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

Percentage Accurate: 100.0% → 100.0%

Time: 10.5s

Alternatives: 7

Speedup: 1.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((1.0d0 / 8.0d0) * x) - ((y * z) / 2.0d0)) + t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((1.0d0 / 8.0d0) * x) - ((y * z) / 2.0d0)) + t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (t - (0.5d0 * (z * y))) - ((-0.125d0) * x)
end function

Java

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

Python

def code(x, y, z, t):
	return (t - (0.5 * (z * y))) - (-0.125 * x)

Julia

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

MATLAB

function tmp = code(x, y, z, t)
	tmp = (t - (0.5 * (z * y))) - (-0.125 * x);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(t - N[(0.5 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(-0.125 * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. add-flip N/A

      \[\leadsto \color{blue}{t - \left(\mathsf{neg}\left(\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right)\right)\right)} \]

   4. lift--.f64 N/A

      \[\leadsto t - \left(\mathsf{neg}\left(\color{blue}{\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right)}\right)\right) \]

   5. sub-negate-rev N/A

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

   6. sub-flip N/A

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

   7. associate--r+ N/A

      \[\leadsto \color{blue}{\left(t - \frac{y \cdot z}{2}\right) - \left(\mathsf{neg}\left(\frac{1}{8} \cdot x\right)\right)} \]

   8. sub-flip N/A

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

   9. +-commutative N/A

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

   10. add-flip-rev N/A

       \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right) - \left(\mathsf{neg}\left(t\right)\right)\right)} - \left(\mathsf{neg}\left(\frac{1}{8} \cdot x\right)\right) \]

   11. lower--.f64 N/A

       \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y \cdot z}{2}\right)\right) - \left(\mathsf{neg}\left(t\right)\right)\right) - \left(\mathsf{neg}\left(\frac{1}{8} \cdot x\right)\right)} \]

3. Applied rewrites 100.0%

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

Alternative 2: 86.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_1 := \frac{y \cdot z}{2}\\ t_2 := 0.125 \cdot x - 0.5 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+167}:\\ \;\;\;\;t + 0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ (* y z) 2.0)) (t_2 (- (* 0.125 x) (* 0.5 (* y z)))))
  (if (<= t_1 -5e+65) t_2 (if (<= t_1 1e+167) (+ t (* 0.125 x)) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) / 2.0;
	double t_2 = (0.125 * x) - (0.5 * (y * z));
	double tmp;
	if (t_1 <= -5e+65) {
		tmp = t_2;
	} else if (t_1 <= 1e+167) {
		tmp = t + (0.125 * x);
	} else {
		tmp = t_2;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * z) / 2.0d0
    t_2 = (0.125d0 * x) - (0.5d0 * (y * z))
    if (t_1 <= (-5d+65)) then
        tmp = t_2
    else if (t_1 <= 1d+167) then
        tmp = t + (0.125d0 * x)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) / 2.0;
	double t_2 = (0.125 * x) - (0.5 * (y * z));
	double tmp;
	if (t_1 <= -5e+65) {
		tmp = t_2;
	} else if (t_1 <= 1e+167) {
		tmp = t + (0.125 * x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) / 2.0
	t_2 = (0.125 * x) - (0.5 * (y * z))
	tmp = 0
	if t_1 <= -5e+65:
		tmp = t_2
	elif t_1 <= 1e+167:
		tmp = t + (0.125 * x)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) / 2.0)
	t_2 = Float64(Float64(0.125 * x) - Float64(0.5 * Float64(y * z)))
	tmp = 0.0
	if (t_1 <= -5e+65)
		tmp = t_2;
	elseif (t_1 <= 1e+167)
		tmp = Float64(t + Float64(0.125 * x));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) / 2.0;
	t_2 = (0.125 * x) - (0.5 * (y * z));
	tmp = 0.0;
	if (t_1 <= -5e+65)
		tmp = t_2;
	elseif (t_1 <= 1e+167)
		tmp = t + (0.125 * x);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(0.125 * x), $MachinePrecision] - N[(0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+65], t$95$2, If[LessEqual[t$95$1, 1e+167], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y z) #s(literal 2 binary64)) < -4.9999999999999997e65 or 1e167 < (/.f64 (*.f64 y z) #s(literal 2 binary64))

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. metadata-eval N/A

         \[\leadsto t + \frac{1}{8} \cdot x \]

      2. lower-+.f64 N/A

         \[\leadsto t + \color{blue}{\frac{1}{8} \cdot x} \]

      3. lower-*.f64 N/A

         \[\leadsto t + \frac{1}{8} \cdot \color{blue}{x} \]

      4. metadata-eval 63.7%

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

   4. Applied rewrites 63.7%

      \[\leadsto \color{blue}{t + 0.125 \cdot x} \]

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 33.5%

      \[\leadsto t \]

   8. Taylor expanded in t around 0

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

      1. metadata-eval N/A

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

      2. lower--.f64 N/A

         \[\leadsto \frac{1}{8} \cdot x - \color{blue}{\frac{1}{2} \cdot \left(y \cdot z\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \frac{1}{8} \cdot x - \color{blue}{\frac{1}{2}} \cdot \left(y \cdot z\right) \]

      4. metadata-eval N/A

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

      5. lower-*.f64 N/A

         \[\leadsto \frac{1}{8} \cdot x - \frac{1}{2} \cdot \color{blue}{\left(y \cdot z\right)} \]

      6. lower-*.f64 67.8%

         \[\leadsto 0.125 \cdot x - 0.5 \cdot \left(y \cdot \color{blue}{z}\right) \]

   10. Applied rewrites 67.8%

       \[\leadsto \color{blue}{0.125 \cdot x - 0.5 \cdot \left(y \cdot z\right)} \]

   if -4.9999999999999997e65 < (/.f64 (*.f64 y z) #s(literal 2 binary64)) < 1e167

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. metadata-eval N/A

         \[\leadsto t + \frac{1}{8} \cdot x \]

      2. lower-+.f64 N/A

         \[\leadsto t + \color{blue}{\frac{1}{8} \cdot x} \]

      3. lower-*.f64 N/A

         \[\leadsto t + \frac{1}{8} \cdot \color{blue}{x} \]

      4. metadata-eval 63.7%

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

   4. Applied rewrites 63.7%

      \[\leadsto \color{blue}{t + 0.125 \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 86.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \frac{y \cdot z}{2}\\ t_2 := -0.5 \cdot \left(y \cdot z\right) + t\\ \mathbf{if}\;t\_1 \leq -8.2 \cdot 10^{+108}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+177}:\\ \;\;\;\;t + 0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ (* y z) 2.0)) (t_2 (+ (* -0.5 (* y z)) t)))
  (if (<= t_1 -8.2e+108)
    t_2
    (if (<= t_1 4e+177) (+ t (* 0.125 x)) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) / 2.0;
	double t_2 = (-0.5 * (y * z)) + t;
	double tmp;
	if (t_1 <= -8.2e+108) {
		tmp = t_2;
	} else if (t_1 <= 4e+177) {
		tmp = t + (0.125 * x);
	} else {
		tmp = t_2;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * z) / 2.0d0
    t_2 = ((-0.5d0) * (y * z)) + t
    if (t_1 <= (-8.2d+108)) then
        tmp = t_2
    else if (t_1 <= 4d+177) then
        tmp = t + (0.125d0 * x)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) / 2.0;
	double t_2 = (-0.5 * (y * z)) + t;
	double tmp;
	if (t_1 <= -8.2e+108) {
		tmp = t_2;
	} else if (t_1 <= 4e+177) {
		tmp = t + (0.125 * x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) / 2.0
	t_2 = (-0.5 * (y * z)) + t
	tmp = 0
	if t_1 <= -8.2e+108:
		tmp = t_2
	elif t_1 <= 4e+177:
		tmp = t + (0.125 * x)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) / 2.0)
	t_2 = Float64(Float64(-0.5 * Float64(y * z)) + t)
	tmp = 0.0
	if (t_1 <= -8.2e+108)
		tmp = t_2;
	elseif (t_1 <= 4e+177)
		tmp = Float64(t + Float64(0.125 * x));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) / 2.0;
	t_2 = (-0.5 * (y * z)) + t;
	tmp = 0.0;
	if (t_1 <= -8.2e+108)
		tmp = t_2;
	elseif (t_1 <= 4e+177)
		tmp = t + (0.125 * x);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(-0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[LessEqual[t$95$1, -8.2e+108], t$95$2, If[LessEqual[t$95$1, 4e+177], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y z) #s(literal 2 binary64)) < -8.1999999999999998e108 or 4e177 < (/.f64 (*.f64 y z) #s(literal 2 binary64))

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0

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

      1. lower-*.f64 N/A

         \[\leadsto \frac{-1}{2} \cdot \color{blue}{\left(y \cdot z\right)} + t \]

      2. lower-*.f64 69.4%

         \[\leadsto -0.5 \cdot \left(y \cdot \color{blue}{z}\right) + t \]

   4. Applied rewrites 69.4%

      \[\leadsto \color{blue}{-0.5 \cdot \left(y \cdot z\right)} + t \]

   if -8.1999999999999998e108 < (/.f64 (*.f64 y z) #s(literal 2 binary64)) < 4e177

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. metadata-eval N/A

         \[\leadsto t + \frac{1}{8} \cdot x \]

      2. lower-+.f64 N/A

         \[\leadsto t + \color{blue}{\frac{1}{8} \cdot x} \]

      3. lower-*.f64 N/A

         \[\leadsto t + \frac{1}{8} \cdot \color{blue}{x} \]

      4. metadata-eval 63.7%

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

   4. Applied rewrites 63.7%

      \[\leadsto \color{blue}{t + 0.125 \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 84.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := \frac{y \cdot z}{2}\\ t_2 := -0.5 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+177}:\\ \;\;\;\;t + 0.125 \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (let* ((t_1 (/ (* y z) 2.0)) (t_2 (* -0.5 (* y z))))
  (if (<= t_1 -2e+123)
    t_2
    (if (<= t_1 4e+177) (+ t (* 0.125 x)) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) / 2.0;
	double t_2 = -0.5 * (y * z);
	double tmp;
	if (t_1 <= -2e+123) {
		tmp = t_2;
	} else if (t_1 <= 4e+177) {
		tmp = t + (0.125 * x);
	} else {
		tmp = t_2;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * z) / 2.0d0
    t_2 = (-0.5d0) * (y * z)
    if (t_1 <= (-2d+123)) then
        tmp = t_2
    else if (t_1 <= 4d+177) then
        tmp = t + (0.125d0 * x)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) / 2.0;
	double t_2 = -0.5 * (y * z);
	double tmp;
	if (t_1 <= -2e+123) {
		tmp = t_2;
	} else if (t_1 <= 4e+177) {
		tmp = t + (0.125 * x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) / 2.0
	t_2 = -0.5 * (y * z)
	tmp = 0
	if t_1 <= -2e+123:
		tmp = t_2
	elif t_1 <= 4e+177:
		tmp = t + (0.125 * x)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) / 2.0)
	t_2 = Float64(-0.5 * Float64(y * z))
	tmp = 0.0
	if (t_1 <= -2e+123)
		tmp = t_2;
	elseif (t_1 <= 4e+177)
		tmp = Float64(t + Float64(0.125 * x));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) / 2.0;
	t_2 = -0.5 * (y * z);
	tmp = 0.0;
	if (t_1 <= -2e+123)
		tmp = t_2;
	elseif (t_1 <= 4e+177)
		tmp = t + (0.125 * x);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] / 2.0), $MachinePrecision]}, Block[{t$95$2 = N[(-0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+123], t$95$2, If[LessEqual[t$95$1, 4e+177], N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y z) #s(literal 2 binary64)) < -2e123 or 4e177 < (/.f64 (*.f64 y z) #s(literal 2 binary64))

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. metadata-eval N/A

         \[\leadsto t + \frac{1}{8} \cdot x \]

      2. lower-+.f64 N/A

         \[\leadsto t + \color{blue}{\frac{1}{8} \cdot x} \]

      3. lower-*.f64 N/A

         \[\leadsto t + \frac{1}{8} \cdot \color{blue}{x} \]

      4. metadata-eval 63.7%

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

   4. Applied rewrites 63.7%

      \[\leadsto \color{blue}{t + 0.125 \cdot x} \]

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 33.5%

      \[\leadsto t \]

   8. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

         \[\leadsto \frac{-1}{2} \cdot \color{blue}{\left(y \cdot z\right)} \]

      2. lower-*.f64 37.9%

         \[\leadsto -0.5 \cdot \left(y \cdot \color{blue}{z}\right) \]

   10. Applied rewrites 37.9%

       \[\leadsto \color{blue}{-0.5 \cdot \left(y \cdot z\right)} \]

   if -2e123 < (/.f64 (*.f64 y z) #s(literal 2 binary64)) < 4e177

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. metadata-eval N/A

         \[\leadsto t + \frac{1}{8} \cdot x \]

      2. lower-+.f64 N/A

         \[\leadsto t + \color{blue}{\frac{1}{8} \cdot x} \]

      3. lower-*.f64 N/A

         \[\leadsto t + \frac{1}{8} \cdot \color{blue}{x} \]

      4. metadata-eval 63.7%

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

   4. Applied rewrites 63.7%

      \[\leadsto \color{blue}{t + 0.125 \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 63.7% accurate, 4.3× speedup

Math

\[t + 0.125 \cdot x \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (+ t (* 0.125 x)))

C

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

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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t + (0.125d0 * x)
end function

Java

public static double code(double x, double y, double z, double t) {
	return t + (0.125 * x);
}

Python

def code(x, y, z, t):
	return t + (0.125 * x)

Julia

function code(x, y, z, t)
	return Float64(t + Float64(0.125 * x))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = t + (0.125 * x);
end

Wolfram

code[x_, y_, z_, t_] := N[(t + N[(0.125 * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around 0

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

   1. metadata-eval N/A

      \[\leadsto t + \frac{1}{8} \cdot x \]

   2. lower-+.f64 N/A

      \[\leadsto t + \color{blue}{\frac{1}{8} \cdot x} \]

   3. lower-*.f64 N/A

      \[\leadsto t + \frac{1}{8} \cdot \color{blue}{x} \]

   4. metadata-eval 63.7%

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

4. Applied rewrites 63.7%

   \[\leadsto \color{blue}{t + 0.125 \cdot x} \]
5. Add Preprocessing

Alternative 6: 50.5% accurate, 2.2× speedup

Math

\[\begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+52}:\\ \;\;\;\;0.125 \cdot x\\ \mathbf{elif}\;x \leq 72000000000000:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;0.125 \cdot x\\ \end{array} \]

FPCore

(FPCore (x y z t)
  :precision binary64
  (if (<= x -1.6e+52)
  (* 0.125 x)
  (if (<= x 72000000000000.0) t (* 0.125 x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.6e+52) {
		tmp = 0.125 * x;
	} else if (x <= 72000000000000.0) {
		tmp = t;
	} else {
		tmp = 0.125 * x;
	}
	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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.6d+52)) then
        tmp = 0.125d0 * x
    else if (x <= 72000000000000.0d0) then
        tmp = t
    else
        tmp = 0.125d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.6e+52) {
		tmp = 0.125 * x;
	} else if (x <= 72000000000000.0) {
		tmp = t;
	} else {
		tmp = 0.125 * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.6e+52:
		tmp = 0.125 * x
	elif x <= 72000000000000.0:
		tmp = t
	else:
		tmp = 0.125 * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.6e+52)
		tmp = Float64(0.125 * x);
	elseif (x <= 72000000000000.0)
		tmp = t;
	else
		tmp = Float64(0.125 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.6e+52)
		tmp = 0.125 * x;
	elseif (x <= 72000000000000.0)
		tmp = t;
	else
		tmp = 0.125 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.6e+52], N[(0.125 * x), $MachinePrecision], If[LessEqual[x, 72000000000000.0], t, N[(0.125 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6e52 or 7.2e13 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. metadata-eval N/A

         \[\leadsto t + \frac{1}{8} \cdot x \]

      2. lower-+.f64 N/A

         \[\leadsto t + \color{blue}{\frac{1}{8} \cdot x} \]

      3. lower-*.f64 N/A

         \[\leadsto t + \frac{1}{8} \cdot \color{blue}{x} \]

      4. metadata-eval 63.7%

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

   4. Applied rewrites 63.7%

      \[\leadsto \color{blue}{t + 0.125 \cdot x} \]

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 33.5%

      \[\leadsto t \]

   8. Taylor expanded in x around inf

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

      1. metadata-eval N/A

         \[\leadsto \frac{1}{8} \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{1}{8} \cdot x \]

      3. metadata-eval 32.1%

         \[\leadsto 0.125 \cdot x \]

   10. Applied rewrites 32.1%

       \[\leadsto 0.125 \cdot \color{blue}{x} \]

   if -1.6e52 < x < 7.2e13

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

      1. metadata-eval N/A

         \[\leadsto t + \frac{1}{8} \cdot x \]

      2. lower-+.f64 N/A

         \[\leadsto t + \color{blue}{\frac{1}{8} \cdot x} \]

      3. lower-*.f64 N/A

         \[\leadsto t + \frac{1}{8} \cdot \color{blue}{x} \]

      4. metadata-eval 63.7%

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

   4. Applied rewrites 63.7%

      \[\leadsto \color{blue}{t + 0.125 \cdot x} \]

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 33.5%

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

Alternative 7: 33.5% accurate, 39.0× speedup

Math

\[t \]

FPCore

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

C

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around 0

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

   1. metadata-eval N/A

      \[\leadsto t + \frac{1}{8} \cdot x \]

   2. lower-+.f64 N/A

      \[\leadsto t + \color{blue}{\frac{1}{8} \cdot x} \]

   3. lower-*.f64 N/A

      \[\leadsto t + \frac{1}{8} \cdot \color{blue}{x} \]

   4. metadata-eval 63.7%

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

4. Applied rewrites 63.7%

   \[\leadsto \color{blue}{t + 0.125 \cdot x} \]

5. Taylor expanded in x around 0

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

7. Applied rewrites 33.5%

   \[\leadsto t \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025258 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64
  (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))