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

Percentage Accurate: 85.2% → 98.2%

Time: 4.0s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.2%

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

3. Applied rewrites 97.4%

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

Alternative 2: 97.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.2%

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

3. Applied rewrites 95.8%

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

Alternative 3: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.2%

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

3. Applied rewrites 98.2%

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

Alternative 4: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -1.3917919735364662 \cdot 10^{+101}:\\ \;\;\;\;x + \mathsf{fma}\left(t, \frac{-y}{z}, t\right)\\ \mathbf{elif}\;z \leq 1.8466671653575995 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{t \cdot y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - y}{z}, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= z -1.3917919735364662e+101)
  (+ x (fma t (/ (- y) z) t))
  (if (<= z 1.8466671653575995e+46)
    (+ x (/ (* t y) (- a z)))
    (fma t (/ (- z y) z) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3917919735364662e+101) {
		tmp = x + fma(t, (-y / z), t);
	} else if (z <= 1.8466671653575995e+46) {
		tmp = x + ((t * y) / (a - z));
	} else {
		tmp = fma(t, ((z - y) / z), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3917919735364662e+101)
		tmp = Float64(x + fma(t, Float64(Float64(-y) / z), t));
	elseif (z <= 1.8466671653575995e+46)
		tmp = Float64(x + Float64(Float64(t * y) / Float64(a - z)));
	else
		tmp = fma(t, Float64(Float64(z - y) / z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3917919735364662e+101], N[(x + N[(t * N[((-y) / z), $MachinePrecision] + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8466671653575995e+46], N[(x + N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(z - y), $MachinePrecision] / z), $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 (z <= (18466671653575994563829447868636263832415633408)) THEN (x + ((t * y) / (a - z))) ELSE ((t * ((z - y) / z)) + x) ENDIF IN
	LET tmp = IF (z <= (-139179197353646615187994754334134776366339498716089086292338886582260482498044354946197299227392999424)) THEN (x + ((t * ((- y) / z)) + t)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if z < -1.3917919735364662e101

   1. Initial program 85.2%

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

   3. Applied rewrites 98.2%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 58.2%

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

   8. Applied rewrites 66.8%

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

   if -1.3917919735364662e101 < z < 1.8466671653575995e46

   1. Initial program 85.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 73.1%

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

   if 1.8466671653575995e46 < z

   1. Initial program 85.2%

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

   3. Applied rewrites 98.2%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 66.8%

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

Alternative 5: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t, \frac{z - y}{z}, x\right)\\ \mathbf{if}\;z \leq -1.3917919735364662 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8466671653575995 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{t \cdot y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma t (/ (- z y) z) x)))
  (if (<= z -1.3917919735364662e+101)
    t_1
    (if (<= z 1.8466671653575995e+46) (+ x (/ (* t y) (- a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(t, ((z - y) / z), x);
	double tmp;
	if (z <= -1.3917919735364662e+101) {
		tmp = t_1;
	} else if (z <= 1.8466671653575995e+46) {
		tmp = x + ((t * y) / (a - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(t, Float64(Float64(z - y) / z), x)
	tmp = 0.0
	if (z <= -1.3917919735364662e+101)
		tmp = t_1;
	elseif (z <= 1.8466671653575995e+46)
		tmp = Float64(x + Float64(Float64(t * y) / Float64(a - z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -1.3917919735364662e+101], t$95$1, If[LessEqual[z, 1.8466671653575995e+46], N[(x + N[(N[(t * y), $MachinePrecision] / N[(a - z), $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 = ((t * ((z - y) / z)) + x) IN
		LET tmp_1 = IF (z <= (18466671653575994563829447868636263832415633408)) THEN (x + ((t * y) / (a - z))) ELSE t_1 ENDIF IN
		LET tmp = IF (z <= (-139179197353646615187994754334134776366339498716089086292338886582260482498044354946197299227392999424)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -1.3917919735364662e101 or 1.8466671653575995e46 < z

   1. Initial program 85.2%

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

   3. Applied rewrites 98.2%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 66.8%

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

   if -1.3917919735364662e101 < z < 1.8466671653575995e46

   1. Initial program 85.2%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 73.1%

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

Alternative 6: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \leq -6.632891920392298 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{elif}\;a \leq 5.778775689756362 \cdot 10^{-13}:\\ \;\;\;\;\mathsf{fma}\left(z - y, \frac{t}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y - z, \frac{t}{a}, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= a -6.632891920392298e-9)
  (fma t (/ (- y z) a) x)
  (if (<= a 5.778775689756362e-13)
    (fma (- z y) (/ t z) x)
    (fma (- y z) (/ t a) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.632891920392298e-9) {
		tmp = fma(t, ((y - z) / a), x);
	} else if (a <= 5.778775689756362e-13) {
		tmp = fma((z - y), (t / z), x);
	} else {
		tmp = fma((y - z), (t / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.632891920392298e-9)
		tmp = fma(t, Float64(Float64(y - z) / a), x);
	elseif (a <= 5.778775689756362e-13)
		tmp = fma(Float64(z - y), Float64(t / z), x);
	else
		tmp = fma(Float64(y - z), Float64(t / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.632891920392298e-9], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[a, 5.778775689756362e-13], N[(N[(z - y), $MachinePrecision] * N[(t / z), $MachinePrecision] + x), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(t / 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 <= (577877568975636198408552582247986833499826808679955547631834633648395538330078125e-93)) THEN (((z - y) * (t / z)) + x) ELSE (((y - z) * (t / a)) + x) ENDIF IN
	LET tmp = IF (a <= (-663289192039229837397824556650093030807369132162421010434627532958984375e-80)) THEN ((t * ((y - z) / a)) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if a < -6.6328919203922984e-9

   1. Initial program 85.2%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 56.8%

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

   6. Applied rewrites 59.6%

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

   if -6.6328919203922984e-9 < a < 5.778775689756362e-13

   1. Initial program 85.2%

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

   3. Applied rewrites 98.2%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 58.2%

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

   8. Applied rewrites 65.2%

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

   if 5.778775689756362e-13 < a

   1. Initial program 85.2%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 56.8%

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

   6. Applied rewrites 60.2%

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

Alternative 7: 81.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -6.632891920392298 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.778775689756362 \cdot 10^{-13}:\\ \;\;\;\;\mathsf{fma}\left(z - y, \frac{t}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma t (/ (- y z) a) x)))
  (if (<= a -6.632891920392298e-9)
    t_1
    (if (<= a 5.778775689756362e-13) (fma (- z y) (/ t z) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(t, ((y - z) / a), x);
	double tmp;
	if (a <= -6.632891920392298e-9) {
		tmp = t_1;
	} else if (a <= 5.778775689756362e-13) {
		tmp = fma((z - y), (t / z), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(t, Float64(Float64(y - z) / a), x)
	tmp = 0.0
	if (a <= -6.632891920392298e-9)
		tmp = t_1;
	elseif (a <= 5.778775689756362e-13)
		tmp = fma(Float64(z - y), Float64(t / z), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -6.632891920392298e-9], t$95$1, If[LessEqual[a, 5.778775689756362e-13], N[(N[(z - y), $MachinePrecision] * N[(t / z), $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 = ((t * ((y - z) / a)) + x) IN
		LET tmp_1 = IF (a <= (577877568975636198408552582247986833499826808679955547631834633648395538330078125e-93)) THEN (((z - y) * (t / z)) + x) ELSE t_1 ENDIF IN
		LET tmp = IF (a <= (-663289192039229837397824556650093030807369132162421010434627532958984375e-80)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if a < -6.6328919203922984e-9 or 5.778775689756362e-13 < a

   1. Initial program 85.2%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 56.8%

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

   6. Applied rewrites 59.6%

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

   if -6.6328919203922984e-9 < a < 5.778775689756362e-13

   1. Initial program 85.2%

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

   3. Applied rewrites 98.2%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 58.2%

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

   8. Applied rewrites 65.2%

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

Alternative 8: 80.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t, \frac{y - z}{a}, x\right)\\ \mathbf{if}\;a \leq -6.632891920392298 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.047689065869472 \cdot 10^{-16}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{z - y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma t (/ (- y z) a) x)))
  (if (<= a -6.632891920392298e-9)
    t_1
    (if (<= a 2.047689065869472e-16) (fma t (/ (- z y) z) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(t, ((y - z) / a), x);
	double tmp;
	if (a <= -6.632891920392298e-9) {
		tmp = t_1;
	} else if (a <= 2.047689065869472e-16) {
		tmp = fma(t, ((z - y) / z), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(t, Float64(Float64(y - z) / a), x)
	tmp = 0.0
	if (a <= -6.632891920392298e-9)
		tmp = t_1;
	elseif (a <= 2.047689065869472e-16)
		tmp = fma(t, Float64(Float64(z - y) / z), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[a, -6.632891920392298e-9], t$95$1, If[LessEqual[a, 2.047689065869472e-16], N[(t * N[(N[(z - y), $MachinePrecision] / z), $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 = ((t * ((y - z) / a)) + x) IN
		LET tmp_1 = IF (a <= (204768906586947190932995823874223971654986203492186669361529993693693540990352630615234375e-105)) THEN ((t * ((z - y) / z)) + x) ELSE t_1 ENDIF IN
		LET tmp = IF (a <= (-663289192039229837397824556650093030807369132162421010434627532958984375e-80)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if a < -6.6328919203922984e-9 or 2.0476890658694719e-16 < a

   1. Initial program 85.2%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 56.8%

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

   6. Applied rewrites 59.6%

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

   if -6.6328919203922984e-9 < a < 2.0476890658694719e-16

   1. Initial program 85.2%

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

   3. Applied rewrites 98.2%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 66.8%

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

Alternative 9: 80.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t, \frac{z - y}{z}, x\right)\\ \mathbf{if}\;z \leq -1.4421885974416013 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.508549014258338 \cdot 10^{-44}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma t (/ (- z y) z) x)))
  (if (<= z -1.4421885974416013e-7)
    t_1
    (if (<= z 8.508549014258338e-44) (+ x (* t (/ y a))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(t, ((z - y) / z), x);
	double tmp;
	if (z <= -1.4421885974416013e-7) {
		tmp = t_1;
	} else if (z <= 8.508549014258338e-44) {
		tmp = x + (t * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(t, Float64(Float64(z - y) / z), x)
	tmp = 0.0
	if (z <= -1.4421885974416013e-7)
		tmp = t_1;
	elseif (z <= 8.508549014258338e-44)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -1.4421885974416013e-7], t$95$1, If[LessEqual[z, 8.508549014258338e-44], N[(x + N[(t * 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 = ((t * ((z - y) / z)) + x) IN
		LET tmp_1 = IF (z <= (850854901425833773236309237762848125960571182619438783402747385146954734733208151442070219696890246054829637346005044573615805347799323499202728271484375e-196)) THEN (x + (t * (y / a))) ELSE t_1 ENDIF IN
		LET tmp = IF (z <= (-144218859744160128040396423761138056107711236109025776386260986328125e-75)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -1.4421885974416013e-7 or 8.5085490142583377e-44 < z

   1. Initial program 85.2%

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

   3. Applied rewrites 98.2%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 66.8%

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

   if -1.4421885974416013e-7 < z < 8.5085490142583377e-44

   1. Initial program 85.2%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 59.8%

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

   6. Applied rewrites 61.6%

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

Alternative 10: 77.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -1.2478311614280187 \cdot 10^{-10}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 7.921979766313861 \cdot 10^{+51}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= z -1.2478311614280187e-10)
  (+ x t)
  (if (<= z 7.921979766313861e+51) (+ x (* t (/ y a))) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2478311614280187e-10) {
		tmp = x + t;
	} else if (z <= 7.921979766313861e+51) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + t;
	}
	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 (z <= (-1.2478311614280187d-10)) then
        tmp = x + t
    else if (z <= 7.921979766313861d+51) then
        tmp = x + (t * (y / a))
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2478311614280187e-10) {
		tmp = x + t;
	} else if (z <= 7.921979766313861e+51) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2478311614280187e-10:
		tmp = x + t
	elif z <= 7.921979766313861e+51:
		tmp = x + (t * (y / a))
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2478311614280187e-10)
		tmp = Float64(x + t);
	elseif (z <= 7.921979766313861e+51)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2478311614280187e-10)
		tmp = x + t;
	elseif (z <= 7.921979766313861e+51)
		tmp = x + (t * (y / a));
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2478311614280187e-10], N[(x + t), $MachinePrecision], If[LessEqual[z, 7.921979766313861e+51], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t), $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 <= (7921979766313861376517055230760247570310723495002112)) THEN (x + (t * (y / a))) ELSE (x + t) ENDIF IN
	LET tmp = IF (z <= (-1247831161428018728235009902088783854956499652644197340123355388641357421875e-85)) THEN (x + t) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -1.2478311614280187e-10 or 7.9219797663138614e51 < z

   1. Initial program 85.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.6%

      \[\leadsto x + t \]

   if -1.2478311614280187e-10 < z < 7.9219797663138614e51

   1. Initial program 85.2%

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

   2. Taylor expanded in z around 0

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

   4. Applied rewrites 59.8%

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

   6. Applied rewrites 61.6%

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

Alternative 11: 63.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{t}{z}, x\right)\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{+41}:\\ \;\;\;\;\frac{t \cdot y}{a - z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+116}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\left(z - y\right) \cdot \frac{t}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (* (- y z) t) (- a z))))
  (if (<= t_1 (- INFINITY))
    (fma z (/ t z) x)
    (if (<= t_1 -4e+41)
      (/ (* t y) (- a z))
      (if (<= t_1 2e+116) (+ x t) (* (- z y) (/ t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma(z, (t / z), x);
	} else if (t_1 <= -4e+41) {
		tmp = (t * y) / (a - z);
	} else if (t_1 <= 2e+116) {
		tmp = x + t;
	} else {
		tmp = (z - y) * (t / z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = fma(z, Float64(t / z), x);
	elseif (t_1 <= -4e+41)
		tmp = Float64(Float64(t * y) / Float64(a - z));
	elseif (t_1 <= 2e+116)
		tmp = Float64(x + t);
	else
		tmp = Float64(Float64(z - y) * Float64(t / z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z * N[(t / z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, -4e+41], N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+116], N[(x + t), $MachinePrecision], N[(N[(z - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0

   1. Initial program 85.2%

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

   3. Applied rewrites 98.2%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 58.2%

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

   8. Applied rewrites 65.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 59.7%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -4e41

   1. Initial program 85.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 39.3%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 21.9%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 18.4%

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

   11. Taylor expanded in a around 0

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

   13. Applied rewrites 26.1%

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

   if -4e41 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 2e116

   1. Initial program 85.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.6%

      \[\leadsto x + t \]

   if 2e116 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 85.2%

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

   3. Applied rewrites 98.2%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 58.2%

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

   7. Taylor expanded in t around inf

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

   9. Applied rewrites 31.2%

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

   11. Applied rewrites 29.5%

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

Alternative 12: 63.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{t}{z}, x\right)\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{+41}:\\ \;\;\;\;\frac{t \cdot y}{a - z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+116}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{y}{z}\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (* (- y z) t) (- a z))))
  (if (<= t_1 (- INFINITY))
    (fma z (/ t z) x)
    (if (<= t_1 -4e+41)
      (/ (* t y) (- a z))
      (if (<= t_1 2e+116) (+ x t) (* t (- 1.0 (/ y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma(z, (t / z), x);
	} else if (t_1 <= -4e+41) {
		tmp = (t * y) / (a - z);
	} else if (t_1 <= 2e+116) {
		tmp = x + t;
	} else {
		tmp = t * (1.0 - (y / z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = fma(z, Float64(t / z), x);
	elseif (t_1 <= -4e+41)
		tmp = Float64(Float64(t * y) / Float64(a - z));
	elseif (t_1 <= 2e+116)
		tmp = Float64(x + t);
	else
		tmp = Float64(t * Float64(1.0 - Float64(y / z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z * N[(t / z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, -4e+41], N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+116], N[(x + t), $MachinePrecision], N[(t * N[(1.0 - N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0

   1. Initial program 85.2%

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

   3. Applied rewrites 98.2%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 58.2%

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

   8. Applied rewrites 65.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 59.7%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -4e41

   1. Initial program 85.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 39.3%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 21.9%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 18.4%

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

   11. Taylor expanded in a around 0

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

   13. Applied rewrites 26.1%

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

   if -4e41 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 2e116

   1. Initial program 85.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.6%

      \[\leadsto x + t \]

   if 2e116 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 85.2%

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

   3. Applied rewrites 98.2%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 58.2%

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

   7. Taylor expanded in t around inf

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

   9. Applied rewrites 31.2%

      \[\leadsto t \cdot \left(1 - \frac{y}{z}\right) \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 13: 63.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{t}{z}, x\right)\\ \mathbf{elif}\;t\_1 \leq -4 \cdot 10^{+41}:\\ \;\;\;\;\frac{t \cdot y}{a - z}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+116}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\frac{z - y}{z} \cdot t\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (* (- y z) t) (- a z))))
  (if (<= t_1 (- INFINITY))
    (fma z (/ t z) x)
    (if (<= t_1 -4e+41)
      (/ (* t y) (- a z))
      (if (<= t_1 2e+116) (+ x t) (* (/ (- z y) z) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma(z, (t / z), x);
	} else if (t_1 <= -4e+41) {
		tmp = (t * y) / (a - z);
	} else if (t_1 <= 2e+116) {
		tmp = x + t;
	} else {
		tmp = ((z - y) / z) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = fma(z, Float64(t / z), x);
	elseif (t_1 <= -4e+41)
		tmp = Float64(Float64(t * y) / Float64(a - z));
	elseif (t_1 <= 2e+116)
		tmp = Float64(x + t);
	else
		tmp = Float64(Float64(Float64(z - y) / z) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z * N[(t / z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, -4e+41], N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+116], N[(x + t), $MachinePrecision], N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -inf.0

   1. Initial program 85.2%

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

   3. Applied rewrites 98.2%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 58.2%

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

   8. Applied rewrites 65.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 59.7%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -4e41

   1. Initial program 85.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 39.3%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 21.9%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 18.4%

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

   11. Taylor expanded in a around 0

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

   13. Applied rewrites 26.1%

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

   if -4e41 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 2e116

   1. Initial program 85.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.6%

      \[\leadsto x + t \]

   if 2e116 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 85.2%

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

   3. Applied rewrites 98.2%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 58.2%

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

   7. Taylor expanded in t around inf

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

   9. Applied rewrites 31.2%

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

   11. Applied rewrites 31.2%

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

Alternative 14: 62.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \frac{t \cdot y}{a - z}\\ \mathbf{if}\;y \leq -1.531587912663493 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6.092521448181553 \cdot 10^{+193}:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (* t y) (- a z))))
  (if (<= y -1.531587912663493e+143)
    t_1
    (if (<= y 6.092521448181553e+193) (+ x t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * y) / (a - z);
	double tmp;
	if (y <= -1.531587912663493e+143) {
		tmp = t_1;
	} else if (y <= 6.092521448181553e+193) {
		tmp = x + 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 = (t * y) / (a - z)
    if (y <= (-1.531587912663493d+143)) then
        tmp = t_1
    else if (y <= 6.092521448181553d+193) then
        tmp = x + 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 = (t * y) / (a - z);
	double tmp;
	if (y <= -1.531587912663493e+143) {
		tmp = t_1;
	} else if (y <= 6.092521448181553e+193) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t * y) / (a - z)
	tmp = 0
	if y <= -1.531587912663493e+143:
		tmp = t_1
	elif y <= 6.092521448181553e+193:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t * y) / Float64(a - z))
	tmp = 0.0
	if (y <= -1.531587912663493e+143)
		tmp = t_1;
	elseif (y <= 6.092521448181553e+193)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t * y) / (a - z);
	tmp = 0.0;
	if (y <= -1.531587912663493e+143)
		tmp = t_1;
	elseif (y <= 6.092521448181553e+193)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.531587912663493e+143], t$95$1, If[LessEqual[y, 6.092521448181553e+193], N[(x + 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 = ((t * y) / (a - z)) IN
		LET tmp_1 = IF (y <= (60925214481815533287399347429575174889349897034536817443908306156043251136047391358947620204881197511744642480148943273613931462310421790368970823517725966818716570458530236440972285171013255168)) THEN (x + t) ELSE t_1 ENDIF IN
		LET tmp = IF (y <= (-153158791266349302059067134646143137419441199017939972137454829263741356177562549975168567005190735022490714260833519588217537330168093707599872)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -1.531587912663493e143 or 6.0925214481815533e193 < y

   1. Initial program 85.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 39.3%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 21.9%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 18.4%

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

   11. Taylor expanded in a around 0

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

   13. Applied rewrites 26.1%

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

   if -1.531587912663493e143 < y < 6.0925214481815533e193

   1. Initial program 85.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.6%

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

Alternative 15: 60.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -4.471781700733622 \cdot 10^{-279}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{t}{z}, x\right)\\ \mathbf{elif}\;x \leq 7.230355534401791 \cdot 10^{-168}:\\ \;\;\;\;t \cdot \frac{y - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= x -4.471781700733622e-279)
  (fma z (/ t z) x)
  (if (<= x 7.230355534401791e-168) (* t (/ (- y z) a)) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.471781700733622e-279) {
		tmp = fma(z, (t / z), x);
	} else if (x <= 7.230355534401791e-168) {
		tmp = t * ((y - z) / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.471781700733622e-279)
		tmp = fma(z, Float64(t / z), x);
	elseif (x <= 7.230355534401791e-168)
		tmp = Float64(t * Float64(Float64(y - z) / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.471781700733622e-279], N[(z * N[(t / z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[x, 7.230355534401791e-168], N[(t * N[(N[(y - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $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 (x <= (723035553440179061352561352621560993881732759182003278982708926814205477430323568515964551786192431536152820598010082440796832470550646541151226489740312827003999609569745125346552420722062502057072507750471046452795505085118543454407850290323250821118698074197245781240272701362288207327590218312019943526757042547118532996372744468279373855008681255293613987176646372447129265567105612560367758627662138071201525235665030777454376220703125e-608)) THEN (t * ((y - z) / a)) ELSE (x + t) ENDIF IN
	LET tmp = IF (x <= (-447178170073362178557708632311810996098825049021955631229958731348672064462896343342495214521937802831800817146163211075604530739126642951537567680084892504512769198617166844547966119067001951550041805069404373666923622585775364960389115020295909301938347872891111119681717416978962976696652759526020570483636296853685632757166217090700430691042594393308709021377419584788589418697179394226408676031653215551827090881228997064129333844133929068335768983250912215848641600986732743469541854331116765397436577399245171934725395872627643317210943098077567863173488798746628306396819282061991486890563113814082204486449009702914859979935356380821138846956368760598987677212790003977715969085693359375e-974)) THEN ((z * (t / z)) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if x < -4.4717817007336218e-279

   1. Initial program 85.2%

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

   3. Applied rewrites 98.2%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 58.2%

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

   8. Applied rewrites 65.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 59.7%

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

   if -4.4717817007336218e-279 < x < 7.2303555344017906e-168

   1. Initial program 85.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 39.3%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 21.9%

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

   9. Applied rewrites 24.5%

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

   if 7.2303555344017906e-168 < x

   1. Initial program 85.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.6%

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

Alternative 16: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -1.7215465460366108 \cdot 10^{-279}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{t}{z}, x\right)\\ \mathbf{elif}\;x \leq 6.516091422738436 \cdot 10^{-168}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= x -1.7215465460366108e-279)
  (fma z (/ t z) x)
  (if (<= x 6.516091422738436e-168) (* t (/ y a)) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.7215465460366108e-279) {
		tmp = fma(z, (t / z), x);
	} else if (x <= 6.516091422738436e-168) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.7215465460366108e-279)
		tmp = fma(z, Float64(t / z), x);
	elseif (x <= 6.516091422738436e-168)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.7215465460366108e-279], N[(z * N[(t / z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[x, 6.516091422738436e-168], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $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 (x <= (65160914227384357657733073792089163811525226353360708673826387731623259040049697671617223710704035433820377750898086629947763880779025383969665405297643406136664507667245342483254438777464162783982191964964392523305620273543886193935337815375417243908019019466315201145408303539505712955517746794859007309333557389235016728693336145189564586809738908110030604129143120246243732976993574917322916127161713806259513148688711225986480712890625e-607)) THEN (t * (y / a)) ELSE (x + t) ENDIF IN
	LET tmp = IF (x <= (-17215465460366108201097688553343575399884158981032218687669198032962580049766882299274720764851645372416217611573948443011275591702301875218659325961754466948217962433950252095943242171685386880345431604514072578410408851235163701988902371495658832208223340840018314948005415408591281677744212718162045400011617733774759554321582212062976394471262892262208708561278641017168669218251482677733631017493565786186100893668319431205487818363548825025627731595182530622851355408493099245412423510239663084618579533827607211863516243145926302423407166633726965276945712944709961142477849653712286471749399319336448040268204697721246392543815365812369675596459428035082950270151513905148021876811981201171875e-979)) THEN ((z * (t / z)) + x) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if x < -1.7215465460366108e-279

   1. Initial program 85.2%

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

   3. Applied rewrites 98.2%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 58.2%

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

   8. Applied rewrites 65.2%

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

   9. Taylor expanded in y around 0

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

   11. Applied rewrites 59.7%

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

   if -1.7215465460366108e-279 < x < 6.5160914227384358e-168

   1. Initial program 85.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 39.3%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 21.9%

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

   9. Applied rewrites 24.5%

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

   10. Taylor expanded in z around 0

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

   12. Applied rewrites 20.1%

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

   if 6.5160914227384358e-168 < x

   1. Initial program 85.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.6%

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

Alternative 17: 59.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \mathbf{if}\;y \leq -1.531587912663493 \cdot 10^{+143}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (if (<= y -1.531587912663493e+143) (* t (/ y a)) (+ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.531587912663493e+143) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	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 (y <= (-1.531587912663493d+143)) then
        tmp = t * (y / a)
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.531587912663493e+143) {
		tmp = t * (y / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.531587912663493e+143:
		tmp = t * (y / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.531587912663493e+143)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.531587912663493e+143)
		tmp = t * (y / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.531587912663493e+143], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET tmp = IF (y <= (-153158791266349302059067134646143137419441199017939972137454829263741356177562549975168567005190735022490714260833519588217537330168093707599872)) THEN (t * (y / a)) ELSE (x + t) ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if y < -1.531587912663493e143

   1. Initial program 85.2%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 39.3%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 21.9%

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

   9. Applied rewrites 24.5%

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

   10. Taylor expanded in z around 0

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

   12. Applied rewrites 20.1%

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

   if -1.531587912663493e143 < y

   1. Initial program 85.2%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.6%

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

Alternative 18: 59.2% accurate, 4.3× speedup

Math

\[x + t \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + t), $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 + t
END code

Derivation

1. Initial program 85.2%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 60.6%

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

Alternative 19: 18.9% accurate, 15.6× speedup

Math

\[t \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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
END code

Derivation

1. Initial program 85.2%

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

2. Taylor expanded in x around 0

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

4. Applied rewrites 39.3%

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

5. Taylor expanded in z around inf

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

7. Applied rewrites 18.9%

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