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

Percentage Accurate: 97.5% → 98.3%

Time: 4.3s

Alternatives: 11

Speedup: 0.5×

• 33.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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]

Initial Program: 97.5% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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]

Alternative 1: 98.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c)))
   (if (<= t_1 INFINITY) t_1 (* y x))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(x * y) + Float64(Float64(z * t) / 16.0)) - Float64(Float64(a * b) / 4.0)) + c)
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64))) c) < +inf.0

   1. Initial program 100.0%

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

   if +inf.0 < (+.f64 (-.f64 (+.f64 (*.f64 x y) (/.f64 (*.f64 z t) #s(literal 16 binary64))) (/.f64 (*.f64 a b) #s(literal 4 binary64))) c)

   1. Initial program 0.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot y} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{x} \]

      2. lower-*.f64 57.4

         \[\leadsto y \cdot \color{blue}{x} \]

   5. Applied rewrites 57.4%

      \[\leadsto \color{blue}{y \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 94.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(y, x, -0.25 \cdot \left(b \cdot a\right)\right)\\ t_2 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+74} \lor \neg \left(t\_2 \leq 5 \cdot 10^{-15}\right):\\ \;\;\;\;\mathsf{fma}\left(0.0625, t, \frac{t\_1}{z}\right) \cdot z + c\\ \mathbf{else}:\\ \;\;\;\;t\_1 + c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (fma y x (* -0.25 (* b a)))) (t_2 (/ (* z t) 16.0)))
   (if (or (<= t_2 -2e+74) (not (<= t_2 5e-15)))
     (+ (* (fma 0.0625 t (/ t_1 z)) z) c)
     (+ t_1 c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(y, x, (-0.25 * (b * a)));
	double t_2 = (z * t) / 16.0;
	double tmp;
	if ((t_2 <= -2e+74) || !(t_2 <= 5e-15)) {
		tmp = (fma(0.0625, t, (t_1 / z)) * z) + c;
	} else {
		tmp = t_1 + c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = fma(y, x, Float64(-0.25 * Float64(b * a)))
	t_2 = Float64(Float64(z * t) / 16.0)
	tmp = 0.0
	if ((t_2 <= -2e+74) || !(t_2 <= 5e-15))
		tmp = Float64(Float64(fma(0.0625, t, Float64(t_1 / z)) * z) + c);
	else
		tmp = Float64(t_1 + c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(y * x + N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -2e+74], N[Not[LessEqual[t$95$2, 5e-15]], $MachinePrecision]], N[(N[(N[(0.0625 * t + N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision] + c), $MachinePrecision], N[(t$95$1 + c), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -1.9999999999999999e74 or 4.99999999999999999e-15 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 94.1%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(\left(\frac{1}{16} \cdot t + \frac{x \cdot y}{z}\right) - \frac{1}{4} \cdot \frac{a \cdot b}{z}\right)} + c \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(\frac{1}{16} \cdot t + \frac{x \cdot y}{z}\right) - \frac{1}{4} \cdot \frac{a \cdot b}{z}\right) \cdot \color{blue}{z} + c \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(\frac{1}{16} \cdot t + \frac{x \cdot y}{z}\right) - \frac{1}{4} \cdot \frac{a \cdot b}{z}\right) \cdot \color{blue}{z} + c \]

   5. Applied rewrites 95.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0625, t, \frac{\mathsf{fma}\left(y, x, -0.25 \cdot \left(b \cdot a\right)\right)}{z}\right) \cdot z} + c \]

   if -1.9999999999999999e74 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 4.99999999999999999e-15

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x \cdot y - \frac{1}{4} \cdot \left(a \cdot b\right)\right)} + c \]
   4. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right) \cdot \left(a \cdot b\right)}\right) + c \]

      2. *-commutative N/A

         \[\leadsto \left(y \cdot x + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right)} \cdot \left(a \cdot b\right)\right) + c \]

      3. metadata-eval N/A

         \[\leadsto \left(y \cdot x + \frac{-1}{4} \cdot \left(\color{blue}{a} \cdot b\right)\right) + c \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{x}, \frac{-1}{4} \cdot \left(a \cdot b\right)\right) + c \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \frac{-1}{4} \cdot \left(a \cdot b\right)\right) + c \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, x, \frac{-1}{4} \cdot \left(b \cdot a\right)\right) + c \]

      7. lower-*.f64 97.5

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

   5. Applied rewrites 97.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, -0.25 \cdot \left(b \cdot a\right)\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot t}{16} \leq -2 \cdot 10^{+74} \lor \neg \left(\frac{z \cdot t}{16} \leq 5 \cdot 10^{-15}\right):\\ \;\;\;\;\mathsf{fma}\left(0.0625, t, \frac{\mathsf{fma}\left(y, x, -0.25 \cdot \left(b \cdot a\right)\right)}{z}\right) \cdot z + c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, -0.25 \cdot \left(b \cdot a\right)\right) + c\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+74} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+93}\right):\\ \;\;\;\;\mathsf{fma}\left(-0.25 \cdot b, a, \left(t \cdot z\right) \cdot 0.0625\right) + c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, -0.25 \cdot \left(b \cdot a\right)\right) + c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* z t) 16.0)))
   (if (or (<= t_1 -2e+74) (not (<= t_1 5e+93)))
     (+ (fma (* -0.25 b) a (* (* t z) 0.0625)) c)
     (+ (fma y x (* -0.25 (* b a))) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * t) / 16.0;
	double tmp;
	if ((t_1 <= -2e+74) || !(t_1 <= 5e+93)) {
		tmp = fma((-0.25 * b), a, ((t * z) * 0.0625)) + c;
	} else {
		tmp = fma(y, x, (-0.25 * (b * a))) + c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(z * t) / 16.0)
	tmp = 0.0
	if ((t_1 <= -2e+74) || !(t_1 <= 5e+93))
		tmp = Float64(fma(Float64(-0.25 * b), a, Float64(Float64(t * z) * 0.0625)) + c);
	else
		tmp = Float64(fma(y, x, Float64(-0.25 * Float64(b * a))) + c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+74], N[Not[LessEqual[t$95$1, 5e+93]], $MachinePrecision]], N[(N[(N[(-0.25 * b), $MachinePrecision] * a + N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision], N[(N[(y * x + N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -1.9999999999999999e74 or 5.0000000000000001e93 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 92.5%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) - \frac{1}{4} \cdot \left(a \cdot b\right)\right)} + c \]
   4. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right) \cdot \left(a \cdot b\right)}\right) + c \]

      2. associate-*r* N/A

         \[\leadsto \left(\left(\frac{1}{16} \cdot t\right) \cdot z + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right)} \cdot \left(a \cdot b\right)\right) + c \]

      3. metadata-eval N/A

         \[\leadsto \left(\left(\frac{1}{16} \cdot t\right) \cdot z + \frac{-1}{4} \cdot \left(\color{blue}{a} \cdot b\right)\right) + c \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{16} \cdot t, \color{blue}{z}, \frac{-1}{4} \cdot \left(a \cdot b\right)\right) + c \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{16} \cdot t, z, \frac{-1}{4} \cdot \left(a \cdot b\right)\right) + c \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{16} \cdot t, z, \frac{-1}{4} \cdot \left(a \cdot b\right)\right) + c \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{16} \cdot t, z, \frac{-1}{4} \cdot \left(b \cdot a\right)\right) + c \]

      8. lower-*.f64 87.8

         \[\leadsto \mathsf{fma}\left(0.0625 \cdot t, z, -0.25 \cdot \left(b \cdot a\right)\right) + c \]

   5. Applied rewrites 87.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0625 \cdot t, z, -0.25 \cdot \left(b \cdot a\right)\right)} + c \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{16} \cdot t, z, \frac{-1}{4} \cdot \left(b \cdot a\right)\right) + c \]

      2. lift-fma.f64 N/A

         \[\leadsto \left(\left(\frac{1}{16} \cdot t\right) \cdot z + \color{blue}{\frac{-1}{4} \cdot \left(b \cdot a\right)}\right) + c \]

      3. associate-*r* N/A

         \[\leadsto \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{\frac{-1}{4}} \cdot \left(b \cdot a\right)\right) + c \]

      4. +-commutative N/A

         \[\leadsto \left(\frac{-1}{4} \cdot \left(b \cdot a\right) + \color{blue}{\frac{1}{16} \cdot \left(t \cdot z\right)}\right) + c \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\frac{-1}{4} \cdot \left(b \cdot a\right) + \frac{1}{16} \cdot \left(t \cdot z\right)\right) + c \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\frac{-1}{4} \cdot \left(b \cdot a\right) + \color{blue}{\frac{1}{16}} \cdot \left(t \cdot z\right)\right) + c \]

      7. associate-*r* N/A

         \[\leadsto \left(\left(\frac{-1}{4} \cdot b\right) \cdot a + \color{blue}{\frac{1}{16}} \cdot \left(t \cdot z\right)\right) + c \]

      8. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{4} \cdot b, \color{blue}{a}, \frac{1}{16} \cdot \left(t \cdot z\right)\right) + c \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{4} \cdot b, a, \frac{1}{16} \cdot \left(t \cdot z\right)\right) + c \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{4} \cdot b, a, \left(t \cdot z\right) \cdot \frac{1}{16}\right) + c \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{4} \cdot b, a, \left(t \cdot z\right) \cdot \frac{1}{16}\right) + c \]

      12. lower-*.f64 87.8

          \[\leadsto \mathsf{fma}\left(-0.25 \cdot b, a, \left(t \cdot z\right) \cdot 0.0625\right) + c \]

   7. Applied rewrites 87.8%

      \[\leadsto \mathsf{fma}\left(-0.25 \cdot b, \color{blue}{a}, \left(t \cdot z\right) \cdot 0.0625\right) + c \]

   if -1.9999999999999999e74 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 5.0000000000000001e93

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x \cdot y - \frac{1}{4} \cdot \left(a \cdot b\right)\right)} + c \]
   4. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right) \cdot \left(a \cdot b\right)}\right) + c \]

      2. *-commutative N/A

         \[\leadsto \left(y \cdot x + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right)} \cdot \left(a \cdot b\right)\right) + c \]

      3. metadata-eval N/A

         \[\leadsto \left(y \cdot x + \frac{-1}{4} \cdot \left(\color{blue}{a} \cdot b\right)\right) + c \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{x}, \frac{-1}{4} \cdot \left(a \cdot b\right)\right) + c \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \frac{-1}{4} \cdot \left(a \cdot b\right)\right) + c \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, x, \frac{-1}{4} \cdot \left(b \cdot a\right)\right) + c \]

      7. lower-*.f64 94.7

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

   5. Applied rewrites 94.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, -0.25 \cdot \left(b \cdot a\right)\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot t}{16} \leq -2 \cdot 10^{+74} \lor \neg \left(\frac{z \cdot t}{16} \leq 5 \cdot 10^{+93}\right):\\ \;\;\;\;\mathsf{fma}\left(-0.25 \cdot b, a, \left(t \cdot z\right) \cdot 0.0625\right) + c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, -0.25 \cdot \left(b \cdot a\right)\right) + c\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -0.25 \cdot \left(b \cdot a\right)\\ t_2 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+74}:\\ \;\;\;\;\mathsf{fma}\left(0.0625 \cdot t, z, t\_1\right) + c\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+93}:\\ \;\;\;\;\mathsf{fma}\left(y, x, t\_1\right) + c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.25 \cdot b, a, \left(t \cdot z\right) \cdot 0.0625\right) + c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* -0.25 (* b a))) (t_2 (/ (* z t) 16.0)))
   (if (<= t_2 -2e+74)
     (+ (fma (* 0.0625 t) z t_1) c)
     (if (<= t_2 5e+93)
       (+ (fma y x t_1) c)
       (+ (fma (* -0.25 b) a (* (* t z) 0.0625)) c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = -0.25 * (b * a);
	double t_2 = (z * t) / 16.0;
	double tmp;
	if (t_2 <= -2e+74) {
		tmp = fma((0.0625 * t), z, t_1) + c;
	} else if (t_2 <= 5e+93) {
		tmp = fma(y, x, t_1) + c;
	} else {
		tmp = fma((-0.25 * b), a, ((t * z) * 0.0625)) + c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(-0.25 * Float64(b * a))
	t_2 = Float64(Float64(z * t) / 16.0)
	tmp = 0.0
	if (t_2 <= -2e+74)
		tmp = Float64(fma(Float64(0.0625 * t), z, t_1) + c);
	elseif (t_2 <= 5e+93)
		tmp = Float64(fma(y, x, t_1) + c);
	else
		tmp = Float64(fma(Float64(-0.25 * b), a, Float64(Float64(t * z) * 0.0625)) + c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+74], N[(N[(N[(0.0625 * t), $MachinePrecision] * z + t$95$1), $MachinePrecision] + c), $MachinePrecision], If[LessEqual[t$95$2, 5e+93], N[(N[(y * x + t$95$1), $MachinePrecision] + c), $MachinePrecision], N[(N[(N[(-0.25 * b), $MachinePrecision] * a + N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -1.9999999999999999e74

   1. Initial program 95.1%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) - \frac{1}{4} \cdot \left(a \cdot b\right)\right)} + c \]
   4. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right) \cdot \left(a \cdot b\right)}\right) + c \]

      2. associate-*r* N/A

         \[\leadsto \left(\left(\frac{1}{16} \cdot t\right) \cdot z + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right)} \cdot \left(a \cdot b\right)\right) + c \]

      3. metadata-eval N/A

         \[\leadsto \left(\left(\frac{1}{16} \cdot t\right) \cdot z + \frac{-1}{4} \cdot \left(\color{blue}{a} \cdot b\right)\right) + c \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{16} \cdot t, \color{blue}{z}, \frac{-1}{4} \cdot \left(a \cdot b\right)\right) + c \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{16} \cdot t, z, \frac{-1}{4} \cdot \left(a \cdot b\right)\right) + c \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{16} \cdot t, z, \frac{-1}{4} \cdot \left(a \cdot b\right)\right) + c \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{16} \cdot t, z, \frac{-1}{4} \cdot \left(b \cdot a\right)\right) + c \]

      8. lower-*.f64 85.9

         \[\leadsto \mathsf{fma}\left(0.0625 \cdot t, z, -0.25 \cdot \left(b \cdot a\right)\right) + c \]

   5. Applied rewrites 85.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0625 \cdot t, z, -0.25 \cdot \left(b \cdot a\right)\right)} + c \]

   if -1.9999999999999999e74 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 5.0000000000000001e93

   1. Initial program 99.4%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x \cdot y - \frac{1}{4} \cdot \left(a \cdot b\right)\right)} + c \]
   4. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right) \cdot \left(a \cdot b\right)}\right) + c \]

      2. *-commutative N/A

         \[\leadsto \left(y \cdot x + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right)} \cdot \left(a \cdot b\right)\right) + c \]

      3. metadata-eval N/A

         \[\leadsto \left(y \cdot x + \frac{-1}{4} \cdot \left(\color{blue}{a} \cdot b\right)\right) + c \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{x}, \frac{-1}{4} \cdot \left(a \cdot b\right)\right) + c \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \frac{-1}{4} \cdot \left(a \cdot b\right)\right) + c \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, x, \frac{-1}{4} \cdot \left(b \cdot a\right)\right) + c \]

      7. lower-*.f64 94.7

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

   5. Applied rewrites 94.7%

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

   if 5.0000000000000001e93 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 89.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(\frac{1}{16} \cdot \left(t \cdot z\right) - \frac{1}{4} \cdot \left(a \cdot b\right)\right)} + c \]
   4. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right) \cdot \left(a \cdot b\right)}\right) + c \]

      2. associate-*r* N/A

         \[\leadsto \left(\left(\frac{1}{16} \cdot t\right) \cdot z + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right)} \cdot \left(a \cdot b\right)\right) + c \]

      3. metadata-eval N/A

         \[\leadsto \left(\left(\frac{1}{16} \cdot t\right) \cdot z + \frac{-1}{4} \cdot \left(\color{blue}{a} \cdot b\right)\right) + c \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{16} \cdot t, \color{blue}{z}, \frac{-1}{4} \cdot \left(a \cdot b\right)\right) + c \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{16} \cdot t, z, \frac{-1}{4} \cdot \left(a \cdot b\right)\right) + c \]

      6. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{16} \cdot t, z, \frac{-1}{4} \cdot \left(a \cdot b\right)\right) + c \]

      7. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{16} \cdot t, z, \frac{-1}{4} \cdot \left(b \cdot a\right)\right) + c \]

      8. lower-*.f64 89.7

         \[\leadsto \mathsf{fma}\left(0.0625 \cdot t, z, -0.25 \cdot \left(b \cdot a\right)\right) + c \]

   5. Applied rewrites 89.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.0625 \cdot t, z, -0.25 \cdot \left(b \cdot a\right)\right)} + c \]
   6. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{1}{16} \cdot t, z, \frac{-1}{4} \cdot \left(b \cdot a\right)\right) + c \]

      2. lift-fma.f64 N/A

         \[\leadsto \left(\left(\frac{1}{16} \cdot t\right) \cdot z + \color{blue}{\frac{-1}{4} \cdot \left(b \cdot a\right)}\right) + c \]

      3. associate-*r* N/A

         \[\leadsto \left(\frac{1}{16} \cdot \left(t \cdot z\right) + \color{blue}{\frac{-1}{4}} \cdot \left(b \cdot a\right)\right) + c \]

      4. +-commutative N/A

         \[\leadsto \left(\frac{-1}{4} \cdot \left(b \cdot a\right) + \color{blue}{\frac{1}{16} \cdot \left(t \cdot z\right)}\right) + c \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\frac{-1}{4} \cdot \left(b \cdot a\right) + \frac{1}{16} \cdot \left(t \cdot z\right)\right) + c \]

      6. lift-*.f64 N/A

         \[\leadsto \left(\frac{-1}{4} \cdot \left(b \cdot a\right) + \color{blue}{\frac{1}{16}} \cdot \left(t \cdot z\right)\right) + c \]

      7. associate-*r* N/A

         \[\leadsto \left(\left(\frac{-1}{4} \cdot b\right) \cdot a + \color{blue}{\frac{1}{16}} \cdot \left(t \cdot z\right)\right) + c \]

      8. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{4} \cdot b, \color{blue}{a}, \frac{1}{16} \cdot \left(t \cdot z\right)\right) + c \]

      9. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{4} \cdot b, a, \frac{1}{16} \cdot \left(t \cdot z\right)\right) + c \]

      10. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{4} \cdot b, a, \left(t \cdot z\right) \cdot \frac{1}{16}\right) + c \]

      11. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(\frac{-1}{4} \cdot b, a, \left(t \cdot z\right) \cdot \frac{1}{16}\right) + c \]

      12. lower-*.f64 92.3

          \[\leadsto \mathsf{fma}\left(-0.25 \cdot b, a, \left(t \cdot z\right) \cdot 0.0625\right) + c \]

   7. Applied rewrites 92.3%

      \[\leadsto \mathsf{fma}\left(-0.25 \cdot b, \color{blue}{a}, \left(t \cdot z\right) \cdot 0.0625\right) + c \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 86.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+225} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+93}\right):\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625 + c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, -0.25 \cdot \left(b \cdot a\right)\right) + c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* z t) 16.0)))
   (if (or (<= t_1 -5e+225) (not (<= t_1 5e+93)))
     (+ (* (* t z) 0.0625) c)
     (+ (fma y x (* -0.25 (* b a))) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * t) / 16.0;
	double tmp;
	if ((t_1 <= -5e+225) || !(t_1 <= 5e+93)) {
		tmp = ((t * z) * 0.0625) + c;
	} else {
		tmp = fma(y, x, (-0.25 * (b * a))) + c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(z * t) / 16.0)
	tmp = 0.0
	if ((t_1 <= -5e+225) || !(t_1 <= 5e+93))
		tmp = Float64(Float64(Float64(t * z) * 0.0625) + c);
	else
		tmp = Float64(fma(y, x, Float64(-0.25 * Float64(b * a))) + c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+225], N[Not[LessEqual[t$95$1, 5e+93]], $MachinePrecision]], N[(N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision] + c), $MachinePrecision], N[(N[(y * x + N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -4.99999999999999981e225 or 5.0000000000000001e93 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 90.3%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

         \[\leadsto \left(t \cdot z\right) \cdot \color{blue}{\frac{1}{16}} + c \]

      2. lower-*.f64 N/A

         \[\leadsto \left(t \cdot z\right) \cdot \color{blue}{\frac{1}{16}} + c \]

      3. lower-*.f64 87.4

         \[\leadsto \left(t \cdot z\right) \cdot 0.0625 + c \]

   5. Applied rewrites 87.4%

      \[\leadsto \color{blue}{\left(t \cdot z\right) \cdot 0.0625} + c \]

   if -4.99999999999999981e225 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 5.0000000000000001e93

   1. Initial program 99.5%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\left(x \cdot y - \frac{1}{4} \cdot \left(a \cdot b\right)\right)} + c \]
   4. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

         \[\leadsto \left(x \cdot y + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right) \cdot \left(a \cdot b\right)}\right) + c \]

      2. *-commutative N/A

         \[\leadsto \left(y \cdot x + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{4}\right)\right)} \cdot \left(a \cdot b\right)\right) + c \]

      3. metadata-eval N/A

         \[\leadsto \left(y \cdot x + \frac{-1}{4} \cdot \left(\color{blue}{a} \cdot b\right)\right) + c \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{x}, \frac{-1}{4} \cdot \left(a \cdot b\right)\right) + c \]

      5. lower-*.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \frac{-1}{4} \cdot \left(a \cdot b\right)\right) + c \]

      6. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(y, x, \frac{-1}{4} \cdot \left(b \cdot a\right)\right) + c \]

      7. lower-*.f64 91.3

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

   5. Applied rewrites 91.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, -0.25 \cdot \left(b \cdot a\right)\right)} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot t}{16} \leq -5 \cdot 10^{+225} \lor \neg \left(\frac{z \cdot t}{16} \leq 5 \cdot 10^{+93}\right):\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625 + c\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, -0.25 \cdot \left(b \cdot a\right)\right) + c\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot t}{16}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+74} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+93}\right):\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625 + c\\ \mathbf{else}:\\ \;\;\;\;y \cdot x + c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* z t) 16.0)))
   (if (or (<= t_1 -2e+74) (not (<= t_1 5e+93)))
     (+ (* (* t z) 0.0625) c)
     (+ (* y x) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (z * t) / 16.0;
	double tmp;
	if ((t_1 <= -2e+74) || !(t_1 <= 5e+93)) {
		tmp = ((t * z) * 0.0625) + c;
	} else {
		tmp = (y * x) + c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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 = (z * t) / 16.0d0
    if ((t_1 <= (-2d+74)) .or. (.not. (t_1 <= 5d+93))) then
        tmp = ((t * z) * 0.0625d0) + c
    else
        tmp = (y * x) + c
    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 = (z * t) / 16.0;
	double tmp;
	if ((t_1 <= -2e+74) || !(t_1 <= 5e+93)) {
		tmp = ((t * z) * 0.0625) + c;
	} else {
		tmp = (y * x) + c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (z * t) / 16.0
	tmp = 0
	if (t_1 <= -2e+74) or not (t_1 <= 5e+93):
		tmp = ((t * z) * 0.0625) + c
	else:
		tmp = (y * x) + c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(z * t) / 16.0)
	tmp = 0.0
	if ((t_1 <= -2e+74) || !(t_1 <= 5e+93))
		tmp = Float64(Float64(Float64(t * z) * 0.0625) + c);
	else
		tmp = Float64(Float64(y * x) + c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (z * t) / 16.0;
	tmp = 0.0;
	if ((t_1 <= -2e+74) || ~((t_1 <= 5e+93)))
		tmp = ((t * z) * 0.0625) + c;
	else
		tmp = (y * x) + c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] / 16.0), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+74], N[Not[LessEqual[t$95$1, 5e+93]], $MachinePrecision]], N[(N[(N[(t * z), $MachinePrecision] * 0.0625), $MachinePrecision] + c), $MachinePrecision], N[(N[(y * x), $MachinePrecision] + c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 z t) #s(literal 16 binary64)) < -1.9999999999999999e74 or 5.0000000000000001e93 < (/.f64 (*.f64 z t) #s(literal 16 binary64))

   1. Initial program 92.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

         \[\leadsto \left(t \cdot z\right) \cdot \color{blue}{\frac{1}{16}} + c \]

      2. lower-*.f64 N/A

         \[\leadsto \left(t \cdot z\right) \cdot \color{blue}{\frac{1}{16}} + c \]

      3. lower-*.f64 78.9

         \[\leadsto \left(t \cdot z\right) \cdot 0.0625 + c \]

   5. Applied rewrites 78.9%

      \[\leadsto \color{blue}{\left(t \cdot z\right) \cdot 0.0625} + c \]

   if -1.9999999999999999e74 < (/.f64 (*.f64 z t) #s(literal 16 binary64)) < 5.0000000000000001e93

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot y} + c \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{x} + c \]

      2. lower-*.f64 65.3

         \[\leadsto y \cdot \color{blue}{x} + c \]

   5. Applied rewrites 65.3%

      \[\leadsto \color{blue}{y \cdot x} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot t}{16} \leq -2 \cdot 10^{+74} \lor \neg \left(\frac{z \cdot t}{16} \leq 5 \cdot 10^{+93}\right):\\ \;\;\;\;\left(t \cdot z\right) \cdot 0.0625 + c\\ \mathbf{else}:\\ \;\;\;\;y \cdot x + c\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+192} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+95}\right):\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right) + c\\ \mathbf{else}:\\ \;\;\;\;y \cdot x + c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) 4.0)))
   (if (or (<= t_1 -5e+192) (not (<= t_1 5e+95)))
     (+ (* -0.25 (* b a)) c)
     (+ (* y x) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double tmp;
	if ((t_1 <= -5e+192) || !(t_1 <= 5e+95)) {
		tmp = (-0.25 * (b * a)) + c;
	} else {
		tmp = (y * x) + c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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 = (a * b) / 4.0d0
    if ((t_1 <= (-5d+192)) .or. (.not. (t_1 <= 5d+95))) then
        tmp = ((-0.25d0) * (b * a)) + c
    else
        tmp = (y * x) + c
    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 = (a * b) / 4.0;
	double tmp;
	if ((t_1 <= -5e+192) || !(t_1 <= 5e+95)) {
		tmp = (-0.25 * (b * a)) + c;
	} else {
		tmp = (y * x) + c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) / 4.0
	tmp = 0
	if (t_1 <= -5e+192) or not (t_1 <= 5e+95):
		tmp = (-0.25 * (b * a)) + c
	else:
		tmp = (y * x) + c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / 4.0)
	tmp = 0.0
	if ((t_1 <= -5e+192) || !(t_1 <= 5e+95))
		tmp = Float64(Float64(-0.25 * Float64(b * a)) + c);
	else
		tmp = Float64(Float64(y * x) + c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) / 4.0;
	tmp = 0.0;
	if ((t_1 <= -5e+192) || ~((t_1 <= 5e+95)))
		tmp = (-0.25 * (b * a)) + c;
	else
		tmp = (y * x) + c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+192], N[Not[LessEqual[t$95$1, 5e+95]], $MachinePrecision]], N[(N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision] + c), $MachinePrecision], N[(N[(y * x), $MachinePrecision] + c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -5.00000000000000033e192 or 5.00000000000000025e95 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 93.8%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

         \[\leadsto \frac{-1}{4} \cdot \color{blue}{\left(a \cdot b\right)} + c \]

      2. *-commutative N/A

         \[\leadsto \frac{-1}{4} \cdot \left(b \cdot \color{blue}{a}\right) + c \]

      3. lower-*.f64 88.0

         \[\leadsto -0.25 \cdot \left(b \cdot \color{blue}{a}\right) + c \]

   5. Applied rewrites 88.0%

      \[\leadsto \color{blue}{-0.25 \cdot \left(b \cdot a\right)} + c \]

   if -5.00000000000000033e192 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 5.00000000000000025e95

   1. Initial program 98.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot y} + c \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{x} + c \]

      2. lower-*.f64 62.4

         \[\leadsto y \cdot \color{blue}{x} + c \]

   5. Applied rewrites 62.4%

      \[\leadsto \color{blue}{y \cdot x} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a \cdot b}{4} \leq -5 \cdot 10^{+192} \lor \neg \left(\frac{a \cdot b}{4} \leq 5 \cdot 10^{+95}\right):\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right) + c\\ \mathbf{else}:\\ \;\;\;\;y \cdot x + c\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a \cdot b}{4}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+192} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+179}\right):\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x + c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (* a b) 4.0)))
   (if (or (<= t_1 -5e+192) (not (<= t_1 5e+179)))
     (* -0.25 (* b a))
     (+ (* y x) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (a * b) / 4.0;
	double tmp;
	if ((t_1 <= -5e+192) || !(t_1 <= 5e+179)) {
		tmp = -0.25 * (b * a);
	} else {
		tmp = (y * x) + c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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 = (a * b) / 4.0d0
    if ((t_1 <= (-5d+192)) .or. (.not. (t_1 <= 5d+179))) then
        tmp = (-0.25d0) * (b * a)
    else
        tmp = (y * x) + c
    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 = (a * b) / 4.0;
	double tmp;
	if ((t_1 <= -5e+192) || !(t_1 <= 5e+179)) {
		tmp = -0.25 * (b * a);
	} else {
		tmp = (y * x) + c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (a * b) / 4.0
	tmp = 0
	if (t_1 <= -5e+192) or not (t_1 <= 5e+179):
		tmp = -0.25 * (b * a)
	else:
		tmp = (y * x) + c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(a * b) / 4.0)
	tmp = 0.0
	if ((t_1 <= -5e+192) || !(t_1 <= 5e+179))
		tmp = Float64(-0.25 * Float64(b * a));
	else
		tmp = Float64(Float64(y * x) + c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (a * b) / 4.0;
	tmp = 0.0;
	if ((t_1 <= -5e+192) || ~((t_1 <= 5e+179)))
		tmp = -0.25 * (b * a);
	else
		tmp = (y * x) + c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(a * b), $MachinePrecision] / 4.0), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+192], N[Not[LessEqual[t$95$1, 5e+179]], $MachinePrecision]], N[(-0.25 * N[(b * a), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] + c), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 a b) #s(literal 4 binary64)) < -5.00000000000000033e192 or 5e179 < (/.f64 (*.f64 a b) #s(literal 4 binary64))

   1. Initial program 92.7%

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

   3. Taylor expanded in a around inf

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

      1. lower-*.f64 N/A

         \[\leadsto \frac{-1}{4} \cdot \color{blue}{\left(a \cdot b\right)} \]

      2. *-commutative N/A

         \[\leadsto \frac{-1}{4} \cdot \left(b \cdot \color{blue}{a}\right) \]

      3. lower-*.f64 86.0

         \[\leadsto -0.25 \cdot \left(b \cdot \color{blue}{a}\right) \]

   5. Applied rewrites 86.0%

      \[\leadsto \color{blue}{-0.25 \cdot \left(b \cdot a\right)} \]

   if -5.00000000000000033e192 < (/.f64 (*.f64 a b) #s(literal 4 binary64)) < 5e179

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot y} + c \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{x} + c \]

      2. lower-*.f64 62.3

         \[\leadsto y \cdot \color{blue}{x} + c \]

   5. Applied rewrites 62.3%

      \[\leadsto \color{blue}{y \cdot x} + c \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a \cdot b}{4} \leq -5 \cdot 10^{+192} \lor \neg \left(\frac{a \cdot b}{4} \leq 5 \cdot 10^{+179}\right):\\ \;\;\;\;-0.25 \cdot \left(b \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x + c\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+43} \lor \neg \left(x \cdot y \leq 10000\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= (* x y) -2e+43) (not (<= (* x y) 10000.0))) (* 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) <= -2e+43) || !((x * y) <= 10000.0)) {
		tmp = y * x;
	} else {
		tmp = c;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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) :: tmp
    if (((x * y) <= (-2d+43)) .or. (.not. ((x * y) <= 10000.0d0))) then
        tmp = y * x
    else
        tmp = c
    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 tmp;
	if (((x * y) <= -2e+43) || !((x * y) <= 10000.0)) {
		tmp = y * x;
	} else {
		tmp = c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if ((x * y) <= -2e+43) or not ((x * y) <= 10000.0):
		tmp = y * x
	else:
		tmp = c
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((Float64(x * y) <= -2e+43) || !(Float64(x * y) <= 10000.0))
		tmp = Float64(y * x);
	else
		tmp = c;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (((x * y) <= -2e+43) || ~(((x * y) <= 10000.0)))
		tmp = y * x;
	else
		tmp = c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[N[(x * y), $MachinePrecision], -2e+43], N[Not[LessEqual[N[(x * y), $MachinePrecision], 10000.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], c]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.00000000000000003e43 or 1e4 < (*.f64 x y)

   1. Initial program 95.1%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot y} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{x} \]

      2. lower-*.f64 59.7

         \[\leadsto y \cdot \color{blue}{x} \]

   5. Applied rewrites 59.7%

      \[\leadsto \color{blue}{y \cdot x} \]

   if -2.00000000000000003e43 < (*.f64 x y) < 1e4

   1. Initial program 99.2%

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

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c} \]
   4. Step-by-step derivation

   5. Applied rewrites 34.5%

      \[\leadsto \color{blue}{c} \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+43} \lor \neg \left(x \cdot y \leq 10000\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;c\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.0% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ y \cdot x + c \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (+ (* y x) c))

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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 = (y * x) + c
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(y * x), $MachinePrecision] + c), $MachinePrecision]

Derivation

1. Initial program 97.3%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x \cdot y} + c \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto y \cdot \color{blue}{x} + c \]

   2. lower-*.f64 52.1

      \[\leadsto y \cdot \color{blue}{x} + c \]

5. Applied rewrites 52.1%

   \[\leadsto \color{blue}{y \cdot x} + c \]
6. Add Preprocessing

Alternative 11: 21.8% accurate, 47.0× speedup

Math

\[\begin{array}{l} \\ c \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 c)

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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 = c
end function

Java

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

Python

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

Julia

function code(x, y, z, t, a, b, c)
	return c
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := c

Derivation

1. Initial program 97.3%

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

3. Taylor expanded in c around inf

   \[\leadsto \color{blue}{c} \]
4. Step-by-step derivation

5. Applied rewrites 22.4%

   \[\leadsto \color{blue}{c} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2025035 
(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))