Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3

Percentage Accurate: 97.1% → 97.1%

Time: 7.0s

Alternatives: 16

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

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

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)
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
    code = x - ((y - z) / (((t - z) + 1.0d0) / a))
end function

Java

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

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))

C

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

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)
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
    code = x - ((y - z) / (((t - z) + 1.0d0) / a))
end function

Java

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

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) + 1.0) / a))

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\frac{\left(t - z\right) - -1}{a}} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (- x (/ (- y z) (/ (- (- t z) -1.0) a))))

C

double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) - -1.0) / a));
}

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)
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
    code = x - ((y - z) / (((t - z) - (-1.0d0)) / a))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x - ((y - z) / (((t - z) - -1.0) / a));
}

Python

def code(x, y, z, t, a):
	return x - ((y - z) / (((t - z) - -1.0) / a))

Julia

function code(x, y, z, t, a)
	return Float64(x - Float64(Float64(y - z) / Float64(Float64(Float64(t - z) - -1.0) / a)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x - ((y - z) / (((t - z) - -1.0) / a));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - N[(N[(y - z), $MachinePrecision] / N[(N[(N[(t - z), $MachinePrecision] - -1.0), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.0%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Add Preprocessing

3. Final simplification 99.0%

   \[\leadsto x - \frac{y - z}{\frac{\left(t - z\right) - -1}{a}} \]
4. Add Preprocessing

Alternative 2: 74.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y - z}{t}, -a, x\right)\\ \mathbf{if}\;t \leq -28000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-237}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 24000000000000:\\ \;\;\;\;x - a \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- y z) t) (- a) x)))
   (if (<= t -28000.0)
     t_1
     (if (<= t -3.4e-237)
       (- x a)
       (if (<= t 24000000000000.0) (- x (* a y)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((y - z) / t), -a, x);
	double tmp;
	if (t <= -28000.0) {
		tmp = t_1;
	} else if (t <= -3.4e-237) {
		tmp = x - a;
	} else if (t <= 24000000000000.0) {
		tmp = x - (a * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(y - z) / t), Float64(-a), x)
	tmp = 0.0
	if (t <= -28000.0)
		tmp = t_1;
	elseif (t <= -3.4e-237)
		tmp = Float64(x - a);
	elseif (t <= 24000000000000.0)
		tmp = Float64(x - Float64(a * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * (-a) + x), $MachinePrecision]}, If[LessEqual[t, -28000.0], t$95$1, If[LessEqual[t, -3.4e-237], N[(x - a), $MachinePrecision], If[LessEqual[t, 24000000000000.0], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -28000 or 2.4e13 < t

   1. Initial program 98.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. associate-*r/ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. mul-1-neg N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-neg.f64 86.3

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

   5. Applied rewrites 86.3%

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

   if -28000 < t < -3.4000000000000002e-237

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 69.7

         \[\leadsto \color{blue}{x - a} \]

   5. Applied rewrites 69.7%

      \[\leadsto \color{blue}{x - a} \]

   if -3.4000000000000002e-237 < t < 2.4e13

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 77.9%

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

Alternative 3: 90.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(1 + t\right) - z\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{+50} \lor \neg \left(y \leq 3.7 \cdot 10^{-9}\right):\\ \;\;\;\;x - \frac{y}{t\_1} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{t\_1}, a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ 1.0 t) z)))
   (if (or (<= y -2.8e+50) (not (<= y 3.7e-9)))
     (- x (* (/ y t_1) a))
     (fma (/ z t_1) a x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (1.0 + t) - z;
	double tmp;
	if ((y <= -2.8e+50) || !(y <= 3.7e-9)) {
		tmp = x - ((y / t_1) * a);
	} else {
		tmp = fma((z / t_1), a, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(1.0 + t) - z)
	tmp = 0.0
	if ((y <= -2.8e+50) || !(y <= 3.7e-9))
		tmp = Float64(x - Float64(Float64(y / t_1) * a));
	else
		tmp = fma(Float64(z / t_1), a, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(1.0 + t), $MachinePrecision] - z), $MachinePrecision]}, If[Or[LessEqual[y, -2.8e+50], N[Not[LessEqual[y, 3.7e-9]], $MachinePrecision]], N[(x - N[(N[(y / t$95$1), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(z / t$95$1), $MachinePrecision] * a + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7999999999999998e50 or 3.7e-9 < y

   1. Initial program 98.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 92.9

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

   5. Applied rewrites 92.9%

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

   if -2.7999999999999998e50 < y < 3.7e-9

   1. Initial program 99.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

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

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z}{\left(1 + t\right) - z}}, a, x\right) \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right) - z}}, a, x\right) \]

      10. lower-+.f64 98.8

          \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right)} - z}, a, x\right) \]

   5. Applied rewrites 98.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+50} \lor \neg \left(y \leq 3.7 \cdot 10^{-9}\right):\\ \;\;\;\;x - \frac{y}{\left(1 + t\right) - z} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -52000 \lor \neg \left(t \leq 2.3 \cdot 10^{+24}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{t}, -a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -52000.0) (not (<= t 2.3e+24)))
   (fma (/ (- y z) t) (- a) x)
   (- x (* (- y z) (/ a (- 1.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -52000.0) || !(t <= 2.3e+24)) {
		tmp = fma(((y - z) / t), -a, x);
	} else {
		tmp = x - ((y - z) * (a / (1.0 - z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -52000.0) || !(t <= 2.3e+24))
		tmp = fma(Float64(Float64(y - z) / t), Float64(-a), x);
	else
		tmp = Float64(x - Float64(Float64(y - z) * Float64(a / Float64(1.0 - z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -52000.0], N[Not[LessEqual[t, 2.3e+24]], $MachinePrecision]], N[(N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision] * (-a) + x), $MachinePrecision], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -52000 or 2.2999999999999999e24 < t

   1. Initial program 98.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

      1. associate-*r/ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. mul-1-neg N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. distribute-rgt-neg-in N/A

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

      8. lower-fma.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower--.f64 N/A

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

      11. lower-neg.f64 86.9

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

   5. Applied rewrites 86.9%

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

   if -52000 < t < 2.2999999999999999e24

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 100.0

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

   5. Applied rewrites 100.0%

      \[\leadsto x - \color{blue}{\left(y - z\right) \cdot \frac{a}{1 - z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -52000 \lor \neg \left(t \leq 2.3 \cdot 10^{+24}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{t}, -a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{a}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+16} \lor \neg \left(z \leq 700000000000\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.75e+16) (not (<= z 700000000000.0)))
   (fma (/ z (- (+ 1.0 t) z)) a x)
   (- x (* (/ y (+ 1.0 t)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.75e+16) || !(z <= 700000000000.0)) {
		tmp = fma((z / ((1.0 + t) - z)), a, x);
	} else {
		tmp = x - ((y / (1.0 + t)) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.75e+16) || !(z <= 700000000000.0))
		tmp = fma(Float64(z / Float64(Float64(1.0 + t) - z)), a, x);
	else
		tmp = Float64(x - Float64(Float64(y / Float64(1.0 + t)) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.75e+16], N[Not[LessEqual[z, 700000000000.0]], $MachinePrecision]], N[(N[(z / N[(N[(1.0 + t), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision], N[(x - N[(N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.75e16 or 7e11 < z

   1. Initial program 98.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

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

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z}{\left(1 + t\right) - z}}, a, x\right) \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right) - z}}, a, x\right) \]

      10. lower-+.f64 86.7

          \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right)} - z}, a, x\right) \]

   5. Applied rewrites 86.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]

   if -2.75e16 < z < 7e11

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

         \[\leadsto x - \color{blue}{a \cdot \frac{y}{1 + t}} \]

      2. *-commutative N/A

         \[\leadsto x - \color{blue}{\frac{y}{1 + t} \cdot a} \]

      3. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y}{1 + t} \cdot a} \]

      4. lower-/.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y}{1 + t}} \cdot a \]

      5. lower-+.f64 93.7

         \[\leadsto x - \frac{y}{\color{blue}{1 + t}} \cdot a \]

   5. Applied rewrites 93.7%

      \[\leadsto x - \color{blue}{\frac{y}{1 + t} \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+16} \lor \neg \left(z \leq 700000000000\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+230}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-5}:\\ \;\;\;\;x - \frac{-y}{z} \cdot a\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+21}:\\ \;\;\;\;x - \left(y - z\right) \cdot \mathsf{fma}\left(a, z, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+230)
   (- x a)
   (if (<= z -4.1e-5)
     (- x (* (/ (- y) z) a))
     (if (<= z 4.6e+21) (- x (* (- y z) (fma a z a))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+230) {
		tmp = x - a;
	} else if (z <= -4.1e-5) {
		tmp = x - ((-y / z) * a);
	} else if (z <= 4.6e+21) {
		tmp = x - ((y - z) * fma(a, z, a));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+230)
		tmp = Float64(x - a);
	elseif (z <= -4.1e-5)
		tmp = Float64(x - Float64(Float64(Float64(-y) / z) * a));
	elseif (z <= 4.6e+21)
		tmp = Float64(x - Float64(Float64(y - z) * fma(a, z, a)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+230], N[(x - a), $MachinePrecision], If[LessEqual[z, -4.1e-5], N[(x - N[(N[((-y) / z), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+21], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a * z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.04999999999999996e230 or 4.6e21 < z

   1. Initial program 97.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 84.6

         \[\leadsto \color{blue}{x - a} \]

   5. Applied rewrites 84.6%

      \[\leadsto \color{blue}{x - a} \]

   if -1.04999999999999996e230 < z < -4.10000000000000005e-5

   1. Initial program 99.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 79.0

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

   5. Applied rewrites 79.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 71.4%

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

   if -4.10000000000000005e-5 < z < 4.6e21

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 73.4

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in z around 0

      \[\leadsto x - \left(y - z\right) \cdot \left(a + \color{blue}{a \cdot z}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 75.1%

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

Alternative 7: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+107}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-5}:\\ \;\;\;\;x - \frac{y}{t} \cdot a\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+21}:\\ \;\;\;\;x - \left(y - z\right) \cdot \mathsf{fma}\left(a, z, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.5e+107)
   (- x a)
   (if (<= z -4.1e-5)
     (- x (* (/ y t) a))
     (if (<= z 4.6e+21) (- x (* (- y z) (fma a z a))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+107) {
		tmp = x - a;
	} else if (z <= -4.1e-5) {
		tmp = x - ((y / t) * a);
	} else if (z <= 4.6e+21) {
		tmp = x - ((y - z) * fma(a, z, a));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.5e+107)
		tmp = Float64(x - a);
	elseif (z <= -4.1e-5)
		tmp = Float64(x - Float64(Float64(y / t) * a));
	elseif (z <= 4.6e+21)
		tmp = Float64(x - Float64(Float64(y - z) * fma(a, z, a)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.5e+107], N[(x - a), $MachinePrecision], If[LessEqual[z, -4.1e-5], N[(x - N[(N[(y / t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+21], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a * z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.4999999999999996e107 or 4.6e21 < z

   1. Initial program 98.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 79.4

         \[\leadsto \color{blue}{x - a} \]

   5. Applied rewrites 79.4%

      \[\leadsto \color{blue}{x - a} \]

   if -7.4999999999999996e107 < z < -4.10000000000000005e-5

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 83.3

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 73.9%

      \[\leadsto x - \frac{y}{t} \cdot a \]

   if -4.10000000000000005e-5 < z < 4.6e21

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 73.4

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in z around 0

      \[\leadsto x - \left(y - z\right) \cdot \left(a + \color{blue}{a \cdot z}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 75.1%

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

Alternative 8: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+106}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-5}:\\ \;\;\;\;x - y \cdot \frac{a}{t}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+21}:\\ \;\;\;\;x - \left(y - z\right) \cdot \mathsf{fma}\left(a, z, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.2e+106)
   (- x a)
   (if (<= z -4.1e-5)
     (- x (* y (/ a t)))
     (if (<= z 4.6e+21) (- x (* (- y z) (fma a z a))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.2e+106) {
		tmp = x - a;
	} else if (z <= -4.1e-5) {
		tmp = x - (y * (a / t));
	} else if (z <= 4.6e+21) {
		tmp = x - ((y - z) * fma(a, z, a));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.2e+106)
		tmp = Float64(x - a);
	elseif (z <= -4.1e-5)
		tmp = Float64(x - Float64(y * Float64(a / t)));
	elseif (z <= 4.6e+21)
		tmp = Float64(x - Float64(Float64(y - z) * fma(a, z, a)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.2e+106], N[(x - a), $MachinePrecision], If[LessEqual[z, -4.1e-5], N[(x - N[(y * N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+21], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a * z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.1999999999999999e106 or 4.6e21 < z

   1. Initial program 98.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 79.4

         \[\leadsto \color{blue}{x - a} \]

   5. Applied rewrites 79.4%

      \[\leadsto \color{blue}{x - a} \]

   if -6.1999999999999999e106 < z < -4.10000000000000005e-5

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

         \[\leadsto x - \color{blue}{a \cdot \frac{y}{1 + t}} \]

      2. *-commutative N/A

         \[\leadsto x - \color{blue}{\frac{y}{1 + t} \cdot a} \]

      3. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y}{1 + t} \cdot a} \]

      4. lower-/.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y}{1 + t}} \cdot a \]

      5. lower-+.f64 80.2

         \[\leadsto x - \frac{y}{\color{blue}{1 + t}} \cdot a \]

   5. Applied rewrites 80.2%

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

   7. Applied rewrites 80.2%

      \[\leadsto x - y \cdot \color{blue}{\frac{a}{t - -1}} \]

   8. Taylor expanded in t around inf

      \[\leadsto x - y \cdot \frac{a}{\color{blue}{t}} \]
   9. Step-by-step derivation

   10. Applied rewrites 73.9%

       \[\leadsto x - y \cdot \frac{a}{\color{blue}{t}} \]

   if -4.10000000000000005e-5 < z < 4.6e21

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 73.4

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in z around 0

      \[\leadsto x - \left(y - z\right) \cdot \left(a + \color{blue}{a \cdot z}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 75.1%

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

Alternative 9: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+106}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-5}:\\ \;\;\;\;x - \frac{a \cdot y}{t}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+21}:\\ \;\;\;\;x - \left(y - z\right) \cdot \mathsf{fma}\left(a, z, a\right)\\ \mathbf{else}:\\ \;\;\;\;x - a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.2e+106)
   (- x a)
   (if (<= z -4.1e-5)
     (- x (/ (* a y) t))
     (if (<= z 4.6e+21) (- x (* (- y z) (fma a z a))) (- x a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.2e+106) {
		tmp = x - a;
	} else if (z <= -4.1e-5) {
		tmp = x - ((a * y) / t);
	} else if (z <= 4.6e+21) {
		tmp = x - ((y - z) * fma(a, z, a));
	} else {
		tmp = x - a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.2e+106)
		tmp = Float64(x - a);
	elseif (z <= -4.1e-5)
		tmp = Float64(x - Float64(Float64(a * y) / t));
	elseif (z <= 4.6e+21)
		tmp = Float64(x - Float64(Float64(y - z) * fma(a, z, a)));
	else
		tmp = Float64(x - a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.2e+106], N[(x - a), $MachinePrecision], If[LessEqual[z, -4.1e-5], N[(x - N[(N[(a * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.6e+21], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a * z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.1999999999999999e106 or 4.6e21 < z

   1. Initial program 98.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 79.4

         \[\leadsto \color{blue}{x - a} \]

   5. Applied rewrites 79.4%

      \[\leadsto \color{blue}{x - a} \]

   if -6.1999999999999999e106 < z < -4.10000000000000005e-5

   1. Initial program 99.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-+.f64 83.3

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

   5. Applied rewrites 83.3%

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

   6. Taylor expanded in t around inf

      \[\leadsto x - \frac{a \cdot y}{\color{blue}{t}} \]
   7. Step-by-step derivation

   8. Applied rewrites 70.6%

      \[\leadsto x - \frac{a \cdot y}{\color{blue}{t}} \]

   if -4.10000000000000005e-5 < z < 4.6e21

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 73.4

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in z around 0

      \[\leadsto x - \left(y - z\right) \cdot \left(a + \color{blue}{a \cdot z}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 75.1%

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

Alternative 10: 82.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+50}:\\ \;\;\;\;x - y \cdot \frac{a}{t - -1}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(z, \frac{a}{\left(t - -1\right) - z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.3e+50)
   (- x (* y (/ a (- t -1.0))))
   (if (<= y 3.7e-9)
     (fma z (/ a (- (- t -1.0) z)) x)
     (- x (* (/ y (+ 1.0 t)) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.3e+50) {
		tmp = x - (y * (a / (t - -1.0)));
	} else if (y <= 3.7e-9) {
		tmp = fma(z, (a / ((t - -1.0) - z)), x);
	} else {
		tmp = x - ((y / (1.0 + t)) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.3e+50)
		tmp = Float64(x - Float64(y * Float64(a / Float64(t - -1.0))));
	elseif (y <= 3.7e-9)
		tmp = fma(z, Float64(a / Float64(Float64(t - -1.0) - z)), x);
	else
		tmp = Float64(x - Float64(Float64(y / Float64(1.0 + t)) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.3e+50], N[(x - N[(y * N[(a / N[(t - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e-9], N[(z * N[(a / N[(N[(t - -1.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], N[(x - N[(N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.3000000000000002e50

   1. Initial program 97.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

         \[\leadsto x - \color{blue}{a \cdot \frac{y}{1 + t}} \]

      2. *-commutative N/A

         \[\leadsto x - \color{blue}{\frac{y}{1 + t} \cdot a} \]

      3. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y}{1 + t} \cdot a} \]

      4. lower-/.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y}{1 + t}} \cdot a \]

      5. lower-+.f64 74.6

         \[\leadsto x - \frac{y}{\color{blue}{1 + t}} \cdot a \]

   5. Applied rewrites 74.6%

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

   7. Applied rewrites 74.7%

      \[\leadsto x - y \cdot \color{blue}{\frac{a}{t - -1}} \]

   if -5.3000000000000002e50 < y < 3.7e-9

   1. Initial program 99.2%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

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

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]

      8. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{z}{\left(1 + t\right) - z}}, a, x\right) \]

      9. lower--.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right) - z}}, a, x\right) \]

      10. lower-+.f64 98.8

          \[\leadsto \mathsf{fma}\left(\frac{z}{\color{blue}{\left(1 + t\right)} - z}, a, x\right) \]

   5. Applied rewrites 98.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 98.1%

      \[\leadsto \mathsf{fma}\left(z, \color{blue}{\frac{a}{\left(t - -1\right) - z}}, x\right) \]

   if 3.7e-9 < y

   1. Initial program 99.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

         \[\leadsto x - \color{blue}{a \cdot \frac{y}{1 + t}} \]

      2. *-commutative N/A

         \[\leadsto x - \color{blue}{\frac{y}{1 + t} \cdot a} \]

      3. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y}{1 + t} \cdot a} \]

      4. lower-/.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y}{1 + t}} \cdot a \]

      5. lower-+.f64 81.8

         \[\leadsto x - \frac{y}{\color{blue}{1 + t}} \cdot a \]

   5. Applied rewrites 81.8%

      \[\leadsto x - \color{blue}{\frac{y}{1 + t} \cdot a} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 84.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+107} \lor \neg \left(z \leq 2.6 \cdot 10^{+35}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.5e+107) (not (<= z 2.6e+35)))
   (- x a)
   (- x (* (/ y (+ 1.0 t)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.5e+107) || !(z <= 2.6e+35)) {
		tmp = x - a;
	} else {
		tmp = x - ((y / (1.0 + t)) * a);
	}
	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)
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) :: tmp
    if ((z <= (-7.5d+107)) .or. (.not. (z <= 2.6d+35))) then
        tmp = x - a
    else
        tmp = x - ((y / (1.0d0 + t)) * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.5e+107) || !(z <= 2.6e+35)) {
		tmp = x - a;
	} else {
		tmp = x - ((y / (1.0 + t)) * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.5e+107) or not (z <= 2.6e+35):
		tmp = x - a
	else:
		tmp = x - ((y / (1.0 + t)) * a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.5e+107) || !(z <= 2.6e+35))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(Float64(y / Float64(1.0 + t)) * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.5e+107) || ~((z <= 2.6e+35)))
		tmp = x - a;
	else
		tmp = x - ((y / (1.0 + t)) * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.5e+107], N[Not[LessEqual[z, 2.6e+35]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.4999999999999996e107 or 2.60000000000000007e35 < z

   1. Initial program 98.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 81.7

         \[\leadsto \color{blue}{x - a} \]

   5. Applied rewrites 81.7%

      \[\leadsto \color{blue}{x - a} \]

   if -7.4999999999999996e107 < z < 2.60000000000000007e35

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

         \[\leadsto x - \color{blue}{a \cdot \frac{y}{1 + t}} \]

      2. *-commutative N/A

         \[\leadsto x - \color{blue}{\frac{y}{1 + t} \cdot a} \]

      3. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y}{1 + t} \cdot a} \]

      4. lower-/.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y}{1 + t}} \cdot a \]

      5. lower-+.f64 88.4

         \[\leadsto x - \frac{y}{\color{blue}{1 + t}} \cdot a \]

   5. Applied rewrites 88.4%

      \[\leadsto x - \color{blue}{\frac{y}{1 + t} \cdot a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+107} \lor \neg \left(z \leq 2.6 \cdot 10^{+35}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+107} \lor \neg \left(z \leq 2.6 \cdot 10^{+35}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a}{t - -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.5e+107) (not (<= z 2.6e+35)))
   (- x a)
   (- x (* y (/ a (- t -1.0))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.5e+107) || !(z <= 2.6e+35)) {
		tmp = x - a;
	} else {
		tmp = x - (y * (a / (t - -1.0)));
	}
	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)
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) :: tmp
    if ((z <= (-7.5d+107)) .or. (.not. (z <= 2.6d+35))) then
        tmp = x - a
    else
        tmp = x - (y * (a / (t - (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.5e+107) || !(z <= 2.6e+35)) {
		tmp = x - a;
	} else {
		tmp = x - (y * (a / (t - -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.5e+107) or not (z <= 2.6e+35):
		tmp = x - a
	else:
		tmp = x - (y * (a / (t - -1.0)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.5e+107) || !(z <= 2.6e+35))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(y * Float64(a / Float64(t - -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -7.5e+107) || ~((z <= 2.6e+35)))
		tmp = x - a;
	else
		tmp = x - (y * (a / (t - -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.5e+107], N[Not[LessEqual[z, 2.6e+35]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(y * N[(a / N[(t - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.4999999999999996e107 or 2.60000000000000007e35 < z

   1. Initial program 98.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 81.7

         \[\leadsto \color{blue}{x - a} \]

   5. Applied rewrites 81.7%

      \[\leadsto \color{blue}{x - a} \]

   if -7.4999999999999996e107 < z < 2.60000000000000007e35

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. associate-/l* N/A

         \[\leadsto x - \color{blue}{a \cdot \frac{y}{1 + t}} \]

      2. *-commutative N/A

         \[\leadsto x - \color{blue}{\frac{y}{1 + t} \cdot a} \]

      3. lower-*.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y}{1 + t} \cdot a} \]

      4. lower-/.f64 N/A

         \[\leadsto x - \color{blue}{\frac{y}{1 + t}} \cdot a \]

      5. lower-+.f64 88.4

         \[\leadsto x - \frac{y}{\color{blue}{1 + t}} \cdot a \]

   5. Applied rewrites 88.4%

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

   7. Applied rewrites 88.3%

      \[\leadsto x - y \cdot \color{blue}{\frac{a}{t - -1}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+107} \lor \neg \left(z \leq 2.6 \cdot 10^{+35}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{a}{t - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 74.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00102 \lor \neg \left(z \leq 4.6 \cdot 10^{+21}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \mathsf{fma}\left(a, z, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -0.00102) (not (<= z 4.6e+21)))
   (- x a)
   (- x (* (- y z) (fma a z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -0.00102) || !(z <= 4.6e+21)) {
		tmp = x - a;
	} else {
		tmp = x - ((y - z) * fma(a, z, a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -0.00102) || !(z <= 4.6e+21))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(Float64(y - z) * fma(a, z, a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -0.00102], N[Not[LessEqual[z, 4.6e+21]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(N[(y - z), $MachinePrecision] * N[(a * z + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.00102 or 4.6e21 < z

   1. Initial program 98.5%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 75.1

         \[\leadsto \color{blue}{x - a} \]

   5. Applied rewrites 75.1%

      \[\leadsto \color{blue}{x - a} \]

   if -0.00102 < z < 4.6e21

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 72.8

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

   5. Applied rewrites 72.8%

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

   6. Taylor expanded in z around 0

      \[\leadsto x - \left(y - z\right) \cdot \left(a + \color{blue}{a \cdot z}\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 74.5%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00102 \lor \neg \left(z \leq 4.6 \cdot 10^{+21}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \mathsf{fma}\left(a, z, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 72.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+84} \lor \neg \left(z \leq 1.65 \cdot 10^{+22}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.4e+84) (not (<= z 1.65e+22))) (- x a) (- x (* a y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.4e+84) || !(z <= 1.65e+22)) {
		tmp = x - a;
	} else {
		tmp = x - (a * y);
	}
	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)
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) :: tmp
    if ((z <= (-2.4d+84)) .or. (.not. (z <= 1.65d+22))) then
        tmp = x - a
    else
        tmp = x - (a * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.4e+84) || !(z <= 1.65e+22)) {
		tmp = x - a;
	} else {
		tmp = x - (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.4e+84) or not (z <= 1.65e+22):
		tmp = x - a
	else:
		tmp = x - (a * y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.4e+84) || !(z <= 1.65e+22))
		tmp = Float64(x - a);
	else
		tmp = Float64(x - Float64(a * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.4e+84) || ~((z <= 1.65e+22)))
		tmp = x - a;
	else
		tmp = x - (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.4e+84], N[Not[LessEqual[z, 1.65e+22]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e84 or 1.6499999999999999e22 < z

   1. Initial program 98.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower--.f64 78.9

         \[\leadsto \color{blue}{x - a} \]

   5. Applied rewrites 78.9%

      \[\leadsto \color{blue}{x - a} \]

   if -2.4e84 < z < 1.6499999999999999e22

   1. Initial program 99.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 70.4

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

   5. Applied rewrites 70.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 69.2%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+84} \lor \neg \left(z \leq 1.65 \cdot 10^{+22}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 59.3% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ x - a \end{array} \]

FPCore

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

C

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

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)
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
    code = x - a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x - a), $MachinePrecision]

Derivation

1. Initial program 99.0%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Add Preprocessing

3. Taylor expanded in z around inf

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

   1. lower--.f64 58.9

      \[\leadsto \color{blue}{x - a} \]

5. Applied rewrites 58.9%

   \[\leadsto \color{blue}{x - a} \]
6. Add Preprocessing

Alternative 16: 16.2% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ -a \end{array} \]

FPCore

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

C

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

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)
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
    code = -a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := (-a)

Derivation

1. Initial program 99.0%

   \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
2. Add Preprocessing

3. Taylor expanded in z around inf

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

   1. lower--.f64 58.9

      \[\leadsto \color{blue}{x - a} \]

5. Applied rewrites 58.9%

   \[\leadsto \color{blue}{x - a} \]

6. Taylor expanded in x around 0

   \[\leadsto -1 \cdot \color{blue}{a} \]
7. Step-by-step derivation

8. Applied rewrites 15.3%

   \[\leadsto -a \]
9. Add Preprocessing

Developer Target 1: 99.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x - \frac{y - z}{\left(t - z\right) + 1} \cdot a \end{array} \]

FPCore

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

C

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

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)
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
    code = x - (((y - z) / ((t - z) + 1.0d0)) * a)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2025015 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.SparkLine:renderSparkLine from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (* (/ (- y z) (+ (- t z) 1)) a)))

  (- x (/ (- y z) (/ (+ (- t z) 1.0) a))))