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

Percentage Accurate: 97.7% → 97.7%

Time: 3.1s

Alternatives: 7

Speedup: 1.0×

• 74.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

3. Applied rewrites 97.7%

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

Alternative 2: 94.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 500000000000:\\ \;\;\;\;z \cdot \frac{x}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (* x (- z t)) y)))
  (if (<= (/ x y) -2000000000000.0)
    t_1
    (if (<= (/ x y) 500000000000.0) (+ (* z (/ x y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * (z - t)) / y;
	double tmp;
	if ((x / y) <= -2000000000000.0) {
		tmp = t_1;
	} else if ((x / y) <= 500000000000.0) {
		tmp = (z * (x / y)) + t;
	} else {
		tmp = t_1;
	}
	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 * (z - t)) / y
    if ((x / y) <= (-2000000000000.0d0)) then
        tmp = t_1
    else if ((x / y) <= 500000000000.0d0) then
        tmp = (z * (x / y)) + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * (z - t)) / y;
	double tmp;
	if ((x / y) <= -2000000000000.0) {
		tmp = t_1;
	} else if ((x / y) <= 500000000000.0) {
		tmp = (z * (x / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * (z - t)) / y
	tmp = 0
	if (x / y) <= -2000000000000.0:
		tmp = t_1
	elif (x / y) <= 500000000000.0:
		tmp = (z * (x / y)) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(z - t)) / y)
	tmp = 0.0
	if (Float64(x / y) <= -2000000000000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 500000000000.0)
		tmp = Float64(Float64(z * Float64(x / y)) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * (z - t)) / y;
	tmp = 0.0;
	if ((x / y) <= -2000000000000.0)
		tmp = t_1;
	elseif ((x / y) <= 500000000000.0)
		tmp = (z * (x / y)) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2000000000000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 500000000000.0], N[(N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

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 * (z - t)) / y) IN
		LET tmp_1 = IF ((x / y) <= (5e11)) THEN ((z * (x / y)) + t) ELSE t_1 ENDIF IN
		LET tmp = IF ((x / y) <= (-2e12)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2e12 or 5e11 < (/.f64 x y)

   1. Initial program 97.7%

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

   3. Applied rewrites 84.5%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 28.7%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 58.6%

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

   if -2e12 < (/.f64 x y) < 5e11

   1. Initial program 97.7%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 72.1%

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

   6. Applied rewrites 75.7%

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

Alternative 3: 93.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := \frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-6}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{z}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (* x (- z t)) y)))
  (if (<= (/ x y) -2e-6)
    t_1
    (if (<= (/ x y) 5e-6) (fma x (/ z y) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * (z - t)) / y;
	double tmp;
	if ((x / y) <= -2e-6) {
		tmp = t_1;
	} else if ((x / y) <= 5e-6) {
		tmp = fma(x, (z / y), t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * Float64(z - t)) / y)
	tmp = 0.0
	if (Float64(x / y) <= -2e-6)
		tmp = t_1;
	elseif (Float64(x / y) <= 5e-6)
		tmp = fma(x, Float64(z / y), t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -2e-6], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 5e-6], N[(x * N[(z / y), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

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 * (z - t)) / y) IN
		LET tmp_1 = IF ((x / y) <= (50000000000000004090152695701565477293115691281855106353759765625e-70)) THEN ((x * (z / y)) + t) ELSE t_1 ENDIF IN
		LET tmp = IF ((x / y) <= (-199999999999999990949622365177251737122787744738161563873291015625e-71)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.9999999999999999e-6 or 5.0000000000000004e-6 < (/.f64 x y)

   1. Initial program 97.7%

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

   3. Applied rewrites 84.5%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 28.7%

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

   7. Taylor expanded in x around inf

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

   9. Applied rewrites 58.6%

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

   if -1.9999999999999999e-6 < (/.f64 x y) < 5.0000000000000004e-6

   1. Initial program 97.7%

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

   3. Applied rewrites 92.6%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 72.3%

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

Alternative 4: 72.3% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.7%

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

3. Applied rewrites 92.6%

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

4. Taylor expanded in z around inf

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

6. Applied rewrites 72.3%

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

Alternative 5: 62.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \frac{x \cdot z}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-11}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 10^{-28}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (/ (* x z) y)))
  (if (<= (/ x y) -5e-11) t_1 (if (<= (/ x y) 1e-28) t t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * z) / y;
	double tmp;
	if ((x / y) <= -5e-11) {
		tmp = t_1;
	} else if ((x / y) <= 1e-28) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	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 * z) / y
    if ((x / y) <= (-5d-11)) then
        tmp = t_1
    else if ((x / y) <= 1d-28) then
        tmp = t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * z) / y;
	double tmp;
	if ((x / y) <= -5e-11) {
		tmp = t_1;
	} else if ((x / y) <= 1e-28) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * z) / y
	tmp = 0
	if (x / y) <= -5e-11:
		tmp = t_1
	elif (x / y) <= 1e-28:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * z) / y)
	tmp = 0.0
	if (Float64(x / y) <= -5e-11)
		tmp = t_1;
	elseif (Float64(x / y) <= 1e-28)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * z) / y;
	tmp = 0.0;
	if ((x / y) <= -5e-11)
		tmp = t_1;
	elseif ((x / y) <= 1e-28)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e-11], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1e-28], t, t$95$1]]]

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 * z) / y) IN
		LET tmp_1 = IF ((x / y) <= (9999999999999999712325434616006196770329693636753639999435544334276007748447435974359365218333550728857517242431640625e-146)) THEN t ELSE t_1 ENDIF IN
		LET tmp = IF ((x / y) <= (-50000000000000001821609865774887078958277353279981980449520051479339599609375e-87)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.0000000000000002e-11 or 9.9999999999999997e-29 < (/.f64 x y)

   1. Initial program 97.7%

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

   3. Applied rewrites 84.5%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 28.7%

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

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 37.2%

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

   if -5.0000000000000002e-11 < (/.f64 x y) < 9.9999999999999997e-29

   1. Initial program 97.7%

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

   2. Taylor expanded in x around 0

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

   4. Applied rewrites 37.8%

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

Alternative 6: 37.8% 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 97.7%

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

2. Taylor expanded in x around 0

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

4. Applied rewrites 37.8%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

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