Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1

Percentage Accurate: 97.3% → 97.3%

Time: 4.2s

Alternatives: 16

Speedup: 0.9×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	((x - y) / (z - y)) * t
END code

Initial Program: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	((x - y) / (z - y)) * t
END code

Alternative 1: 97.3% accurate, 0.9× speedup

Math

\[\frac{t}{\frac{y - z}{y - x}} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	t / ((y - z) / (y - x))
END code

Derivation

1. Initial program 97.3%

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

3. Applied rewrites 83.8%

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

5. Applied rewrites 97.3%

   \[\leadsto \frac{t}{\frac{y - z}{y - x}} \]
6. Add Preprocessing

Alternative 2: 96.9% accurate, 0.5× speedup

Math

\[\mathsf{copysign}\left(1, t\right) \cdot \begin{array}{l} \mathbf{if}\;\left|t\right| \leq 6.006193981458982 \cdot 10^{-11}:\\ \;\;\;\;\frac{\left|t\right| \cdot \left(x - y\right)}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{\left|t\right|}{z - y}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (*
 (copysign 1.0 t)
 (if (<= (fabs t) 6.006193981458982e-11)
   (/ (* (fabs t) (- x y)) (- z y))
   (* (- x y) (/ (fabs t) (- z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (fabs(t) <= 6.006193981458982e-11) {
		tmp = (fabs(t) * (x - y)) / (z - y);
	} else {
		tmp = (x - y) * (fabs(t) / (z - y));
	}
	return copysign(1.0, t) * tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (Math.abs(t) <= 6.006193981458982e-11) {
		tmp = (Math.abs(t) * (x - y)) / (z - y);
	} else {
		tmp = (x - y) * (Math.abs(t) / (z - y));
	}
	return Math.copySign(1.0, t) * tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if math.fabs(t) <= 6.006193981458982e-11:
		tmp = (math.fabs(t) * (x - y)) / (z - y)
	else:
		tmp = (x - y) * (math.fabs(t) / (z - y))
	return math.copysign(1.0, t) * tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (abs(t) <= 6.006193981458982e-11)
		tmp = Float64(Float64(abs(t) * Float64(x - y)) / Float64(z - y));
	else
		tmp = Float64(Float64(x - y) * Float64(abs(t) / Float64(z - y)));
	end
	return Float64(copysign(1.0, t) * tmp)
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (abs(t) <= 6.006193981458982e-11)
		tmp = (abs(t) * (x - y)) / (z - y);
	else
		tmp = (x - y) * (abs(t) / (z - y));
	end
	tmp_2 = (sign(t) * abs(1.0)) * tmp;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[With[{TMP1 = Abs[1.0], TMP2 = Sign[t]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision] * If[LessEqual[N[Abs[t], $MachinePrecision], 6.006193981458982e-11], N[(N[(N[Abs[t], $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(N[Abs[t], $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if t < 6.0061939814589824e-11

   1. Initial program 97.3%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 83.9%

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

   if 6.0061939814589824e-11 < t

   1. Initial program 97.3%

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

   3. Applied rewrites 85.0%

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

Alternative 3: 94.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -200000:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;t\_1 \leq 0.2:\\ \;\;\;\;\frac{x - y}{z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 5:\\ \;\;\;\;\frac{y - x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- x y) (- z y))))
  (if (<= t_1 -200000.0)
    (* x (/ t (- z y)))
    (if (<= t_1 0.2)
      (* (/ (- x y) z) t)
      (if (<= t_1 5.0) (* (/ (- y x) y) t) (* (/ x (- z y)) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -200000.0) {
		tmp = x * (t / (z - y));
	} else if (t_1 <= 0.2) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 5.0) {
		tmp = ((y - x) / y) * t;
	} else {
		tmp = (x / (z - y)) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= (-200000.0d0)) then
        tmp = x * (t / (z - y))
    else if (t_1 <= 0.2d0) then
        tmp = ((x - y) / z) * t
    else if (t_1 <= 5.0d0) then
        tmp = ((y - x) / y) * t
    else
        tmp = (x / (z - y)) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -200000.0) {
		tmp = x * (t / (z - y));
	} else if (t_1 <= 0.2) {
		tmp = ((x - y) / z) * t;
	} else if (t_1 <= 5.0) {
		tmp = ((y - x) / y) * t;
	} else {
		tmp = (x / (z - y)) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -200000.0:
		tmp = x * (t / (z - y))
	elif t_1 <= 0.2:
		tmp = ((x - y) / z) * t
	elif t_1 <= 5.0:
		tmp = ((y - x) / y) * t
	else:
		tmp = (x / (z - y)) * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -200000.0)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (t_1 <= 0.2)
		tmp = Float64(Float64(Float64(x - y) / z) * t);
	elseif (t_1 <= 5.0)
		tmp = Float64(Float64(Float64(y - x) / y) * t);
	else
		tmp = Float64(Float64(x / Float64(z - y)) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -200000.0)
		tmp = x * (t / (z - y));
	elseif (t_1 <= 0.2)
		tmp = ((x - y) / z) * t;
	elseif (t_1 <= 5.0)
		tmp = ((y - x) / y) * t;
	else
		tmp = (x / (z - y)) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -200000.0], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.2], N[(N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 5.0], N[(N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision] * t), $MachinePrecision], N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((x - y) / (z - y)) IN
		LET tmp_2 = IF (t_1 <= (5)) THEN (((y - x) / y) * t) ELSE ((x / (z - y)) * t) ENDIF IN
		LET tmp_1 = IF (t_1 <= (200000000000000011102230246251565404236316680908203125e-54)) THEN (((x - y) / z) * t) ELSE tmp_2 ENDIF IN
		LET tmp = IF (t_1 <= (-2e5)) THEN (x * (t / (z - y))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -2e5

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.7%

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

   6. Applied rewrites 50.5%

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

   if -2e5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.20000000000000001

   1. Initial program 97.3%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 51.1%

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

   if 0.20000000000000001 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5

   1. Initial program 97.3%

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

   3. Applied rewrites 97.1%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 52.1%

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

   if 5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 53.9%

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

Alternative 4: 91.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -9 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-17}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;t\_1 \leq 5:\\ \;\;\;\;\frac{y - x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y} \cdot t\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- x y) (- z y))))
  (if (<= t_1 -9e-5)
    (* x (/ t (- z y)))
    (if (<= t_1 2e-17)
      (/ (* t (- x y)) z)
      (if (<= t_1 5.0) (* (/ (- y x) y) t) (* (/ x (- z y)) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -9e-5) {
		tmp = x * (t / (z - y));
	} else if (t_1 <= 2e-17) {
		tmp = (t * (x - y)) / z;
	} else if (t_1 <= 5.0) {
		tmp = ((y - x) / y) * t;
	} else {
		tmp = (x / (z - y)) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= (-9d-5)) then
        tmp = x * (t / (z - y))
    else if (t_1 <= 2d-17) then
        tmp = (t * (x - y)) / z
    else if (t_1 <= 5.0d0) then
        tmp = ((y - x) / y) * t
    else
        tmp = (x / (z - y)) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -9e-5) {
		tmp = x * (t / (z - y));
	} else if (t_1 <= 2e-17) {
		tmp = (t * (x - y)) / z;
	} else if (t_1 <= 5.0) {
		tmp = ((y - x) / y) * t;
	} else {
		tmp = (x / (z - y)) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -9e-5:
		tmp = x * (t / (z - y))
	elif t_1 <= 2e-17:
		tmp = (t * (x - y)) / z
	elif t_1 <= 5.0:
		tmp = ((y - x) / y) * t
	else:
		tmp = (x / (z - y)) * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -9e-5)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (t_1 <= 2e-17)
		tmp = Float64(Float64(t * Float64(x - y)) / z);
	elseif (t_1 <= 5.0)
		tmp = Float64(Float64(Float64(y - x) / y) * t);
	else
		tmp = Float64(Float64(x / Float64(z - y)) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -9e-5)
		tmp = x * (t / (z - y));
	elseif (t_1 <= 2e-17)
		tmp = (t * (x - y)) / z;
	elseif (t_1 <= 5.0)
		tmp = ((y - x) / y) * t;
	else
		tmp = (x / (z - y)) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -9e-5], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-17], N[(N[(t * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 5.0], N[(N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision] * t), $MachinePrecision], N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((x - y) / (z - y)) IN
		LET tmp_2 = IF (t_1 <= (5)) THEN (((y - x) / y) * t) ELSE ((x / (z - y)) * t) ENDIF IN
		LET tmp_1 = IF (t_1 <= (20000000000000001430848481092438490170561123698464954523412728804032667540013790130615234375e-108)) THEN ((t * (x - y)) / z) ELSE tmp_2 ENDIF IN
		LET tmp = IF (t_1 <= (-90000000000000005668208957754217180990963242948055267333984375e-66)) THEN (x * (t / (z - y))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -9.0000000000000006e-5

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.7%

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

   6. Applied rewrites 50.5%

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

   if -9.0000000000000006e-5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2.0000000000000001e-17

   1. Initial program 97.3%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 47.9%

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

   if 2.0000000000000001e-17 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5

   1. Initial program 97.3%

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

   3. Applied rewrites 97.1%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 52.1%

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

   if 5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 53.9%

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

Alternative 5: 91.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -9 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-17}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;t\_1 \leq 5:\\ \;\;\;\;\frac{y - x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- x y) (- z y))))
  (if (<= t_1 -9e-5)
    (* x (/ t (- z y)))
    (if (<= t_1 2e-17)
      (/ (* t (- x y)) z)
      (if (<= t_1 5.0) (* (/ (- y x) y) t) (/ (* t x) (- z y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -9e-5) {
		tmp = x * (t / (z - y));
	} else if (t_1 <= 2e-17) {
		tmp = (t * (x - y)) / z;
	} else if (t_1 <= 5.0) {
		tmp = ((y - x) / y) * t;
	} else {
		tmp = (t * x) / (z - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= (-9d-5)) then
        tmp = x * (t / (z - y))
    else if (t_1 <= 2d-17) then
        tmp = (t * (x - y)) / z
    else if (t_1 <= 5.0d0) then
        tmp = ((y - x) / y) * t
    else
        tmp = (t * x) / (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -9e-5) {
		tmp = x * (t / (z - y));
	} else if (t_1 <= 2e-17) {
		tmp = (t * (x - y)) / z;
	} else if (t_1 <= 5.0) {
		tmp = ((y - x) / y) * t;
	} else {
		tmp = (t * x) / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -9e-5:
		tmp = x * (t / (z - y))
	elif t_1 <= 2e-17:
		tmp = (t * (x - y)) / z
	elif t_1 <= 5.0:
		tmp = ((y - x) / y) * t
	else:
		tmp = (t * x) / (z - y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -9e-5)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (t_1 <= 2e-17)
		tmp = Float64(Float64(t * Float64(x - y)) / z);
	elseif (t_1 <= 5.0)
		tmp = Float64(Float64(Float64(y - x) / y) * t);
	else
		tmp = Float64(Float64(t * x) / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -9e-5)
		tmp = x * (t / (z - y));
	elseif (t_1 <= 2e-17)
		tmp = (t * (x - y)) / z;
	elseif (t_1 <= 5.0)
		tmp = ((y - x) / y) * t;
	else
		tmp = (t * x) / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -9e-5], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-17], N[(N[(t * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 5.0], N[(N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision] * t), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((x - y) / (z - y)) IN
		LET tmp_2 = IF (t_1 <= (5)) THEN (((y - x) / y) * t) ELSE ((t * x) / (z - y)) ENDIF IN
		LET tmp_1 = IF (t_1 <= (20000000000000001430848481092438490170561123698464954523412728804032667540013790130615234375e-108)) THEN ((t * (x - y)) / z) ELSE tmp_2 ENDIF IN
		LET tmp = IF (t_1 <= (-90000000000000005668208957754217180990963242948055267333984375e-66)) THEN (x * (t / (z - y))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -9.0000000000000006e-5

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.7%

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

   6. Applied rewrites 50.5%

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

   if -9.0000000000000006e-5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2.0000000000000001e-17

   1. Initial program 97.3%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 47.9%

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

   if 2.0000000000000001e-17 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5

   1. Initial program 97.3%

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

   3. Applied rewrites 97.1%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 52.1%

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

   if 5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.7%

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

Alternative 6: 91.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -9 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\frac{y}{y - z} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- x y) (- z y))))
  (if (<= t_1 -9e-5)
    (* x (/ t (- z y)))
    (if (<= t_1 2e-5)
      (/ (* t (- x y)) z)
      (if (<= t_1 2.0) (* (/ y (- y z)) t) (/ (* t x) (- z y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -9e-5) {
		tmp = x * (t / (z - y));
	} else if (t_1 <= 2e-5) {
		tmp = (t * (x - y)) / z;
	} else if (t_1 <= 2.0) {
		tmp = (y / (y - z)) * t;
	} else {
		tmp = (t * x) / (z - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= (-9d-5)) then
        tmp = x * (t / (z - y))
    else if (t_1 <= 2d-5) then
        tmp = (t * (x - y)) / z
    else if (t_1 <= 2.0d0) then
        tmp = (y / (y - z)) * t
    else
        tmp = (t * x) / (z - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -9e-5) {
		tmp = x * (t / (z - y));
	} else if (t_1 <= 2e-5) {
		tmp = (t * (x - y)) / z;
	} else if (t_1 <= 2.0) {
		tmp = (y / (y - z)) * t;
	} else {
		tmp = (t * x) / (z - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= -9e-5:
		tmp = x * (t / (z - y))
	elif t_1 <= 2e-5:
		tmp = (t * (x - y)) / z
	elif t_1 <= 2.0:
		tmp = (y / (y - z)) * t
	else:
		tmp = (t * x) / (z - y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -9e-5)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (t_1 <= 2e-5)
		tmp = Float64(Float64(t * Float64(x - y)) / z);
	elseif (t_1 <= 2.0)
		tmp = Float64(Float64(y / Float64(y - z)) * t);
	else
		tmp = Float64(Float64(t * x) / Float64(z - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= -9e-5)
		tmp = x * (t / (z - y));
	elseif (t_1 <= 2e-5)
		tmp = (t * (x - y)) / z;
	elseif (t_1 <= 2.0)
		tmp = (y / (y - z)) * t;
	else
		tmp = (t * x) / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -9e-5], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e-5], N[(N[(t * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((x - y) / (z - y)) IN
		LET tmp_2 = IF (t_1 <= (2)) THEN ((y / (y - z)) * t) ELSE ((t * x) / (z - y)) ENDIF IN
		LET tmp_1 = IF (t_1 <= (2000000000000000163606107828062619091724627651274204254150390625e-68)) THEN ((t * (x - y)) / z) ELSE tmp_2 ENDIF IN
		LET tmp = IF (t_1 <= (-90000000000000005668208957754217180990963242948055267333984375e-66)) THEN (x * (t / (z - y))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -9.0000000000000006e-5

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.7%

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

   6. Applied rewrites 50.5%

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

   if -9.0000000000000006e-5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2.0000000000000002e-5

   1. Initial program 97.3%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 47.9%

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

   if 2.0000000000000002e-5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 97.3%

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

   3. Applied rewrites 97.1%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 53.8%

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

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.7%

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

Alternative 7: 90.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq -9 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;t\_1 \leq 0.2:\\ \;\;\;\;\frac{t \cdot \left(x - y\right)}{z}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, t, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- x y) (- z y))))
  (if (<= t_1 -9e-5)
    (* x (/ t (- z y)))
    (if (<= t_1 0.2)
      (/ (* t (- x y)) z)
      (if (<= t_1 2.0) (fma (/ z y) t t) (/ (* t x) (- z y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= -9e-5) {
		tmp = x * (t / (z - y));
	} else if (t_1 <= 0.2) {
		tmp = (t * (x - y)) / z;
	} else if (t_1 <= 2.0) {
		tmp = fma((z / y), t, t);
	} else {
		tmp = (t * x) / (z - y);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= -9e-5)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (t_1 <= 0.2)
		tmp = Float64(Float64(t * Float64(x - y)) / z);
	elseif (t_1 <= 2.0)
		tmp = fma(Float64(z / y), t, t);
	else
		tmp = Float64(Float64(t * x) / Float64(z - y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -9e-5], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 0.2], N[(N[(t * N[(x - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(N[(z / y), $MachinePrecision] * t + t), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((x - y) / (z - y)) IN
		LET tmp_2 = IF (t_1 <= (2)) THEN (((z / y) * t) + t) ELSE ((t * x) / (z - y)) ENDIF IN
		LET tmp_1 = IF (t_1 <= (200000000000000011102230246251565404236316680908203125e-54)) THEN ((t * (x - y)) / z) ELSE tmp_2 ENDIF IN
		LET tmp = IF (t_1 <= (-90000000000000005668208957754217180990963242948055267333984375e-66)) THEN (x * (t / (z - y))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < -9.0000000000000006e-5

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.7%

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

   6. Applied rewrites 50.5%

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

   if -9.0000000000000006e-5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 0.20000000000000001

   1. Initial program 97.3%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 47.9%

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

   if 0.20000000000000001 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 97.3%

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

   3. Applied rewrites 47.1%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 44.2%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 32.9%

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

   11. Applied rewrites 34.5%

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

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.7%

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

Alternative 8: 80.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 0.2:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, t, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z - y}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- x y) (- z y))))
  (if (<= t_1 0.2)
    (* x (/ t (- z y)))
    (if (<= t_1 2.0) (fma (/ z y) t t) (/ (* t x) (- z y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 0.2) {
		tmp = x * (t / (z - y));
	} else if (t_1 <= 2.0) {
		tmp = fma((z / y), t, t);
	} else {
		tmp = (t * x) / (z - y);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 0.2)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (t_1 <= 2.0)
		tmp = fma(Float64(z / y), t, t);
	else
		tmp = Float64(Float64(t * x) / Float64(z - y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.2], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2.0], N[(N[(z / y), $MachinePrecision] * t + t), $MachinePrecision], N[(N[(t * x), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((x - y) / (z - y)) IN
		LET tmp_1 = IF (t_1 <= (2)) THEN (((z / y) * t) + t) ELSE ((t * x) / (z - y)) ENDIF IN
		LET tmp = IF (t_1 <= (200000000000000011102230246251565404236316680908203125e-54)) THEN (x * (t / (z - y))) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 0.20000000000000001

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.7%

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

   6. Applied rewrites 50.5%

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

   if 0.20000000000000001 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 97.3%

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

   3. Applied rewrites 47.1%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 44.2%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 32.9%

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

   11. Applied rewrites 34.5%

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

   if 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.7%

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

Alternative 9: 80.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := x \cdot \frac{t}{z - y}\\ \mathbf{if}\;t\_1 \leq 0.2:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, t, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* x (/ t (- z y)))))
  (if (<= t_1 0.2) t_2 (if (<= t_1 2.0) (fma (/ z y) t t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = x * (t / (z - y));
	double tmp;
	if (t_1 <= 0.2) {
		tmp = t_2;
	} else if (t_1 <= 2.0) {
		tmp = fma((z / y), t, t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(x * Float64(t / Float64(z - y)))
	tmp = 0.0
	if (t_1 <= 0.2)
		tmp = t_2;
	elseif (t_1 <= 2.0)
		tmp = fma(Float64(z / y), t, t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.2], t$95$2, If[LessEqual[t$95$1, 2.0], N[(N[(z / y), $MachinePrecision] * t + t), $MachinePrecision], t$95$2]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((x - y) / (z - y)) IN
		LET t_2 = (x * (t / (z - y))) IN
			LET tmp_1 = IF (t_1 <= (2)) THEN (((z / y) * t) + t) ELSE t_2 ENDIF IN
			LET tmp = IF (t_1 <= (200000000000000011102230246251565404236316680908203125e-54)) THEN t_2 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 0.20000000000000001 or 2 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 50.7%

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

   6. Applied rewrites 50.5%

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

   if 0.20000000000000001 < (/.f64 (-.f64 x y) (-.f64 z y)) < 2

   1. Initial program 97.3%

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

   3. Applied rewrites 47.1%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 44.2%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 32.9%

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

   11. Applied rewrites 34.5%

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

Alternative 10: 70.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 0.2:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;t\_1 \leq 5:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{y}, t, t\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- x y) (- z y))))
  (if (<= t_1 0.2)
    (/ t (/ z x))
    (if (<= t_1 5.0) (fma (/ z y) t t) (* (/ x z) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 0.2) {
		tmp = t / (z / x);
	} else if (t_1 <= 5.0) {
		tmp = fma((z / y), t, t);
	} else {
		tmp = (x / z) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 0.2)
		tmp = Float64(t / Float64(z / x));
	elseif (t_1 <= 5.0)
		tmp = fma(Float64(z / y), t, t);
	else
		tmp = Float64(Float64(x / z) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 0.2], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5.0], N[(N[(z / y), $MachinePrecision] * t + t), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((x - y) / (z - y)) IN
		LET tmp_1 = IF (t_1 <= (5)) THEN (((z / y) * t) + t) ELSE ((x / z) * t) ENDIF IN
		LET tmp = IF (t_1 <= (200000000000000011102230246251565404236316680908203125e-54)) THEN (t / (z / x)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 0.20000000000000001

   1. Initial program 97.3%

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

   3. Applied rewrites 83.8%

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

   5. Applied rewrites 97.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 39.9%

      \[\leadsto \frac{t}{\frac{z}{x}} \]

   if 0.20000000000000001 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5

   1. Initial program 97.3%

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

   3. Applied rewrites 47.1%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 44.2%

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

   7. Taylor expanded in y around inf

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

   9. Applied rewrites 32.9%

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

   11. Applied rewrites 34.5%

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

   if 5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 40.0%

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

Alternative 11: 69.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;t\_1 \leq 5:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot t\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- x y) (- z y))))
  (if (<= t_1 2e-5) (/ t (/ z x)) (if (<= t_1 5.0) t (* (/ x z) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 2e-5) {
		tmp = t / (z / x);
	} else if (t_1 <= 5.0) {
		tmp = t;
	} else {
		tmp = (x / z) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 2d-5) then
        tmp = t / (z / x)
    else if (t_1 <= 5.0d0) then
        tmp = t
    else
        tmp = (x / z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 2e-5) {
		tmp = t / (z / x);
	} else if (t_1 <= 5.0) {
		tmp = t;
	} else {
		tmp = (x / z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 2e-5:
		tmp = t / (z / x)
	elif t_1 <= 5.0:
		tmp = t
	else:
		tmp = (x / z) * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 2e-5)
		tmp = Float64(t / Float64(z / x));
	elseif (t_1 <= 5.0)
		tmp = t;
	else
		tmp = Float64(Float64(x / z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 2e-5)
		tmp = t / (z / x);
	elseif (t_1 <= 5.0)
		tmp = t;
	else
		tmp = (x / z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e-5], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5.0], t, N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((x - y) / (z - y)) IN
		LET tmp_1 = IF (t_1 <= (5)) THEN t ELSE ((x / z) * t) ENDIF IN
		LET tmp = IF (t_1 <= (2000000000000000163606107828062619091724627651274204254150390625e-68)) THEN (t / (z / x)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 2.0000000000000002e-5

   1. Initial program 97.3%

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

   3. Applied rewrites 83.8%

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

   5. Applied rewrites 97.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 39.9%

      \[\leadsto \frac{t}{\frac{z}{x}} \]

   if 2.0000000000000002e-5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5

   1. Initial program 97.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 34.2%

      \[\leadsto t \]

   if 5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 40.0%

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

Alternative 12: 69.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := \frac{x}{z} \cdot t\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* (/ x z) t)))
  (if (<= t_1 2e-5) t_2 (if (<= t_1 5.0) t t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / z) * t;
	double tmp;
	if (t_1 <= 2e-5) {
		tmp = t_2;
	} else if (t_1 <= 5.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = (x / z) * t
    if (t_1 <= 2d-5) then
        tmp = t_2
    else if (t_1 <= 5.0d0) then
        tmp = t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = (x / z) * t;
	double tmp;
	if (t_1 <= 2e-5) {
		tmp = t_2;
	} else if (t_1 <= 5.0) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = (x / z) * t
	tmp = 0
	if t_1 <= 2e-5:
		tmp = t_2
	elif t_1 <= 5.0:
		tmp = t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(Float64(x / z) * t)
	tmp = 0.0
	if (t_1 <= 2e-5)
		tmp = t_2;
	elseif (t_1 <= 5.0)
		tmp = t;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = (x / z) * t;
	tmp = 0.0;
	if (t_1 <= 2e-5)
		tmp = t_2;
	elseif (t_1 <= 5.0)
		tmp = t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, 2e-5], t$95$2, If[LessEqual[t$95$1, 5.0], t, t$95$2]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((x - y) / (z - y)) IN
		LET t_2 = ((x / z) * t) IN
			LET tmp_1 = IF (t_1 <= (5)) THEN t ELSE t_2 ENDIF IN
			LET tmp = IF (t_1 <= (2000000000000000163606107828062619091724627651274204254150390625e-68)) THEN t_2 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 2.0000000000000002e-5 or 5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 40.0%

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

   if 2.0000000000000002e-5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5

   1. Initial program 97.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 34.2%

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

Alternative 13: 67.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;t\_1 \leq 5:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot x}{z}\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- x y) (- z y))))
  (if (<= t_1 2e-5) (* x (/ t z)) (if (<= t_1 5.0) t (/ (* t x) z)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 2e-5) {
		tmp = x * (t / z);
	} else if (t_1 <= 5.0) {
		tmp = t;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    if (t_1 <= 2d-5) then
        tmp = x * (t / z)
    else if (t_1 <= 5.0d0) then
        tmp = t
    else
        tmp = (t * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double tmp;
	if (t_1 <= 2e-5) {
		tmp = x * (t / z);
	} else if (t_1 <= 5.0) {
		tmp = t;
	} else {
		tmp = (t * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	tmp = 0
	if t_1 <= 2e-5:
		tmp = x * (t / z)
	elif t_1 <= 5.0:
		tmp = t
	else:
		tmp = (t * x) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	tmp = 0.0
	if (t_1 <= 2e-5)
		tmp = Float64(x * Float64(t / z));
	elseif (t_1 <= 5.0)
		tmp = t;
	else
		tmp = Float64(Float64(t * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	tmp = 0.0;
	if (t_1 <= 2e-5)
		tmp = x * (t / z);
	elseif (t_1 <= 5.0)
		tmp = t;
	else
		tmp = (t * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e-5], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5.0], t, N[(N[(t * x), $MachinePrecision] / z), $MachinePrecision]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((x - y) / (z - y)) IN
		LET tmp_1 = IF (t_1 <= (5)) THEN t ELSE ((t * x) / z) ENDIF IN
		LET tmp = IF (t_1 <= (2000000000000000163606107828062619091724627651274204254150390625e-68)) THEN (x * (t / z)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 2.0000000000000002e-5

   1. Initial program 97.3%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 38.0%

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

   6. Applied rewrites 37.7%

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

   if 2.0000000000000002e-5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 5

   1. Initial program 97.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 34.2%

      \[\leadsto t \]

   if 5 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 38.0%

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

Alternative 14: 67.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{x - y}{z - y}\\ t_2 := x \cdot \frac{t}{z}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+22}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (- x y) (- z y))) (t_2 (* x (/ t z))))
  (if (<= t_1 2e-5) t_2 (if (<= t_1 5e+22) t t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = x * (t / z);
	double tmp;
	if (t_1 <= 2e-5) {
		tmp = t_2;
	} else if (t_1 <= 5e+22) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - y) / (z - y)
    t_2 = x * (t / z)
    if (t_1 <= 2d-5) then
        tmp = t_2
    else if (t_1 <= 5d+22) then
        tmp = t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) / (z - y);
	double t_2 = x * (t / z);
	double tmp;
	if (t_1 <= 2e-5) {
		tmp = t_2;
	} else if (t_1 <= 5e+22) {
		tmp = t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) / (z - y)
	t_2 = x * (t / z)
	tmp = 0
	if t_1 <= 2e-5:
		tmp = t_2
	elif t_1 <= 5e+22:
		tmp = t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) / Float64(z - y))
	t_2 = Float64(x * Float64(t / z))
	tmp = 0.0
	if (t_1 <= 2e-5)
		tmp = t_2;
	elseif (t_1 <= 5e+22)
		tmp = t;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) / (z - y);
	t_2 = x * (t / z);
	tmp = 0.0;
	if (t_1 <= 2e-5)
		tmp = t_2;
	elseif (t_1 <= 5e+22)
		tmp = t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e-5], t$95$2, If[LessEqual[t$95$1, 5e+22], t, t$95$2]]]]

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	LET t_1 = ((x - y) / (z - y)) IN
		LET t_2 = (x * (t / z)) IN
			LET tmp_1 = IF (t_1 <= (49999999999999995805696)) THEN t ELSE t_2 ENDIF IN
			LET tmp = IF (t_1 <= (2000000000000000163606107828062619091724627651274204254150390625e-68)) THEN t_2 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) (-.f64 z y)) < 2.0000000000000002e-5 or 4.9999999999999996e22 < (/.f64 (-.f64 x y) (-.f64 z y))

   1. Initial program 97.3%

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

   2. Taylor expanded in y around 0

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

   4. Applied rewrites 38.0%

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

   6. Applied rewrites 37.7%

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

   if 2.0000000000000002e-5 < (/.f64 (-.f64 x y) (-.f64 z y)) < 4.9999999999999996e22

   1. Initial program 97.3%

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

   2. Taylor expanded in y around inf

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

   4. Applied rewrites 34.2%

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

Alternative 15: 34.2% accurate, 13.0× speedup

Math

\[t \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z, t):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t: real): real =
	t
END code

Derivation

1. Initial program 97.3%

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

2. Taylor expanded in y around inf

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

4. Applied rewrites 34.2%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64
  (* (/ (- x y) (- z y)) t))