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

Percentage Accurate: 98.0% → 98.0%

Time: 2.9s

Alternatives: 15

Speedup: 0.3×

Specification

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $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: 98.0% accurate, 1.0× speedup

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $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, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := \mathsf{fma}\left(t, \frac{y}{a - z}, x\right)\\ \mathbf{if}\;t\_1 \leq -5:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.0005:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - z}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{z - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- z a))) (t_2 (fma t (/ y (- a z)) x)))
  (if (<= t_1 -5.0)
    t_2
    (if (<= t_1 0.0005)
      (fma y (/ (- t z) a) x)
      (if (<= t_1 2.0) (fma y (/ z (- z a)) x) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double t_2 = fma(t, (y / (a - z)), x);
	double tmp;
	if (t_1 <= -5.0) {
		tmp = t_2;
	} else if (t_1 <= 0.0005) {
		tmp = fma(y, ((t - z) / a), x);
	} else if (t_1 <= 2.0) {
		tmp = fma(y, (z / (z - a)), x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	t_2 = fma(t, Float64(y / Float64(a - z)), x)
	tmp = 0.0
	if (t_1 <= -5.0)
		tmp = t_2;
	elseif (t_1 <= 0.0005)
		tmp = fma(y, Float64(Float64(t - z) / a), x);
	elseif (t_1 <= 2.0)
		tmp = fma(y, Float64(z / Float64(z - a)), x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$1, -5.0], t$95$2, If[LessEqual[t$95$1, 0.0005], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$2]]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((z - t) / (z - a)) IN
		LET t_2 = ((t * (y / (a - z))) + x) IN
			LET tmp_2 = IF (t_1 <= (2)) THEN ((y * (z / (z - a))) + x) ELSE t_2 ENDIF IN
			LET tmp_1 = IF (t_1 <= (5000000000000000104083408558608425664715468883514404296875e-61)) THEN ((y * ((t - z) / a)) + x) ELSE tmp_2 ENDIF IN
			LET tmp = IF (t_1 <= (-5)) THEN t_2 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -5 or 2 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 98.0%

      \[x + y \cdot \frac{z - t}{z - a} \]
   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 -5 < (/.f64 (-.f64 z t) (-.f64 z a)) < 5.0000000000000001e-4

   1. Initial program 98.0%

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

   8. Applied rewrites 59.7%

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

   if 5.0000000000000001e-4 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2

   1. Initial program 98.0%

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

   3. Applied rewrites 98.0%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 71.6%

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

Alternative 2: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.0%

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

3. Applied rewrites 98.0%

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

Alternative 3: 87.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+70}:\\ \;\;\;\;\frac{y}{a - z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 0.0005:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t - z}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{z}, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- z a))))
  (if (<= t_1 -5e+70)
    (* (/ y (- a z)) t)
    (if (<= t_1 0.0005)
      (fma y (/ (- t z) a) x)
      (fma y (/ (- z t) z) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -5e+70) {
		tmp = (y / (a - z)) * t;
	} else if (t_1 <= 0.0005) {
		tmp = fma(y, ((t - z) / a), x);
	} else {
		tmp = fma(y, ((z - t) / z), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -5e+70)
		tmp = Float64(Float64(y / Float64(a - z)) * t);
	elseif (t_1 <= 0.0005)
		tmp = fma(y, Float64(Float64(t - z) / a), x);
	else
		tmp = fma(y, Float64(Float64(z - t) / z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+70], N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 0.0005], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(y * N[(N[(z - t), $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 t_1 = ((z - t) / (z - a)) IN
		LET tmp_1 = IF (t_1 <= (5000000000000000104083408558608425664715468883514404296875e-61)) THEN ((y * ((t - z) / a)) + x) ELSE ((y * ((z - t) / z)) + x) ENDIF IN
		LET tmp = IF (t_1 <= (-50000000000000002094076278210572897949571693332016914157171385590349824)) THEN ((y / (a - z)) * t) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -5.0000000000000002e70

   1. Initial program 98.0%

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

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

   6. Applied rewrites 26.4%

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

   8. Applied rewrites 28.6%

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

   if -5.0000000000000002e70 < (/.f64 (-.f64 z t) (-.f64 z a)) < 5.0000000000000001e-4

   1. Initial program 98.0%

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

   8. Applied rewrites 59.7%

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

   if 5.0000000000000001e-4 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 98.0%

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

   3. Applied rewrites 98.0%

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

   4. Taylor expanded in a around 0

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

   6. Applied rewrites 66.9%

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

Alternative 4: 84.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := \frac{y}{a - z} \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+74}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 1000000000000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{z - a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- z a))) (t_2 (* (/ y (- a z)) t)))
  (if (<= t_1 -5e+74)
    t_2
    (if (<= t_1 1000000000000.0) (fma y (/ z (- z a)) x) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double t_2 = (y / (a - z)) * t;
	double tmp;
	if (t_1 <= -5e+74) {
		tmp = t_2;
	} else if (t_1 <= 1000000000000.0) {
		tmp = fma(y, (z / (z - a)), x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	t_2 = Float64(Float64(y / Float64(a - z)) * t)
	tmp = 0.0
	if (t_1 <= -5e+74)
		tmp = t_2;
	elseif (t_1 <= 1000000000000.0)
		tmp = fma(y, Float64(z / Float64(z - a)), x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+74], t$95$2, If[LessEqual[t$95$1, 1000000000000.0], N[(y * N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$2]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((z - t) / (z - a)) IN
		LET t_2 = ((y / (a - z)) * t) IN
			LET tmp_1 = IF (t_1 <= (1e12)) THEN ((y * (z / (z - a))) + x) ELSE t_2 ENDIF IN
			LET tmp = IF (t_1 <= (-499999999999999963269890588240599461754401607599733943631323209890181152768)) THEN t_2 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -4.9999999999999996e74 or 1e12 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 98.0%

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

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

   6. Applied rewrites 26.4%

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

   8. Applied rewrites 28.6%

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

   if -4.9999999999999996e74 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1e12

   1. Initial program 98.0%

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

   3. Applied rewrites 98.0%

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

   4. Taylor expanded in t around 0

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

   6. Applied rewrites 71.6%

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

Alternative 5: 83.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := \frac{y}{a - z} \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.0005:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 1000000000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- z a))) (t_2 (* (/ y (- a z)) t)))
  (if (<= t_1 -5e+70)
    t_2
    (if (<= t_1 0.0005)
      (fma y (/ t a) x)
      (if (<= t_1 1000000000000.0) (+ x y) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double t_2 = (y / (a - z)) * t;
	double tmp;
	if (t_1 <= -5e+70) {
		tmp = t_2;
	} else if (t_1 <= 0.0005) {
		tmp = fma(y, (t / a), x);
	} else if (t_1 <= 1000000000000.0) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	t_2 = Float64(Float64(y / Float64(a - z)) * t)
	tmp = 0.0
	if (t_1 <= -5e+70)
		tmp = t_2;
	elseif (t_1 <= 0.0005)
		tmp = fma(y, Float64(t / a), x);
	elseif (t_1 <= 1000000000000.0)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+70], t$95$2, If[LessEqual[t$95$1, 0.0005], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 1000000000000.0], N[(x + y), $MachinePrecision], t$95$2]]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((z - t) / (z - a)) IN
		LET t_2 = ((y / (a - z)) * t) IN
			LET tmp_2 = IF (t_1 <= (1e12)) THEN (x + y) ELSE t_2 ENDIF IN
			LET tmp_1 = IF (t_1 <= (5000000000000000104083408558608425664715468883514404296875e-61)) THEN ((y * (t / a)) + x) ELSE tmp_2 ENDIF IN
			LET tmp = IF (t_1 <= (-50000000000000002094076278210572897949571693332016914157171385590349824)) THEN t_2 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -5.0000000000000002e70 or 1e12 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 98.0%

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

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

   6. Applied rewrites 26.4%

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

   8. Applied rewrites 28.6%

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

   if -5.0000000000000002e70 < (/.f64 (-.f64 z t) (-.f64 z a)) < 5.0000000000000001e-4

   1. Initial program 98.0%

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

   3. Applied rewrites 98.0%

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

   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%

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

   if 5.0000000000000001e-4 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1e12

   1. Initial program 98.0%

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

   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 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 83.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+70}:\\ \;\;\;\;\frac{t \cdot y}{a - z}\\ \mathbf{elif}\;t\_1 \leq 0.0005:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 1000000000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a - z}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- z a))))
  (if (<= t_1 -5e+70)
    (/ (* t y) (- a z))
    (if (<= t_1 0.0005)
      (fma y (/ t a) x)
      (if (<= t_1 1000000000000.0) (+ x y) (* y (/ t (- a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -5e+70) {
		tmp = (t * y) / (a - z);
	} else if (t_1 <= 0.0005) {
		tmp = fma(y, (t / a), x);
	} else if (t_1 <= 1000000000000.0) {
		tmp = x + y;
	} else {
		tmp = y * (t / (a - z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -5e+70)
		tmp = Float64(Float64(t * y) / Float64(a - z));
	elseif (t_1 <= 0.0005)
		tmp = fma(y, Float64(t / a), x);
	elseif (t_1 <= 1000000000000.0)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(t / Float64(a - z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+70], N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0005], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 1000000000000.0], N[(x + y), $MachinePrecision], N[(y * N[(t / 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 =
	LET t_1 = ((z - t) / (z - a)) IN
		LET tmp_2 = IF (t_1 <= (1e12)) THEN (x + y) ELSE (y * (t / (a - z))) ENDIF IN
		LET tmp_1 = IF (t_1 <= (5000000000000000104083408558608425664715468883514404296875e-61)) THEN ((y * (t / a)) + x) ELSE tmp_2 ENDIF IN
		LET tmp = IF (t_1 <= (-50000000000000002094076278210572897949571693332016914157171385590349824)) THEN ((t * y) / (a - z)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -5.0000000000000002e70

   1. Initial program 98.0%

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

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

   6. Applied rewrites 26.4%

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

   if -5.0000000000000002e70 < (/.f64 (-.f64 z t) (-.f64 z a)) < 5.0000000000000001e-4

   1. Initial program 98.0%

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

   3. Applied rewrites 98.0%

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

   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%

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

   if 5.0000000000000001e-4 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1e12

   1. Initial program 98.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.8%

      \[\leadsto x + y \]

   if 1e12 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 98.0%

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

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

   6. Applied rewrites 26.4%

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

   8. Applied rewrites 28.8%

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

Alternative 7: 83.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := y \cdot \frac{t}{a - z}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 0.0005:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 1000000000000:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- z a))) (t_2 (* y (/ t (- a z)))))
  (if (<= t_1 -5e+70)
    t_2
    (if (<= t_1 0.0005)
      (fma y (/ t a) x)
      (if (<= t_1 1000000000000.0) (+ x y) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double t_2 = y * (t / (a - z));
	double tmp;
	if (t_1 <= -5e+70) {
		tmp = t_2;
	} else if (t_1 <= 0.0005) {
		tmp = fma(y, (t / a), x);
	} else if (t_1 <= 1000000000000.0) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	t_2 = Float64(y * Float64(t / Float64(a - z)))
	tmp = 0.0
	if (t_1 <= -5e+70)
		tmp = t_2;
	elseif (t_1 <= 0.0005)
		tmp = fma(y, Float64(t / a), x);
	elseif (t_1 <= 1000000000000.0)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+70], t$95$2, If[LessEqual[t$95$1, 0.0005], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 1000000000000.0], N[(x + y), $MachinePrecision], t$95$2]]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((z - t) / (z - a)) IN
		LET t_2 = (y * (t / (a - z))) IN
			LET tmp_2 = IF (t_1 <= (1e12)) THEN (x + y) ELSE t_2 ENDIF IN
			LET tmp_1 = IF (t_1 <= (5000000000000000104083408558608425664715468883514404296875e-61)) THEN ((y * (t / a)) + x) ELSE tmp_2 ENDIF IN
			LET tmp = IF (t_1 <= (-50000000000000002094076278210572897949571693332016914157171385590349824)) THEN t_2 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -5.0000000000000002e70 or 1e12 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 98.0%

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

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

   6. Applied rewrites 26.4%

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

   8. Applied rewrites 28.8%

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

   if -5.0000000000000002e70 < (/.f64 (-.f64 z t) (-.f64 z a)) < 5.0000000000000001e-4

   1. Initial program 98.0%

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

   3. Applied rewrites 98.0%

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

   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%

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

   if 5.0000000000000001e-4 < (/.f64 (-.f64 z t) (-.f64 z a)) < 1e12

   1. Initial program 98.0%

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

   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 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 81.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{z - t}{z}\\ \mathbf{elif}\;t\_1 \leq 0.0005:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- z a))))
  (if (<= t_1 -2e+82)
    (* y (/ (- z t) z))
    (if (<= t_1 0.0005)
      (fma y (/ t a) x)
      (if (<= t_1 2.0) (+ x y) (fma t (/ y a) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -2e+82) {
		tmp = y * ((z - t) / z);
	} else if (t_1 <= 0.0005) {
		tmp = fma(y, (t / a), x);
	} else if (t_1 <= 2.0) {
		tmp = x + y;
	} else {
		tmp = fma(t, (y / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -2e+82)
		tmp = Float64(y * Float64(Float64(z - t) / z));
	elseif (t_1 <= 0.0005)
		tmp = fma(y, Float64(t / a), x);
	elseif (t_1 <= 2.0)
		tmp = Float64(x + y);
	else
		tmp = fma(t, Float64(y / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+82], N[(y * N[(N[(z - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.0005], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(x + y), $MachinePrecision], N[(t * N[(y / 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 t_1 = ((z - t) / (z - a)) IN
		LET tmp_2 = IF (t_1 <= (2)) THEN (x + y) ELSE ((t * (y / a)) + x) ENDIF IN
		LET tmp_1 = IF (t_1 <= (5000000000000000104083408558608425664715468883514404296875e-61)) THEN ((y * (t / a)) + x) ELSE tmp_2 ENDIF IN
		LET tmp = IF (t_1 <= (-19999999999999999268135931261773148422054286450547135587360727686854173003085774848)) THEN (y * ((z - t) / z)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -1.9999999999999999e82

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 39.6%

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

   6. Applied rewrites 49.5%

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

   7. Taylor expanded in a around 0

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

   9. Applied rewrites 31.4%

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

   if -1.9999999999999999e82 < (/.f64 (-.f64 z t) (-.f64 z a)) < 5.0000000000000001e-4

   1. Initial program 98.0%

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

   3. Applied rewrites 98.0%

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

   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%

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

   if 5.0000000000000001e-4 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2

   1. Initial program 98.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.8%

      \[\leadsto x + y \]

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

   1. Initial program 98.0%

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

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

   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 4 regimes into one program.
4. Add Preprocessing

Alternative 9: 81.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+82}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{z}\\ \mathbf{elif}\;t\_1 \leq 0.0005:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- z a))))
  (if (<= t_1 -2e+82)
    (/ (* y (- z t)) z)
    (if (<= t_1 0.0005)
      (fma y (/ t a) x)
      (if (<= t_1 2.0) (+ x y) (fma t (/ y a) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double tmp;
	if (t_1 <= -2e+82) {
		tmp = (y * (z - t)) / z;
	} else if (t_1 <= 0.0005) {
		tmp = fma(y, (t / a), x);
	} else if (t_1 <= 2.0) {
		tmp = x + y;
	} else {
		tmp = fma(t, (y / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	tmp = 0.0
	if (t_1 <= -2e+82)
		tmp = Float64(Float64(y * Float64(z - t)) / z);
	elseif (t_1 <= 0.0005)
		tmp = fma(y, Float64(t / a), x);
	elseif (t_1 <= 2.0)
		tmp = Float64(x + y);
	else
		tmp = fma(t, Float64(y / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+82], N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 0.0005], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(x + y), $MachinePrecision], N[(t * N[(y / 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 t_1 = ((z - t) / (z - a)) IN
		LET tmp_2 = IF (t_1 <= (2)) THEN (x + y) ELSE ((t * (y / a)) + x) ENDIF IN
		LET tmp_1 = IF (t_1 <= (5000000000000000104083408558608425664715468883514404296875e-61)) THEN ((y * (t / a)) + x) ELSE tmp_2 ENDIF IN
		LET tmp = IF (t_1 <= (-19999999999999999268135931261773148422054286450547135587360727686854173003085774848)) THEN ((y * (z - t)) / z) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < -1.9999999999999999e82

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 39.6%

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

   6. Applied rewrites 49.5%

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

   7. Taylor expanded in a around 0

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

   9. Applied rewrites 24.2%

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

   if -1.9999999999999999e82 < (/.f64 (-.f64 z t) (-.f64 z a)) < 5.0000000000000001e-4

   1. Initial program 98.0%

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

   3. Applied rewrites 98.0%

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

   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%

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

   if 5.0000000000000001e-4 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2

   1. Initial program 98.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.8%

      \[\leadsto x + y \]

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

   1. Initial program 98.0%

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

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

   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 4 regimes into one program.
4. Add Preprocessing

Alternative 10: 80.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := \mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \mathbf{if}\;t\_1 \leq 0.0005:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- z a))) (t_2 (fma t (/ y a) x)))
  (if (<= t_1 0.0005) t_2 (if (<= t_1 2.0) (+ x y) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double t_2 = fma(t, (y / a), x);
	double tmp;
	if (t_1 <= 0.0005) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	t_2 = fma(t, Float64(y / a), x)
	tmp = 0.0
	if (t_1 <= 0.0005)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$1, 0.0005], t$95$2, If[LessEqual[t$95$1, 2.0], N[(x + y), $MachinePrecision], t$95$2]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((z - t) / (z - a)) IN
		LET t_2 = ((t * (y / a)) + x) IN
			LET tmp_1 = IF (t_1 <= (2)) THEN (x + y) ELSE t_2 ENDIF IN
			LET tmp = IF (t_1 <= (5000000000000000104083408558608425664715468883514404296875e-61)) THEN t_2 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < 5.0000000000000001e-4 or 2 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 98.0%

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

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

   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%

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

   if 5.0000000000000001e-4 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2

   1. Initial program 98.0%

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

   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 11: 80.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{z - a}\\ t_2 := \mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{if}\;t\_1 \leq 0.0005:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- z t) (- z a))) (t_2 (fma y (/ t a) x)))
  (if (<= t_1 0.0005) t_2 (if (<= t_1 2.0) (+ x y) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (z - a);
	double t_2 = fma(y, (t / a), x);
	double tmp;
	if (t_1 <= 0.0005) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(z - a))
	t_2 = fma(y, Float64(t / a), x)
	tmp = 0.0
	if (t_1 <= 0.0005)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[t$95$1, 0.0005], t$95$2, If[LessEqual[t$95$1, 2.0], N[(x + y), $MachinePrecision], t$95$2]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = ((z - t) / (z - a)) IN
		LET t_2 = ((y * (t / a)) + x) IN
			LET tmp_1 = IF (t_1 <= (2)) THEN (x + y) ELSE t_2 ENDIF IN
			LET tmp = IF (t_1 <= (5000000000000000104083408558608425664715468883514404296875e-61)) THEN t_2 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 z a)) < 5.0000000000000001e-4 or 2 < (/.f64 (-.f64 z t) (-.f64 z a))

   1. Initial program 98.0%

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

   3. Applied rewrites 98.0%

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

   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%

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

   if 5.0000000000000001e-4 < (/.f64 (-.f64 z t) (-.f64 z a)) < 2

   1. Initial program 98.0%

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

   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 12: 65.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+295}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{elif}\;t\_1 \leq 10^{+269}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* y (/ (- z t) (- z a)))))
  (if (<= t_1 -1e+295)
    (/ (* t y) a)
    (if (<= t_1 1e+269) (+ x y) (* y (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (z - a));
	double tmp;
	if (t_1 <= -1e+295) {
		tmp = (t * y) / a;
	} else if (t_1 <= 1e+269) {
		tmp = x + y;
	} else {
		tmp = y * (t / a);
	}
	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 = y * ((z - t) / (z - a))
    if (t_1 <= (-1d+295)) then
        tmp = (t * y) / a
    else if (t_1 <= 1d+269) then
        tmp = x + y
    else
        tmp = y * (t / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (z - a));
	double tmp;
	if (t_1 <= -1e+295) {
		tmp = (t * y) / a;
	} else if (t_1 <= 1e+269) {
		tmp = x + y;
	} else {
		tmp = y * (t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (z - a))
	tmp = 0
	if t_1 <= -1e+295:
		tmp = (t * y) / a
	elif t_1 <= 1e+269:
		tmp = x + y
	else:
		tmp = y * (t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(z - a)))
	tmp = 0.0
	if (t_1 <= -1e+295)
		tmp = Float64(Float64(t * y) / a);
	elseif (t_1 <= 1e+269)
		tmp = Float64(x + y);
	else
		tmp = Float64(y * Float64(t / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (z - a));
	tmp = 0.0;
	if (t_1 <= -1e+295)
		tmp = (t * y) / a;
	elseif (t_1 <= 1e+269)
		tmp = x + y;
	else
		tmp = y * (t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+295], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t$95$1, 1e+269], N[(x + y), $MachinePrecision], N[(y * N[(t / a), $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 t_1 = (y * ((z - t) / (z - a))) IN
		LET tmp_1 = IF (t_1 <= (100000000000000004675381888545612798918960543133041028684136487274401643939455589461036825818030333693907688813404495028932616818466243033147431327741697981638738927986463793558699752023835231102266007829372867138519293326106230343475263802678137754874196788463928344576)) THEN (x + y) ELSE (y * (t / a)) ENDIF IN
		LET tmp = IF (t_1 <= (-9999999999999999813486777206230041577815560719820581330098483720446847883279500839884297726782854580737362697004022581572770293687044935910015528960168049498887207223940204684198896264456339658487887951484580004902758521100414464490983962613190835886243290260424727924570510530141380583845003264)) THEN ((t * y) / a) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) < -9.9999999999999998e294

   1. Initial program 98.0%

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

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

   6. Applied rewrites 26.4%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 18.7%

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

   if -9.9999999999999998e294 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) < 1e269

   1. Initial program 98.0%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.8%

      \[\leadsto x + y \]

   if 1e269 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 39.6%

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

   6. Applied rewrites 49.5%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 20.3%

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

Alternative 13: 65.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := y \cdot \frac{t}{a}\\ t_2 := y \cdot \frac{z - t}{z - a}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+295}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+269}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* y (/ t a))) (t_2 (* y (/ (- z t) (- z a)))))
  (if (<= t_2 -1e+295) t_1 (if (<= t_2 1e+269) (+ x y) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double t_2 = y * ((z - t) / (z - a));
	double tmp;
	if (t_2 <= -1e+295) {
		tmp = t_1;
	} else if (t_2 <= 1e+269) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (t / a)
    t_2 = y * ((z - t) / (z - a))
    if (t_2 <= (-1d+295)) then
        tmp = t_1
    else if (t_2 <= 1d+269) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double t_2 = y * ((z - t) / (z - a));
	double tmp;
	if (t_2 <= -1e+295) {
		tmp = t_1;
	} else if (t_2 <= 1e+269) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / a)
	t_2 = y * ((z - t) / (z - a))
	tmp = 0
	if t_2 <= -1e+295:
		tmp = t_1
	elif t_2 <= 1e+269:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / a))
	t_2 = Float64(y * Float64(Float64(z - t) / Float64(z - a)))
	tmp = 0.0
	if (t_2 <= -1e+295)
		tmp = t_1;
	elseif (t_2 <= 1e+269)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / a);
	t_2 = y * ((z - t) / (z - a));
	tmp = 0.0;
	if (t_2 <= -1e+295)
		tmp = t_1;
	elseif (t_2 <= 1e+269)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+295], t$95$1, If[LessEqual[t$95$2, 1e+269], N[(x + y), $MachinePrecision], t$95$1]]]]

ReFlow

f(x, y, z, t, a):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a: real): real =
	LET t_1 = (y * (t / a)) IN
		LET t_2 = (y * ((z - t) / (z - a))) IN
			LET tmp_1 = IF (t_2 <= (100000000000000004675381888545612798918960543133041028684136487274401643939455589461036825818030333693907688813404495028932616818466243033147431327741697981638738927986463793558699752023835231102266007829372867138519293326106230343475263802678137754874196788463928344576)) THEN (x + y) ELSE t_1 ENDIF IN
			LET tmp = IF (t_2 <= (-9999999999999999813486777206230041577815560719820581330098483720446847883279500839884297726782854580737362697004022581572770293687044935910015528960168049498887207223940204684198896264456339658487887951484580004902758521100414464490983962613190835886243290260424727924570510530141380583845003264)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) < -9.9999999999999998e294 or 1e269 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

   1. Initial program 98.0%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 39.6%

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

   6. Applied rewrites 49.5%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 20.3%

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

   if -9.9999999999999998e294 < (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))) < 1e269

   1. Initial program 98.0%

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

   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 14: 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 98.0%

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

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 15: 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 98.0%

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

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:renderAxisLine from plot-0.2.3.4, A"
  :precision binary64
  (+ x (* y (/ (- z t) (- z a)))))