Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, B

Percentage Accurate: 100.0% → 100.0%

Time: 1.9s

Alternatives: 7

Speedup: 1.4×

Specification

Math

\[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))

C

double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + 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 = (((1.0d0 / 8.0d0) * x) - ((y * z) / 2.0d0)) + t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}

Python

def code(x, y, z, t):
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(1.0 / 8.0) * x) - Float64(Float64(y * z) / 2.0)) + t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / 2.0), $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 =
	((((1) / (8)) * x) - ((y * z) / (2))) + t
END code

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))

C

double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + 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 = (((1.0d0 / 8.0d0) * x) - ((y * z) / 2.0d0)) + t
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
}

Python

def code(x, y, z, t):
	return (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(1.0 / 8.0) * x) - Float64(Float64(y * z) / 2.0)) + t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((1.0 / 8.0) * x) - ((y * z) / 2.0)) + t;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(1.0 / 8.0), $MachinePrecision] * x), $MachinePrecision] - N[(N[(y * z), $MachinePrecision] / 2.0), $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 =
	((((1) / (8)) * x) - ((y * z) / (2))) + t
END code

Alternative 1: 100.0% accurate, 1.4× speedup

Math

\[\mathsf{fma}\left(y, z \cdot -0.5, \mathsf{fma}\left(x, 0.125, t\right)\right) \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (fma y (* z -0.5) (fma x 0.125 t)))

C

double code(double x, double y, double z, double t) {
	return fma(y, (z * -0.5), fma(x, 0.125, t));
}

Julia

function code(x, y, z, t)
	return fma(y, Float64(z * -0.5), fma(x, 0.125, t))
end

Wolfram

code[x_, y_, z_, t_] := N[(y * N[(z * -0.5), $MachinePrecision] + N[(x * 0.125 + t), $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 =
	(y * (z * (-5e-1))) + ((x * (125e-3)) + t)
END code

Derivation

1. Initial program 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]
2. Step-by-step derivation

3. Applied rewrites 100.0%

   \[\leadsto \mathsf{fma}\left(y, z \cdot -0.5, \mathsf{fma}\left(x, 0.125, t\right)\right) \]
4. Add Preprocessing

Alternative 2: 86.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := -0.5 \cdot \left(y \cdot z\right) + t\\ \mathbf{if}\;t \leq -1.6770947112847438 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 76298940059016.36:\\ \;\;\;\;\mathsf{fma}\left(y, -0.5 \cdot z, 0.125 \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (+ (* -0.5 (* y z)) t)))
  (if (<= t -1.6770947112847438e-50)
    t_1
    (if (<= t 76298940059016.36) (fma y (* -0.5 z) (* 0.125 x)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-0.5 * (y * z)) + t;
	double tmp;
	if (t <= -1.6770947112847438e-50) {
		tmp = t_1;
	} else if (t <= 76298940059016.36) {
		tmp = fma(y, (-0.5 * z), (0.125 * x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-0.5 * Float64(y * z)) + t)
	tmp = 0.0
	if (t <= -1.6770947112847438e-50)
		tmp = t_1;
	elseif (t <= 76298940059016.36)
		tmp = fma(y, Float64(-0.5 * z), Float64(0.125 * x));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(-0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[t, -1.6770947112847438e-50], t$95$1, If[LessEqual[t, 76298940059016.36], N[(y * N[(-0.5 * z), $MachinePrecision] + N[(0.125 * x), $MachinePrecision]), $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 = (((-5e-1) * (y * z)) + t) IN
		LET tmp_1 = IF (t <= (76298940059016359375e-6)) THEN ((y * ((-5e-1) * z)) + ((125e-3) * x)) ELSE t_1 ENDIF IN
		LET tmp = IF (t <= (-167709471128474384815647562929888437797664347855967950775217343270676325862336514112358919563496671100570645038506509306522611509049358602396750939078629016876220703125e-217)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if t < -1.6770947112847438e-50 or 76298940059016.359 < t

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{-1}{2} \cdot \left(y \cdot z\right) + t \]
   3. Step-by-step derivation

   4. Applied rewrites 67.8%

      \[\leadsto -0.5 \cdot \left(y \cdot z\right) + t \]

   if -1.6770947112847438e-50 < t < 76298940059016.359

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

   2. Taylor expanded in y around 0

      \[\leadsto t + \frac{1}{8} \cdot x \]
   3. Step-by-step derivation

   4. Applied rewrites 64.6%

      \[\leadsto t + 0.125 \cdot x \]

   6. Applied rewrites 64.6%

      \[\leadsto \mathsf{fma}\left(0.125, x, t\right) \]

   7. Taylor expanded in t around 0

      \[\leadsto \frac{1}{8} \cdot x - \frac{1}{2} \cdot \left(y \cdot z\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 68.2%

      \[\leadsto 0.125 \cdot x - 0.5 \cdot \left(y \cdot z\right) \]

   11. Applied rewrites 68.2%

       \[\leadsto \mathsf{fma}\left(y, -0.5 \cdot z, 0.125 \cdot x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 85.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := -0.5 \cdot \left(y \cdot z\right) + t\\ \mathbf{if}\;y \cdot z \leq -3.811187879761372 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \cdot z \leq 5.193479599924079 \cdot 10^{-49}:\\ \;\;\;\;\mathsf{fma}\left(0.125, x, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (+ (* -0.5 (* y z)) t)))
  (if (<= (* y z) -3.811187879761372e-39)
    t_1
    (if (<= (* y z) 5.193479599924079e-49) (fma 0.125 x t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-0.5 * (y * z)) + t;
	double tmp;
	if ((y * z) <= -3.811187879761372e-39) {
		tmp = t_1;
	} else if ((y * z) <= 5.193479599924079e-49) {
		tmp = fma(0.125, x, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-0.5 * Float64(y * z)) + t)
	tmp = 0.0
	if (Float64(y * z) <= -3.811187879761372e-39)
		tmp = t_1;
	elseif (Float64(y * z) <= 5.193479599924079e-49)
		tmp = fma(0.125, x, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(-0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -3.811187879761372e-39], t$95$1, If[LessEqual[N[(y * z), $MachinePrecision], 5.193479599924079e-49], N[(0.125 * x + 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 = (((-5e-1) * (y * z)) + t) IN
		LET tmp_1 = IF ((y * z) <= (519347959992407922738789092435664841483204930658308108660499036343171355847186042158132009909050298978109699785556393355719952131810401851907954551279544830322265625e-213)) THEN (((125e-3) * x) + t) ELSE t_1 ENDIF IN
		LET tmp = IF ((y * z) <= (-3811187879761372015349719338492753709029299134921760281036981209992095526189864673376994075372514204913532154250788153149187564849853515625e-177)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -3.811187879761372e-39 or 5.1934795999240792e-49 < (*.f64 y z)

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

   2. Taylor expanded in x around 0

      \[\leadsto \frac{-1}{2} \cdot \left(y \cdot z\right) + t \]
   3. Step-by-step derivation

   4. Applied rewrites 67.8%

      \[\leadsto -0.5 \cdot \left(y \cdot z\right) + t \]

   if -3.811187879761372e-39 < (*.f64 y z) < 5.1934795999240792e-49

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

   2. Taylor expanded in y around 0

      \[\leadsto t + \frac{1}{8} \cdot x \]
   3. Step-by-step derivation

   4. Applied rewrites 64.6%

      \[\leadsto t + 0.125 \cdot x \]

   6. Applied rewrites 64.6%

      \[\leadsto \mathsf{fma}\left(0.125, x, t\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 83.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} t_1 := -0.5 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \cdot z \leq -5.175013782460881 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \cdot z \leq 6.4573354302613295 \cdot 10^{+72}:\\ \;\;\;\;\mathsf{fma}\left(0.125, x, t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* -0.5 (* y z))))
  (if (<= (* y z) -5.175013782460881e+99)
    t_1
    (if (<= (* y z) 6.4573354302613295e+72) (fma 0.125 x t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -0.5 * (y * z);
	double tmp;
	if ((y * z) <= -5.175013782460881e+99) {
		tmp = t_1;
	} else if ((y * z) <= 6.4573354302613295e+72) {
		tmp = fma(0.125, x, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(-0.5 * Float64(y * z))
	tmp = 0.0
	if (Float64(y * z) <= -5.175013782460881e+99)
		tmp = t_1;
	elseif (Float64(y * z) <= 6.4573354302613295e+72)
		tmp = fma(0.125, x, t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -5.175013782460881e+99], t$95$1, If[LessEqual[N[(y * z), $MachinePrecision], 6.4573354302613295e+72], N[(0.125 * x + 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 = ((-5e-1) * (y * z)) IN
		LET tmp_1 = IF ((y * z) <= (6457335430261329547810767699390821776343632049679724029847141179088437248)) THEN (((125e-3) * x) + t) ELSE t_1 ENDIF IN
		LET tmp = IF ((y * z) <= (-5175013782460881157524174131526843532796470125390131372701020118359893052427140865462262724732911616)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -5.1750137824608812e99 or 6.4573354302613295e72 < (*.f64 y z)

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

   2. Taylor expanded in y around 0

      \[\leadsto t + \frac{1}{8} \cdot x \]
   3. Step-by-step derivation

   4. Applied rewrites 64.6%

      \[\leadsto t + 0.125 \cdot x \]

   6. Applied rewrites 64.6%

      \[\leadsto \mathsf{fma}\left(0.125, x, t\right) \]

   7. Taylor expanded in y around inf

      \[\leadsto \frac{-1}{2} \cdot \left(y \cdot z\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 36.8%

      \[\leadsto -0.5 \cdot \left(y \cdot z\right) \]

   if -5.1750137824608812e99 < (*.f64 y z) < 6.4573354302613295e72

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

   2. Taylor expanded in y around 0

      \[\leadsto t + \frac{1}{8} \cdot x \]
   3. Step-by-step derivation

   4. Applied rewrites 64.6%

      \[\leadsto t + 0.125 \cdot x \]

   6. Applied rewrites 64.6%

      \[\leadsto \mathsf{fma}\left(0.125, x, t\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 64.6% accurate, 3.3× speedup

Math

\[\mathsf{fma}\left(0.125, x, t\right) \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (fma 0.125 x t))

C

double code(double x, double y, double z, double t) {
	return fma(0.125, x, t);
}

Julia

function code(x, y, z, t)
	return fma(0.125, x, t)
end

Wolfram

code[x_, y_, z_, t_] := N[(0.125 * x + 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 =
	((125e-3) * x) + t
END code

Derivation

1. Initial program 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

2. Taylor expanded in y around 0

   \[\leadsto t + \frac{1}{8} \cdot x \]
3. Step-by-step derivation

4. Applied rewrites 64.6%

   \[\leadsto t + 0.125 \cdot x \]

6. Applied rewrites 64.6%

   \[\leadsto \mathsf{fma}\left(0.125, x, t\right) \]
7. Add Preprocessing

Alternative 6: 50.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -1.6770947112847438 \cdot 10^{-50}:\\ \;\;\;\;t\\ \mathbf{elif}\;t \leq 9.624175003052535 \cdot 10^{+19}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  :pre TRUE
  (if (<= t -1.6770947112847438e-50)
  t
  (if (<= t 9.624175003052535e+19) (* 0.125 x) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.6770947112847438e-50) {
		tmp = t;
	} else if (t <= 9.624175003052535e+19) {
		tmp = 0.125 * x;
	} else {
		tmp = 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) :: tmp
    if (t <= (-1.6770947112847438d-50)) then
        tmp = t
    else if (t <= 9.624175003052535d+19) then
        tmp = 0.125d0 * x
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.6770947112847438e-50) {
		tmp = t;
	} else if (t <= 9.624175003052535e+19) {
		tmp = 0.125 * x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.6770947112847438e-50:
		tmp = t
	elif t <= 9.624175003052535e+19:
		tmp = 0.125 * x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.6770947112847438e-50)
		tmp = t;
	elseif (t <= 9.624175003052535e+19)
		tmp = Float64(0.125 * x);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.6770947112847438e-50)
		tmp = t;
	elseif (t <= 9.624175003052535e+19)
		tmp = 0.125 * x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.6770947112847438e-50], t, If[LessEqual[t, 9.624175003052535e+19], N[(0.125 * x), $MachinePrecision], 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 =
	LET tmp_1 = IF (t <= (96241750030525349888)) THEN ((125e-3) * x) ELSE t ENDIF IN
	LET tmp = IF (t <= (-167709471128474384815647562929888437797664347855967950775217343270676325862336514112358919563496671100570645038506509306522611509049358602396750939078629016876220703125e-217)) THEN t ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if t < -1.6770947112847438e-50 or 96241750030525350000 < t

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

   2. Taylor expanded in y around 0

      \[\leadsto t + \frac{1}{8} \cdot x \]
   3. Step-by-step derivation

   4. Applied rewrites 64.6%

      \[\leadsto t + 0.125 \cdot x \]

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 33.1%

      \[\leadsto t \]

   if -1.6770947112847438e-50 < t < 96241750030525350000

   1. Initial program 100.0%

      \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

   2. Taylor expanded in y around 0

      \[\leadsto t + \frac{1}{8} \cdot x \]
   3. Step-by-step derivation

   4. Applied rewrites 64.6%

      \[\leadsto t + 0.125 \cdot x \]

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 33.1%

      \[\leadsto t \]

   8. Taylor expanded in x around inf

      \[\leadsto \frac{1}{8} \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 33.3%

       \[\leadsto 0.125 \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 33.1% accurate, 19.8× 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 100.0%

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t \]

2. Taylor expanded in y around 0

   \[\leadsto t + \frac{1}{8} \cdot x \]
3. Step-by-step derivation

4. Applied rewrites 64.6%

   \[\leadsto t + 0.125 \cdot x \]

5. Taylor expanded in x around 0

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

7. Applied rewrites 33.1%

   \[\leadsto t \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64
  (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))