if (<= z 1.0860344461208277e+99) (fma t (/ y (- a z)) x) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2006332828584774e+119) {
		tmp = x + y;
	} else if (z <= 1.0860344461208277e+99) {
		tmp = fma(t, (y / (a - z)), x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2006332828584774e+119)
		tmp = Float64(x + y);
	elseif (z <= 1.0860344461208277e+99)
		tmp = fma(t, Float64(y / Float64(a - z)), x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2006332828584774e+119], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.0860344461208277e+99], N[(t * N[(y / N[(a - z), $MachinePrecision]), $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 (z <= (1086034446120827697090662479796224499285448762806101703935024084579163397898706478714132622724825088)) THEN ((t * (y / (a - z))) + x) ELSE (x + y) ENDIF IN
	LET tmp = IF (z <= (-320063328285847740642475589212748460854842850679856893256051146611229254908990277072698266432116104144165336245453455360)) THEN (x + y) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -3.2006332828584774e119 or 1.0860344461208277e99 < z

   1. Initial program 85.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.8%

      \[\leadsto x + y \]

   if -3.2006332828584774e119 < z < 1.0860344461208277e99

   1. Initial program 85.4%

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 76.6%

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

Alternative 5: 84.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -3.2006332828584774 \cdot 10^{+119}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 1.0860344461208277 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= z -3.2006332828584774e+119)
  (+ x y)
  (if (<= z 1.0860344461208277e+99) (fma y (/ t (- a z)) x) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.2006332828584774e+119) {
		tmp = x + y;
	} else if (z <= 1.0860344461208277e+99) {
		tmp = fma(y, (t / (a - z)), x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.2006332828584774e+119)
		tmp = Float64(x + y);
	elseif (z <= 1.0860344461208277e+99)
		tmp = fma(y, Float64(t / Float64(a - z)), x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.2006332828584774e+119], N[(x + y), $MachinePrecision], If[LessEqual[z, 1.0860344461208277e+99], N[(y * N[(t / N[(a - z), $MachinePrecision]), $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 (z <= (1086034446120827697090662479796224499285448762806101703935024084579163397898706478714132622724825088)) THEN ((y * (t / (a - z))) + x) ELSE (x + y) ENDIF IN
	LET tmp = IF (z <= (-320063328285847740642475589212748460854842850679856893256051146611229254908990277072698266432116104144165336245453455360)) THEN (x + y) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -3.2006332828584774e119 or 1.0860344461208277e99 < z

   1. Initial program 85.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.8%

      \[\leadsto x + y \]

   if -3.2006332828584774e119 < z < 1.0860344461208277e99

   1. Initial program 85.4%

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

   3. Applied rewrites 98.0%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 76.6%

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

Alternative 6: 75.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -4.0092119274769696 \cdot 10^{+119}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.3441364266120796 \cdot 10^{-60}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= z -4.0092119274769696e+119)
  (+ x y)
  (if (<= z 4.3441364266120796e-60) (fma t (/ y a) x) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.0092119274769696e+119) {
		tmp = x + y;
	} else if (z <= 4.3441364266120796e-60) {
		tmp = fma(t, (y / a), x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.0092119274769696e+119)
		tmp = Float64(x + y);
	elseif (z <= 4.3441364266120796e-60)
		tmp = fma(t, Float64(y / a), x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.0092119274769696e+119], N[(x + y), $MachinePrecision], If[LessEqual[z, 4.3441364266120796e-60], N[(t * N[(y / a), $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 (z <= (4344136426612079645920148933154515727349672138600712276858992012262299831984205013002927057406112051808796001553322894713288419961440763238661038627384802790487583479261957108974456787109375e-249)) THEN ((t * (y / a)) + x) ELSE (x + y) ENDIF IN
	LET tmp = IF (z <= (-400921192747696963113054246837181747459421505472127106883111382938515538004897083551881961629901330165306159503274672128)) THEN (x + y) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -4.0092119274769696e119 or 4.3441364266120796e-60 < z

   1. Initial program 85.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.8%

      \[\leadsto x + y \]

   if -4.0092119274769696e119 < z < 4.3441364266120796e-60

   1. Initial program 85.4%

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 60.7%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 62.1%

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

Alternative 7: 75.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -3.730626024354086 \cdot 10^{+119}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;z \leq 4.3441364266120796 \cdot 10^{-60}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= z -3.730626024354086e+119)
  (+ x y)
  (if (<= z 4.3441364266120796e-60) (fma y (/ t a) x) (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.730626024354086e+119) {
		tmp = x + y;
	} else if (z <= 4.3441364266120796e-60) {
		tmp = fma(y, (t / a), x);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.730626024354086e+119)
		tmp = Float64(x + y);
	elseif (z <= 4.3441364266120796e-60)
		tmp = fma(y, Float64(t / a), x);
	else
		tmp = Float64(x + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.730626024354086e+119], N[(x + y), $MachinePrecision], If[LessEqual[z, 4.3441364266120796e-60], N[(y * N[(t / a), $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 (z <= (4344136426612079645920148933154515727349672138600712276858992012262299831984205013002927057406112051808796001553322894713288419961440763238661038627384802790487583479261957108974456787109375e-249)) THEN ((y * (t / a)) + x) ELSE (x + y) ENDIF IN
	LET tmp = IF (z <= (-373062602435408611268023258533161310779105162733438353724830879843969544358556523973484928988005879896485031666954272768)) THEN (x + y) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -3.7306260243540861e119 or 4.3441364266120796e-60 < z

   1. Initial program 85.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.8%

      \[\leadsto x + y \]

   if -3.7306260243540861e119 < z < 4.3441364266120796e-60

   1. Initial program 85.4%

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

   3. Applied rewrites 98.0%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 62.0%

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

Alternative 8: 63.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -1.3285211566063567 \cdot 10^{+112}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;a \leq 6.616817877193918 \cdot 10^{+145}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{x}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= a -1.3285211566063567e+112)
  (* x 1.0)
  (if (<= a 6.616817877193918e+145) (fma x (/ y x) x) (* x 1.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.3285211566063567e+112) {
		tmp = x * 1.0;
	} else if (a <= 6.616817877193918e+145) {
		tmp = fma(x, (y / x), x);
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.3285211566063567e+112)
		tmp = Float64(x * 1.0);
	elseif (a <= 6.616817877193918e+145)
		tmp = fma(x, Float64(y / x), x);
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.3285211566063567e+112], N[(x * 1.0), $MachinePrecision], If[LessEqual[a, 6.616817877193918e+145], N[(x * N[(y / x), $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 <= (66168178771939178204990947541812968272369034485745516188850647501402849663680844545393345493574237644211583979946265929614112052047736234892591104)) THEN ((x * (y / x)) + x) ELSE (x * (1)) ENDIF IN
	LET tmp = IF (a <= (-13285211566063566635443518051383323030722052257711134291813311174740145788415668192172421166668371452940450267136)) THEN (x * (1)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if a < -1.3285211566063567e112 or 6.6168178771939178e145 < a

   1. Initial program 85.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.8%

      \[\leadsto x + y \]

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 58.3%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 50.6%

       \[\leadsto x \cdot 1 \]

   if -1.3285211566063567e112 < a < 6.6168178771939178e145

   1. Initial program 85.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.8%

      \[\leadsto x + y \]

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 58.3%

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

   9. Applied rewrites 58.3%

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

Alternative 9: 61.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -5.356308163371003 \cdot 10^{+111}:\\ \;\;\;\;x \cdot 1\\ \mathbf{elif}\;a \leq 6.616817877193918 \cdot 10^{+145}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= a -5.356308163371003e+111)
  (* x 1.0)
  (if (<= a 6.616817877193918e+145) (+ x y) (* x 1.0))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.356308163371003e+111) {
		tmp = x * 1.0;
	} else if (a <= 6.616817877193918e+145) {
		tmp = x + y;
	} else {
		tmp = x * 1.0;
	}
	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 (a <= (-5.356308163371003d+111)) then
        tmp = x * 1.0d0
    else if (a <= 6.616817877193918d+145) then
        tmp = x + y
    else
        tmp = x * 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.356308163371003e+111) {
		tmp = x * 1.0;
	} else if (a <= 6.616817877193918e+145) {
		tmp = x + y;
	} else {
		tmp = x * 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.356308163371003e+111:
		tmp = x * 1.0
	elif a <= 6.616817877193918e+145:
		tmp = x + y
	else:
		tmp = x * 1.0
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.356308163371003e+111)
		tmp = Float64(x * 1.0);
	elseif (a <= 6.616817877193918e+145)
		tmp = Float64(x + y);
	else
		tmp = Float64(x * 1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.356308163371003e+111)
		tmp = x * 1.0;
	elseif (a <= 6.616817877193918e+145)
		tmp = x + y;
	else
		tmp = x * 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.356308163371003e+111], N[(x * 1.0), $MachinePrecision], If[LessEqual[a, 6.616817877193918e+145], N[(x + y), $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 <= (66168178771939178204990947541812968272369034485745516188850647501402849663680844545393345493574237644211583979946265929614112052047736234892591104)) THEN (x + y) ELSE (x * (1)) ENDIF IN
	LET tmp = IF (a <= (-5356308163371002738388645935106676408412253501957477659145052997366278447263337038267430594153630977805130924032)) THEN (x * (1)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if a < -5.3563081633710027e111 or 6.6168178771939178e145 < a

   1. Initial program 85.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.8%

      \[\leadsto x + y \]

   5. Taylor expanded in x around inf

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

   7. Applied rewrites 58.3%

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

   8. Taylor expanded in x around inf

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

   10. Applied rewrites 50.6%

       \[\leadsto x \cdot 1 \]

   if -5.3563081633710027e111 < a < 6.6168178771939178e145

   1. Initial program 85.4%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.8%

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

Alternative 10: 60.8% 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 85.4%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 60.8%

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

Alternative 11: 19.0% 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 85.4%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 60.8%

   \[\leadsto x + y \]

5. Taylor expanded in x around 0

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

7. Applied rewrites 19.0%

   \[\leadsto y \]
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, A"
  :precision binary64
  (+ x (/ (* y (- z t)) (- z a))))