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

Percentage Accurate: 97.7% → 97.7%

Time: 1.8s

Alternatives: 10

Speedup: 1.2×

• 67.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  :pre TRUE
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

ReFlow

f(x, y, z, t, a, b, c):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c: real): real =
	(((x * y) + ((z * t) / (16))) - ((a * b) / (4))) + c
END code

Initial Program: 97.7% accurate, 1.0× speedup

Math

\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  :pre TRUE
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (((x * y) + ((z * t) / 16.0d0)) - ((a * b) / 4.0d0)) + c
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

Python

def code(x, y, z, t, a, b, c):
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision] - N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]

ReFlow

f(x, y, z, t, a, b, c):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c: real): real =
	(((x * y) + ((z * t) / (16))) - ((a * b) / (4))) + c
END code

Alternative 1: 97.7% accurate, 1.2× speedup

Math

\[\mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, \mathsf{fma}\left(y, x, c\right)\right) \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  :pre TRUE
  (fma (fma (* t z) -0.25 (* b a)) -0.25 (fma y x c)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return fma(fma((t * z), -0.25, (b * a)), -0.25, fma(y, x, c));
}

Julia

function code(x, y, z, t, a, b, c)
	return fma(fma(Float64(t * z), -0.25, Float64(b * a)), -0.25, fma(y, x, c))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(t * z), $MachinePrecision] * -0.25 + N[(b * a), $MachinePrecision]), $MachinePrecision] * -0.25 + N[(y * x + c), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y, z, t, a, b, c):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c: real): real =
	((((t * z) * (-25e-2)) + (b * a)) * (-25e-2)) + ((y * x) + c)
END code

Derivation

1. Initial program 97.7%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
2. Step-by-step derivation

3. Applied rewrites 97.7%

   \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, \mathsf{fma}\left(y, x, c\right)\right) \]
4. Add Preprocessing

Alternative 2: 89.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+134}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, -0.25, \mathsf{fma}\left(y, x, c\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.0625 \cdot z, t, \mathsf{fma}\left(y, x, c\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  :pre TRUE
  (if (<= (* x y) -4e+134)
  (fma (* a b) -0.25 (fma y x c))
  (if (<= (* x y) 5e+59)
    (fma (fma (* t z) -0.25 (* b a)) -0.25 c)
    (fma (* 0.0625 z) t (fma y x c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x * y) <= -4e+134) {
		tmp = fma((a * b), -0.25, fma(y, x, c));
	} else if ((x * y) <= 5e+59) {
		tmp = fma(fma((t * z), -0.25, (b * a)), -0.25, c);
	} else {
		tmp = fma((0.0625 * z), t, fma(y, x, c));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(x * y) <= -4e+134)
		tmp = fma(Float64(a * b), -0.25, fma(y, x, c));
	elseif (Float64(x * y) <= 5e+59)
		tmp = fma(fma(Float64(t * z), -0.25, Float64(b * a)), -0.25, c);
	else
		tmp = fma(Float64(0.0625 * z), t, fma(y, x, c));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(x * y), $MachinePrecision], -4e+134], N[(N[(a * b), $MachinePrecision] * -0.25 + N[(y * x + c), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+59], N[(N[(N[(t * z), $MachinePrecision] * -0.25 + N[(b * a), $MachinePrecision]), $MachinePrecision] * -0.25 + c), $MachinePrecision], N[(N[(0.0625 * z), $MachinePrecision] * t + N[(y * x + c), $MachinePrecision]), $MachinePrecision]]]

ReFlow

f(x, y, z, t, a, b, c):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c: real): real =
	LET tmp_1 = IF ((x * y) <= (499999999999999974693567648537009433481822505506705036541952)) THEN (((((t * z) * (-25e-2)) + (b * a)) * (-25e-2)) + c) ELSE ((((625e-4) * z) * t) + ((y * x) + c)) ENDIF IN
	LET tmp = IF ((x * y) <= (-399999999999999968592814598682797260030199309491889846017500444199393206430641297891429046460580357712197457831351381962129679723790336)) THEN (((a * b) * (-25e-2)) + ((y * x) + c)) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.9999999999999997e134

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

   3. Applied rewrites 97.7%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, \mathsf{fma}\left(y, x, c\right)\right) \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(a \cdot b, -0.25, \mathsf{fma}\left(y, x, c\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 73.7%

      \[\leadsto \mathsf{fma}\left(a \cdot b, -0.25, \mathsf{fma}\left(y, x, c\right)\right) \]

   if -3.9999999999999997e134 < (*.f64 x y) < 4.9999999999999997e59

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

   3. Applied rewrites 97.7%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, \mathsf{fma}\left(y, x, c\right)\right) \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, c\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 74.0%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, c\right) \]

   if 4.9999999999999997e59 < (*.f64 x y)

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0

      \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 72.9%

      \[\leadsto c + \mathsf{fma}\left(0.0625, t \cdot z, x \cdot y\right) \]

   6. Applied rewrites 73.4%

      \[\leadsto \mathsf{fma}\left(0.0625 \cdot z, t, \mathsf{fma}\left(y, x, c\right)\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(a \cdot b, -0.25, \mathsf{fma}\left(y, x, c\right)\right)\\ \mathbf{if}\;a \cdot b \leq -1.5414268888085725 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 1766690827.541296:\\ \;\;\;\;\mathsf{fma}\left(0.0625 \cdot z, t, \mathsf{fma}\left(y, x, c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma (* a b) -0.25 (fma y x c))))
  (if (<= (* a b) -1.5414268888085725e+44)
    t_1
    (if (<= (* a b) 1766690827.541296)
      (fma (* 0.0625 z) t (fma y x c))
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((a * b), -0.25, fma(y, x, c));
	double tmp;
	if ((a * b) <= -1.5414268888085725e+44) {
		tmp = t_1;
	} else if ((a * b) <= 1766690827.541296) {
		tmp = fma((0.0625 * z), t, fma(y, x, c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = fma(Float64(a * b), -0.25, fma(y, x, c))
	tmp = 0.0
	if (Float64(a * b) <= -1.5414268888085725e+44)
		tmp = t_1;
	elseif (Float64(a * b) <= 1766690827.541296)
		tmp = fma(Float64(0.0625 * z), t, fma(y, x, c));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * -0.25 + N[(y * x + c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.5414268888085725e+44], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1766690827.541296], N[(N[(0.0625 * z), $MachinePrecision] * t + N[(y * x + c), $MachinePrecision]), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a, b, c):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c: real): real =
	LET t_1 = (((a * b) * (-25e-2)) + ((y * x) + c)) IN
		LET tmp_1 = IF ((a * b) <= (17666908275412960052490234375e-19)) THEN ((((625e-4) * z) * t) + ((y * x) + c)) ELSE t_1 ENDIF IN
		LET tmp = IF ((a * b) <= (-154142688880857253015249070331368326419185664)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.5414268888085725e44 or 1766690827.541296 < (*.f64 a b)

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

   3. Applied rewrites 97.7%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, \mathsf{fma}\left(y, x, c\right)\right) \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(a \cdot b, -0.25, \mathsf{fma}\left(y, x, c\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 73.7%

      \[\leadsto \mathsf{fma}\left(a \cdot b, -0.25, \mathsf{fma}\left(y, x, c\right)\right) \]

   if -1.5414268888085725e44 < (*.f64 a b) < 1766690827.541296

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0

      \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 72.9%

      \[\leadsto c + \mathsf{fma}\left(0.0625, t \cdot z, x \cdot y\right) \]

   6. Applied rewrites 73.4%

      \[\leadsto \mathsf{fma}\left(0.0625 \cdot z, t, \mathsf{fma}\left(y, x, c\right)\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 86.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;a \cdot b \leq -6.113484582340225 \cdot 10^{+147}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, -0.25, c\right)\\ \mathbf{elif}\;a \cdot b \leq 1.5070441306524407 \cdot 10^{+65}:\\ \;\;\;\;\mathsf{fma}\left(0.0625 \cdot z, t, \mathsf{fma}\left(y, x, c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, -0.25, x \cdot y\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  :pre TRUE
  (if (<= (* a b) -6.113484582340225e+147)
  (fma (* a b) -0.25 c)
  (if (<= (* a b) 1.5070441306524407e+65)
    (fma (* 0.0625 z) t (fma y x c))
    (fma (* a b) -0.25 (* x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((a * b) <= -6.113484582340225e+147) {
		tmp = fma((a * b), -0.25, c);
	} else if ((a * b) <= 1.5070441306524407e+65) {
		tmp = fma((0.0625 * z), t, fma(y, x, c));
	} else {
		tmp = fma((a * b), -0.25, (x * y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(a * b) <= -6.113484582340225e+147)
		tmp = fma(Float64(a * b), -0.25, c);
	elseif (Float64(a * b) <= 1.5070441306524407e+65)
		tmp = fma(Float64(0.0625 * z), t, fma(y, x, c));
	else
		tmp = fma(Float64(a * b), -0.25, Float64(x * y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(a * b), $MachinePrecision], -6.113484582340225e+147], N[(N[(a * b), $MachinePrecision] * -0.25 + c), $MachinePrecision], If[LessEqual[N[(a * b), $MachinePrecision], 1.5070441306524407e+65], N[(N[(0.0625 * z), $MachinePrecision] * t + N[(y * x + c), $MachinePrecision]), $MachinePrecision], N[(N[(a * b), $MachinePrecision] * -0.25 + N[(x * y), $MachinePrecision]), $MachinePrecision]]]

ReFlow

f(x, y, z, t, a, b, c):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c: real): real =
	LET tmp_1 = IF ((a * b) <= (150704413065244067728363383409005260300575989330546438268036055040)) THEN ((((625e-4) * z) * t) + ((y * x) + c)) ELSE (((a * b) * (-25e-2)) + (x * y)) ENDIF IN
	LET tmp = IF ((a * b) <= (-6113484582340225114390863045446215144041674693067911482818513430441622931783418051058031799825177560164563247997174162910212413505938552196970840064)) THEN (((a * b) * (-25e-2)) + c) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 3 regimes

2. if (*.f64 a b) < -6.1134845823402251e147

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

   3. Applied rewrites 97.7%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, \mathsf{fma}\left(y, x, c\right)\right) \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, c\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 74.0%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, c\right) \]

   7. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(a \cdot b, -0.25, c\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 49.1%

      \[\leadsto \mathsf{fma}\left(a \cdot b, -0.25, c\right) \]

   if -6.1134845823402251e147 < (*.f64 a b) < 1.5070441306524407e65

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0

      \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 72.9%

      \[\leadsto c + \mathsf{fma}\left(0.0625, t \cdot z, x \cdot y\right) \]

   6. Applied rewrites 73.4%

      \[\leadsto \mathsf{fma}\left(0.0625 \cdot z, t, \mathsf{fma}\left(y, x, c\right)\right) \]

   if 1.5070441306524407e65 < (*.f64 a b)

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

   3. Applied rewrites 97.7%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, \mathsf{fma}\left(y, x, c\right)\right) \]

   4. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(a \cdot b, -0.25, \mathsf{fma}\left(y, x, c\right)\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 73.7%

      \[\leadsto \mathsf{fma}\left(a \cdot b, -0.25, \mathsf{fma}\left(y, x, c\right)\right) \]

   7. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(a \cdot b, -0.25, x \cdot y\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 53.4%

      \[\leadsto \mathsf{fma}\left(a \cdot b, -0.25, x \cdot y\right) \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 77.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(0.0625 \cdot z, t, x \cdot y\right)\\ t_2 := x \cdot y + \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+103}:\\ \;\;\;\;\mathsf{fma}\left(a \cdot b, -0.25, c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma (* 0.0625 z) t (* x y)))
       (t_2 (+ (* x y) (/ (* z t) 16.0))))
  (if (<= t_2 -5e+177)
    t_1
    (if (<= t_2 5e+103) (fma (* a b) -0.25 c) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((0.0625 * z), t, (x * y));
	double t_2 = (x * y) + ((z * t) / 16.0);
	double tmp;
	if (t_2 <= -5e+177) {
		tmp = t_1;
	} else if (t_2 <= 5e+103) {
		tmp = fma((a * b), -0.25, c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = fma(Float64(0.0625 * z), t, Float64(x * y))
	t_2 = Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0))
	tmp = 0.0
	if (t_2 <= -5e+177)
		tmp = t_1;
	elseif (t_2 <= 5e+103)
		tmp = fma(Float64(a * b), -0.25, c);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(0.0625 * z), $MachinePrecision] * t + N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+177], t$95$1, If[LessEqual[t$95$2, 5e+103], N[(N[(a * b), $MachinePrecision] * -0.25 + c), $MachinePrecision], t$95$1]]]]

ReFlow

f(x, y, z, t, a, b, c):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c: real): real =
	LET t_1 = ((((625e-4) * z) * t) + (x * y)) IN
		LET t_2 = ((x * y) + ((z * t) / (16))) IN
			LET tmp_1 = IF (t_2 <= (50000000000000000095783754286733436810797756363259600557640175729968966210199437798061807255409016176640)) THEN (((a * b) * (-25e-2)) + c) ELSE t_1 ENDIF IN
			LET tmp = IF (t_2 <= (-5000000000000000262190592237531418597736900077214862305283068621659030917376859431910478415443928807994362318208466088914672700840093622075866148980296178635908453530060388827136)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) < -5.0000000000000003e177 or 5e103 < (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64)))

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0

      \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 72.9%

      \[\leadsto c + \mathsf{fma}\left(0.0625, t \cdot z, x \cdot y\right) \]

   6. Applied rewrites 73.4%

      \[\leadsto \mathsf{fma}\left(0.0625 \cdot z, t, \mathsf{fma}\left(y, x, c\right)\right) \]

   7. Taylor expanded in x around inf

      \[\leadsto \mathsf{fma}\left(0.0625 \cdot z, t, x \cdot y\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 53.0%

      \[\leadsto \mathsf{fma}\left(0.0625 \cdot z, t, x \cdot y\right) \]

   if -5.0000000000000003e177 < (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) < 5e103

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

   3. Applied rewrites 97.7%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, \mathsf{fma}\left(y, x, c\right)\right) \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, c\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 74.0%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, c\right) \]

   7. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(a \cdot b, -0.25, c\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 49.1%

      \[\leadsto \mathsf{fma}\left(a \cdot b, -0.25, c\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 64.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(a \cdot b, -0.25, c\right)\\ \mathbf{if}\;a \cdot b \leq -1.5414268888085725 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 1766690827.541296:\\ \;\;\;\;\mathsf{fma}\left(0.0625 \cdot z, t, c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma (* a b) -0.25 c)))
  (if (<= (* a b) -1.5414268888085725e+44)
    t_1
    (if (<= (* a b) 1766690827.541296) (fma (* 0.0625 z) t c) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((a * b), -0.25, c);
	double tmp;
	if ((a * b) <= -1.5414268888085725e+44) {
		tmp = t_1;
	} else if ((a * b) <= 1766690827.541296) {
		tmp = fma((0.0625 * z), t, c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = fma(Float64(a * b), -0.25, c)
	tmp = 0.0
	if (Float64(a * b) <= -1.5414268888085725e+44)
		tmp = t_1;
	elseif (Float64(a * b) <= 1766690827.541296)
		tmp = fma(Float64(0.0625 * z), t, c);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * -0.25 + c), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.5414268888085725e+44], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1766690827.541296], N[(N[(0.0625 * z), $MachinePrecision] * t + c), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a, b, c):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c: real): real =
	LET t_1 = (((a * b) * (-25e-2)) + c) IN
		LET tmp_1 = IF ((a * b) <= (17666908275412960052490234375e-19)) THEN ((((625e-4) * z) * t) + c) ELSE t_1 ENDIF IN
		LET tmp = IF ((a * b) <= (-154142688880857253015249070331368326419185664)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.5414268888085725e44 or 1766690827.541296 < (*.f64 a b)

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

   3. Applied rewrites 97.7%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, \mathsf{fma}\left(y, x, c\right)\right) \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, c\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 74.0%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, c\right) \]

   7. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(a \cdot b, -0.25, c\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 49.1%

      \[\leadsto \mathsf{fma}\left(a \cdot b, -0.25, c\right) \]

   if -1.5414268888085725e44 < (*.f64 a b) < 1766690827.541296

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0

      \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 72.9%

      \[\leadsto c + \mathsf{fma}\left(0.0625, t \cdot z, x \cdot y\right) \]

   6. Applied rewrites 73.4%

      \[\leadsto \mathsf{fma}\left(0.0625 \cdot z, t, \mathsf{fma}\left(y, x, c\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(0.0625 \cdot z, t, c\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 48.3%

      \[\leadsto \mathsf{fma}\left(0.0625 \cdot z, t, c\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 64.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := \mathsf{fma}\left(a \cdot b, -0.25, c\right)\\ \mathbf{if}\;a \cdot b \leq -1.5414268888085725 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 1766690827.541296:\\ \;\;\;\;c + 0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (fma (* a b) -0.25 c)))
  (if (<= (* a b) -1.5414268888085725e+44)
    t_1
    (if (<= (* a b) 1766690827.541296) (+ c (* 0.0625 (* t z))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma((a * b), -0.25, c);
	double tmp;
	if ((a * b) <= -1.5414268888085725e+44) {
		tmp = t_1;
	} else if ((a * b) <= 1766690827.541296) {
		tmp = c + (0.0625 * (t * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = fma(Float64(a * b), -0.25, c)
	tmp = 0.0
	if (Float64(a * b) <= -1.5414268888085725e+44)
		tmp = t_1;
	elseif (Float64(a * b) <= 1766690827.541296)
		tmp = Float64(c + Float64(0.0625 * Float64(t * z)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] * -0.25 + c), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.5414268888085725e+44], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1766690827.541296], N[(c + N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a, b, c):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c: real): real =
	LET t_1 = (((a * b) * (-25e-2)) + c) IN
		LET tmp_1 = IF ((a * b) <= (17666908275412960052490234375e-19)) THEN (c + ((625e-4) * (t * z))) ELSE t_1 ENDIF IN
		LET tmp = IF ((a * b) <= (-154142688880857253015249070331368326419185664)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.5414268888085725e44 or 1766690827.541296 < (*.f64 a b)

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]
   2. Step-by-step derivation

   3. Applied rewrites 97.7%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, \mathsf{fma}\left(y, x, c\right)\right) \]

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, c\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 74.0%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(t \cdot z, -0.25, b \cdot a\right), -0.25, c\right) \]

   7. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(a \cdot b, -0.25, c\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 49.1%

      \[\leadsto \mathsf{fma}\left(a \cdot b, -0.25, c\right) \]

   if -1.5414268888085725e44 < (*.f64 a b) < 1766690827.541296

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0

      \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 72.9%

      \[\leadsto c + \mathsf{fma}\left(0.0625, t \cdot z, x \cdot y\right) \]

   5. Taylor expanded in x around 0

      \[\leadsto c + \frac{1}{16} \cdot \left(t \cdot z\right) \]
   6. Step-by-step derivation

   7. Applied rewrites 48.2%

      \[\leadsto c + 0.0625 \cdot \left(t \cdot z\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 8: 62.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} t_1 := -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \cdot b \leq -6.113484582340225 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 2.0022127870946247 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(0.0625 \cdot z, t, c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* -0.25 (* a b))))
  (if (<= (* a b) -6.113484582340225e+147)
    t_1
    (if (<= (* a b) 2.0022127870946247e+68)
      (fma (* 0.0625 z) t c)
      t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -0.25 * (a * b);
	double tmp;
	if ((a * b) <= -6.113484582340225e+147) {
		tmp = t_1;
	} else if ((a * b) <= 2.0022127870946247e+68) {
		tmp = fma((0.0625 * z), t, c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-0.25 * Float64(a * b))
	tmp = 0.0
	if (Float64(a * b) <= -6.113484582340225e+147)
		tmp = t_1;
	elseif (Float64(a * b) <= 2.0022127870946247e+68)
		tmp = fma(Float64(0.0625 * z), t, c);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -6.113484582340225e+147], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 2.0022127870946247e+68], N[(N[(0.0625 * z), $MachinePrecision] * t + c), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a, b, c):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c: real): real =
	LET t_1 = ((-25e-2) * (a * b)) IN
		LET tmp_1 = IF ((a * b) <= (200221278709462465866775332606168549858544853579378552827786519642112)) THEN ((((625e-4) * z) * t) + c) ELSE t_1 ENDIF IN
		LET tmp = IF ((a * b) <= (-6113484582340225114390863045446215144041674693067911482818513430441622931783418051058031799825177560164563247997174162910212413505938552196970840064)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -6.1134845823402251e147 or 2.0022127870946247e68 < (*.f64 a b)

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0

      \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 72.9%

      \[\leadsto c + \mathsf{fma}\left(0.0625, t \cdot z, x \cdot y\right) \]

   6. Applied rewrites 73.4%

      \[\leadsto \mathsf{fma}\left(0.0625 \cdot z, t, \mathsf{fma}\left(y, x, c\right)\right) \]

   7. Taylor expanded in a around inf

      \[\leadsto \frac{-1}{4} \cdot \left(a \cdot b\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 29.0%

      \[\leadsto -0.25 \cdot \left(a \cdot b\right) \]

   if -6.1134845823402251e147 < (*.f64 a b) < 2.0022127870946247e68

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0

      \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 72.9%

      \[\leadsto c + \mathsf{fma}\left(0.0625, t \cdot z, x \cdot y\right) \]

   6. Applied rewrites 73.4%

      \[\leadsto \mathsf{fma}\left(0.0625 \cdot z, t, \mathsf{fma}\left(y, x, c\right)\right) \]

   7. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(0.0625 \cdot z, t, c\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 48.3%

      \[\leadsto \mathsf{fma}\left(0.0625 \cdot z, t, c\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 44.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_1 := -0.25 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;a \cdot b \leq -1.5414268888085725 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \cdot b \leq 1766690827.541296:\\ \;\;\;\;0.0625 \cdot \left(t \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  :pre TRUE
  (let* ((t_1 (* -0.25 (* a b))))
  (if (<= (* a b) -1.5414268888085725e+44)
    t_1
    (if (<= (* a b) 1766690827.541296) (* 0.0625 (* t z)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -0.25 * (a * b);
	double tmp;
	if ((a * b) <= -1.5414268888085725e+44) {
		tmp = t_1;
	} else if ((a * b) <= 1766690827.541296) {
		tmp = 0.0625 * (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-0.25d0) * (a * b)
    if ((a * b) <= (-1.5414268888085725d+44)) then
        tmp = t_1
    else if ((a * b) <= 1766690827.541296d0) then
        tmp = 0.0625d0 * (t * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -0.25 * (a * b);
	double tmp;
	if ((a * b) <= -1.5414268888085725e+44) {
		tmp = t_1;
	} else if ((a * b) <= 1766690827.541296) {
		tmp = 0.0625 * (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = -0.25 * (a * b)
	tmp = 0
	if (a * b) <= -1.5414268888085725e+44:
		tmp = t_1
	elif (a * b) <= 1766690827.541296:
		tmp = 0.0625 * (t * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-0.25 * Float64(a * b))
	tmp = 0.0
	if (Float64(a * b) <= -1.5414268888085725e+44)
		tmp = t_1;
	elseif (Float64(a * b) <= 1766690827.541296)
		tmp = Float64(0.0625 * Float64(t * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = -0.25 * (a * b);
	tmp = 0.0;
	if ((a * b) <= -1.5414268888085725e+44)
		tmp = t_1;
	elseif ((a * b) <= 1766690827.541296)
		tmp = 0.0625 * (t * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a * b), $MachinePrecision], -1.5414268888085725e+44], t$95$1, If[LessEqual[N[(a * b), $MachinePrecision], 1766690827.541296], N[(0.0625 * N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]

ReFlow

f(x, y, z, t, a, b, c):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c: real): real =
	LET t_1 = ((-25e-2) * (a * b)) IN
		LET tmp_1 = IF ((a * b) <= (17666908275412960052490234375e-19)) THEN ((625e-4) * (t * z)) ELSE t_1 ENDIF IN
		LET tmp = IF ((a * b) <= (-154142688880857253015249070331368326419185664)) THEN t_1 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if (*.f64 a b) < -1.5414268888085725e44 or 1766690827.541296 < (*.f64 a b)

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0

      \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 72.9%

      \[\leadsto c + \mathsf{fma}\left(0.0625, t \cdot z, x \cdot y\right) \]

   6. Applied rewrites 73.4%

      \[\leadsto \mathsf{fma}\left(0.0625 \cdot z, t, \mathsf{fma}\left(y, x, c\right)\right) \]

   7. Taylor expanded in a around inf

      \[\leadsto \frac{-1}{4} \cdot \left(a \cdot b\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 29.0%

      \[\leadsto -0.25 \cdot \left(a \cdot b\right) \]

   if -1.5414268888085725e44 < (*.f64 a b) < 1766690827.541296

   1. Initial program 97.7%

      \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

   2. Taylor expanded in a around 0

      \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]
   3. Step-by-step derivation

   4. Applied rewrites 72.9%

      \[\leadsto c + \mathsf{fma}\left(0.0625, t \cdot z, x \cdot y\right) \]

   6. Applied rewrites 73.4%

      \[\leadsto \mathsf{fma}\left(0.0625 \cdot z, t, \mathsf{fma}\left(y, x, c\right)\right) \]

   7. Taylor expanded in a around inf

      \[\leadsto \frac{-1}{4} \cdot \left(a \cdot b\right) \]
   8. Step-by-step derivation

   9. Applied rewrites 29.0%

      \[\leadsto -0.25 \cdot \left(a \cdot b\right) \]

   10. Taylor expanded in z around inf

       \[\leadsto \frac{1}{16} \cdot \left(t \cdot z\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 28.1%

       \[\leadsto 0.0625 \cdot \left(t \cdot z\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 29.0% accurate, 3.6× speedup

Math

\[-0.25 \cdot \left(a \cdot b\right) \]

FPCore

(FPCore (x y z t a b c)
  :precision binary64
  :pre TRUE
  (* -0.25 (* a b)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return -0.25 * (a * b);
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (-0.25d0) * (a * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return -0.25 * (a * b);
}

Python

def code(x, y, z, t, a, b, c):
	return -0.25 * (a * b)

Julia

function code(x, y, z, t, a, b, c)
	return Float64(-0.25 * Float64(a * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = -0.25 * (a * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(-0.25 * N[(a * b), $MachinePrecision]), $MachinePrecision]

ReFlow

f(x, y, z, t, a, b, c):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf],
	t in [-inf, +inf],
	a in [-inf, +inf],
	b in [-inf, +inf],
	c in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z, t, a, b, c: real): real =
	(-25e-2) * (a * b)
END code

Derivation

1. Initial program 97.7%

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c \]

2. Taylor expanded in a around 0

   \[\leadsto c + \left(\frac{1}{16} \cdot \left(t \cdot z\right) + x \cdot y\right) \]
3. Step-by-step derivation

4. Applied rewrites 72.9%

   \[\leadsto c + \mathsf{fma}\left(0.0625, t \cdot z, x \cdot y\right) \]

6. Applied rewrites 73.4%

   \[\leadsto \mathsf{fma}\left(0.0625 \cdot z, t, \mathsf{fma}\left(y, x, c\right)\right) \]

7. Taylor expanded in a around inf

   \[\leadsto \frac{-1}{4} \cdot \left(a \cdot b\right) \]
8. Step-by-step derivation

9. Applied rewrites 29.0%

   \[\leadsto -0.25 \cdot \left(a \cdot b\right) \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))