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

Percentage Accurate: 96.8% → 96.8%

Time: 8.6s

Alternatives: 13

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: 96.8% 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: 96.8% 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 96.9%

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

Alternative 2: 74.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{z - y}{t}, a, x\right)\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.35 \cdot 10^{-95}:\\ \;\;\;\;x - a\\ \mathbf{elif}\;t \leq 3900000000000:\\ \;\;\;\;x - \mathsf{fma}\left(-y, t, y\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ (- z y) t) a x)))
   (if (<= t -4.5e+24)
     t_1
     (if (<= t -2.35e-95)
       (- x a)
       (if (<= t 3900000000000.0) (- x (* (fma (- y) t y) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma(((z - y) / t), a, x);
	double tmp;
	if (t <= -4.5e+24) {
		tmp = t_1;
	} else if (t <= -2.35e-95) {
		tmp = x - a;
	} else if (t <= 3900000000000.0) {
		tmp = x - (fma(-y, t, y) * a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(Float64(z - y) / t), a, x)
	tmp = 0.0
	if (t <= -4.5e+24)
		tmp = t_1;
	elseif (t <= -2.35e-95)
		tmp = Float64(x - a);
	elseif (t <= 3900000000000.0)
		tmp = Float64(x - Float64(fma(Float64(-y), t, y) * a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision] * a + x), $MachinePrecision]}, If[LessEqual[t, -4.5e+24], t$95$1, If[LessEqual[t, -2.35e-95], N[(x - a), $MachinePrecision], If[LessEqual[t, 3900000000000.0], N[(x - N[(N[((-y) * t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.50000000000000019e24 or 3.9e12 < t

   1. Initial program 95.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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-lft-neg-in N/A

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

      8. lower-fma.f64 N/A

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

      9. distribute-neg-frac N/A

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

      10. lower-/.f64 N/A

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

      11. *-lft-identity N/A

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

      12. metadata-eval N/A

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

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

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

      14. mul-1-neg N/A

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

      15. distribute-neg-in N/A

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

      16. mul-1-neg N/A

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

      17. mul-1-neg N/A

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

      18. distribute-lft-neg-in N/A

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

      19. metadata-eval N/A

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

      20. *-lft-identity N/A

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

      21. lower-fma.f64 87.3

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

   5. Applied rewrites 87.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 87.3%

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

   if -4.50000000000000019e24 < t < -2.3499999999999999e-95

   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 66.3

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

   5. Applied rewrites 66.3%

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

   if -2.3499999999999999e-95 < t < 3.9e12

   1. Initial program 98.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 85.8

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

   5. Applied rewrites 85.8%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 86.8

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

   7. Applied rewrites 86.8%

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

   8. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 68.4

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

   10. Applied rewrites 68.4%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 68.2%

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

Alternative 3: 91.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+25} \lor \neg \left(t \leq 7.6 \cdot 10^{+90}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{t}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.8e+25) (not (<= t 7.6e+90)))
   (fma (/ (- z y) t) a x)
   (- x (* a (/ (- y z) (- 1.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.8e+25) || !(t <= 7.6e+90)) {
		tmp = fma(((z - y) / t), a, x);
	} else {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.8e+25) || !(t <= 7.6e+90))
		tmp = fma(Float64(Float64(z - y) / t), a, x);
	else
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / Float64(1.0 - z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.8e+25], N[Not[LessEqual[t, 7.6e+90]], $MachinePrecision]], N[(N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision] * a + x), $MachinePrecision], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8000000000000002e25 or 7.6000000000000002e90 < t

   1. Initial program 95.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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-lft-neg-in N/A

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

      8. lower-fma.f64 N/A

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

      9. distribute-neg-frac N/A

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

      10. lower-/.f64 N/A

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

      11. *-lft-identity N/A

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

      12. metadata-eval N/A

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

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

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

      14. mul-1-neg N/A

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

      15. distribute-neg-in N/A

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

      16. mul-1-neg N/A

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

      17. mul-1-neg N/A

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

      18. distribute-lft-neg-in N/A

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

      19. metadata-eval N/A

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

      20. *-lft-identity N/A

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

      21. lower-fma.f64 92.4

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

   5. Applied rewrites 92.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 92.4%

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

   if -2.8000000000000002e25 < t < 7.6000000000000002e90

   1. Initial program 97.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 92.1

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

   5. Applied rewrites 92.1%

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

   7. Applied rewrites 93.5%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+25} \lor \neg \left(t \leq 7.6 \cdot 10^{+90}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{t}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-15}:\\ \;\;\;\;x - \frac{y}{\left(1 + t\right) - z} \cdot a\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+90}:\\ \;\;\;\;x - a \cdot \frac{y - z}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{t}, a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.2e-15)
   (- x (* (/ y (- (+ 1.0 t) z)) a))
   (if (<= t 7.6e+90)
     (- x (* a (/ (- y z) (- 1.0 z))))
     (fma (/ (- z y) t) a x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e-15) {
		tmp = x - ((y / ((1.0 + t) - z)) * a);
	} else if (t <= 7.6e+90) {
		tmp = x - (a * ((y - z) / (1.0 - z)));
	} else {
		tmp = fma(((z - y) / t), a, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.2e-15)
		tmp = Float64(x - Float64(Float64(y / Float64(Float64(1.0 + t) - z)) * a));
	elseif (t <= 7.6e+90)
		tmp = Float64(x - Float64(a * Float64(Float64(y - z) / Float64(1.0 - z))));
	else
		tmp = fma(Float64(Float64(z - y) / t), a, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.2e-15], N[(x - N[(N[(y / N[(N[(1.0 + t), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.6e+90], N[(x - N[(a * N[(N[(y - z), $MachinePrecision] / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision] * a + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.1999999999999998e-15

   1. Initial program 97.1%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 86.8

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

   5. Applied rewrites 86.8%

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

   if -6.1999999999999998e-15 < t < 7.6000000000000002e90

   1. Initial program 97.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 93.9

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

   5. Applied rewrites 93.9%

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

   7. Applied rewrites 95.4%

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

   if 7.6000000000000002e90 < t

   1. Initial program 94.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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-lft-neg-in N/A

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

      8. lower-fma.f64 N/A

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

      9. distribute-neg-frac N/A

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

      10. lower-/.f64 N/A

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

      11. *-lft-identity N/A

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

      12. metadata-eval N/A

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

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

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

      14. mul-1-neg N/A

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

      15. distribute-neg-in N/A

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

      16. mul-1-neg N/A

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

      17. mul-1-neg N/A

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

      18. distribute-lft-neg-in N/A

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

      19. metadata-eval N/A

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

      20. *-lft-identity N/A

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

      21. lower-fma.f64 96.7

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

   5. Applied rewrites 96.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 96.7%

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

Alternative 5: 88.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+51} \lor \neg \left(z \leq 400\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.6e+51) (not (<= z 400.0)))
   (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 <= -1.6e+51) || !(z <= 400.0)) {
		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 <= -1.6e+51) || !(z <= 400.0))
		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, -1.6e+51], N[Not[LessEqual[z, 400.0]], $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 < -1.6000000000000001e51 or 400 < z

   1. Initial program 96.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 88.8

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

   5. Applied rewrites 88.8%

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

   if -1.6000000000000001e51 < z < 400

   1. Initial program 97.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 92.0

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

   5. Applied rewrites 92.0%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+51} \lor \neg \left(z \leq 400\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.38 \cdot 10^{+51}:\\ \;\;\;\;x - \left(y - z\right) \cdot \frac{-a}{z}\\ \mathbf{elif}\;z \leq 400:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{\left(1 + t\right) - z}, a, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.38e+51)
   (- x (* (- y z) (/ (- a) z)))
   (if (<= z 400.0)
     (- x (* (/ y (+ 1.0 t)) a))
     (fma (/ z (- (+ 1.0 t) z)) a x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.38e+51) {
		tmp = x - ((y - z) * (-a / z));
	} else if (z <= 400.0) {
		tmp = x - ((y / (1.0 + t)) * a);
	} else {
		tmp = fma((z / ((1.0 + t) - z)), a, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.38e+51)
		tmp = Float64(x - Float64(Float64(y - z) * Float64(Float64(-a) / z)));
	elseif (z <= 400.0)
		tmp = Float64(x - Float64(Float64(y / Float64(1.0 + t)) * a));
	else
		tmp = fma(Float64(z / Float64(Float64(1.0 + t) - z)), a, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.38e+51], N[(x - N[(N[(y - z), $MachinePrecision] * N[((-a) / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 400.0], N[(x - N[(N[(y / N[(1.0 + t), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(z / N[(N[(1.0 + t), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] * a + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.38000000000000006e51

   1. Initial program 98.0%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 89.3

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

   5. Applied rewrites 89.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 89.3%

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

   if -1.38000000000000006e51 < z < 400

   1. Initial program 97.3%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 92.0

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

   5. Applied rewrites 92.0%

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

   if 400 < z

   1. Initial program 94.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 92.6

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

   5. Applied rewrites 92.6%

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

Alternative 7: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.66 \cdot 10^{+52} \lor \neg \left(z \leq 5.6 \cdot 10^{+58}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.66e+52) (not (<= z 5.6e+58)))
   (- 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 <= -1.66e+52) || !(z <= 5.6e+58)) {
		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 <= (-1.66d+52)) .or. (.not. (z <= 5.6d+58))) 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 <= -1.66e+52) || !(z <= 5.6e+58)) {
		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 <= -1.66e+52) or not (z <= 5.6e+58):
		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 <= -1.66e+52) || !(z <= 5.6e+58))
		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 <= -1.66e+52) || ~((z <= 5.6e+58)))
		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, -1.66e+52], N[Not[LessEqual[z, 5.6e+58]], $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 < -1.65999999999999994e52 or 5.5999999999999996e58 < z

   1. Initial program 96.1%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 80.0

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

   5. Applied rewrites 80.0%

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

   if -1.65999999999999994e52 < z < 5.5999999999999996e58

   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 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 91.8

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

   5. Applied rewrites 91.8%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.66 \cdot 10^{+52} \lor \neg \left(z \leq 5.6 \cdot 10^{+58}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{1 + t} \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+24} \lor \neg \left(t \leq 6.2 \cdot 10^{+20}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{t}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.3e+24) (not (<= t 6.2e+20)))
   (fma (/ (- z y) t) a x)
   (- x (* a (/ y (- 1.0 z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.3e+24) || !(t <= 6.2e+20)) {
		tmp = fma(((z - y) / t), a, x);
	} else {
		tmp = x - (a * (y / (1.0 - z)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.3e+24) || !(t <= 6.2e+20))
		tmp = fma(Float64(Float64(z - y) / t), a, x);
	else
		tmp = Float64(x - Float64(a * Float64(y / Float64(1.0 - z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.3e+24], N[Not[LessEqual[t, 6.2e+20]], $MachinePrecision]], N[(N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision] * a + x), $MachinePrecision], N[(x - N[(a * N[(y / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.29999999999999987e24 or 6.2e20 < t

   1. Initial program 95.7%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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-lft-neg-in N/A

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

      8. lower-fma.f64 N/A

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

      9. distribute-neg-frac N/A

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

      10. lower-/.f64 N/A

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

      11. *-lft-identity N/A

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

      12. metadata-eval N/A

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

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

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

      14. mul-1-neg N/A

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

      15. distribute-neg-in N/A

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

      16. mul-1-neg N/A

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

      17. mul-1-neg N/A

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

      18. distribute-lft-neg-in N/A

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

      19. metadata-eval N/A

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

      20. *-lft-identity N/A

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

      21. lower-fma.f64 87.9

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

   5. Applied rewrites 87.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 87.9%

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

   if -4.29999999999999987e24 < t < 6.2e20

   1. Initial program 98.4%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 95.4

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

   5. Applied rewrites 95.4%

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

   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 56.4%

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

   9. Taylor expanded in y around inf

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

   11. Applied rewrites 73.4%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+24} \lor \neg \left(t \leq 6.2 \cdot 10^{+20}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{z - y}{t}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot \frac{y}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \lor \neg \left(t \leq 0.75\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{-y}{t}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(-y, t, y\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.0) (not (<= t 0.75)))
   (fma (/ (- y) t) a x)
   (- x (* (fma (- y) t y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.0) || !(t <= 0.75)) {
		tmp = fma((-y / t), a, x);
	} else {
		tmp = x - (fma(-y, t, y) * a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.0) || !(t <= 0.75))
		tmp = fma(Float64(Float64(-y) / t), a, x);
	else
		tmp = Float64(x - Float64(fma(Float64(-y), t, y) * a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.0], N[Not[LessEqual[t, 0.75]], $MachinePrecision]], N[(N[((-y) / t), $MachinePrecision] * a + x), $MachinePrecision], N[(x - N[(N[((-y) * t + y), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1 or 0.75 < t

   1. Initial program 95.9%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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-lft-neg-in N/A

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

      8. lower-fma.f64 N/A

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

      9. distribute-neg-frac N/A

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

      10. lower-/.f64 N/A

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

      11. *-lft-identity N/A

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

      12. metadata-eval N/A

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

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

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

      14. mul-1-neg N/A

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

      15. distribute-neg-in N/A

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

      16. mul-1-neg N/A

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

      17. mul-1-neg N/A

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

      18. distribute-lft-neg-in N/A

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

      19. metadata-eval N/A

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

      20. *-lft-identity N/A

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

      21. lower-fma.f64 84.1

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

   5. Applied rewrites 84.1%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 79.6%

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

   if -1 < t < 0.75

   1. Initial program 98.3%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 85.2

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

   5. Applied rewrites 85.2%

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

      1. lift-/.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lower-/.f64 86.0

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

   7. Applied rewrites 86.0%

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

   8. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 67.0

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

   10. Applied rewrites 67.0%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 66.8%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \lor \neg \left(t \leq 0.75\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{-y}{t}, a, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \mathsf{fma}\left(-y, t, y\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{-46} \lor \neg \left(z \leq 2.2 \cdot 10^{-6}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \mathsf{fma}\left(a, z, a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.45e-46) (not (<= z 2.2e-6)))
   (- 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 <= -3.45e-46) || !(z <= 2.2e-6)) {
		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 <= -3.45e-46) || !(z <= 2.2e-6))
		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, -3.45e-46], N[Not[LessEqual[z, 2.2e-6]], $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 < -3.4499999999999999e-46 or 2.2000000000000001e-6 < z

   1. Initial program 96.3%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 73.4

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

   5. Applied rewrites 73.4%

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

   if -3.4499999999999999e-46 < z < 2.2000000000000001e-6

   1. Initial program 97.6%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 67.7

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

   5. Applied rewrites 67.7%

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

   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 67.7%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.45 \cdot 10^{-46} \lor \neg \left(z \leq 2.2 \cdot 10^{-6}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - z\right) \cdot \mathsf{fma}\left(a, z, a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 72.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.3 \cdot 10^{-13} \lor \neg \left(z \leq 3.4 \cdot 10^{+58}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.3e-13) (not (<= z 3.4e+58))) (- x a) (- x (* a y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.3e-13) || !(z <= 3.4e+58)) {
		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 <= (-7.3d-13)) .or. (.not. (z <= 3.4d+58))) 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 <= -7.3e-13) || !(z <= 3.4e+58)) {
		tmp = x - a;
	} else {
		tmp = x - (a * y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.3e-13) or not (z <= 3.4e+58):
		tmp = x - a
	else:
		tmp = x - (a * y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.3e-13) || !(z <= 3.4e+58))
		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 <= -7.3e-13) || ~((z <= 3.4e+58)))
		tmp = x - a;
	else
		tmp = x - (a * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.3e-13], N[Not[LessEqual[z, 3.4e+58]], $MachinePrecision]], N[(x - a), $MachinePrecision], N[(x - N[(a * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.3000000000000002e-13 or 3.4000000000000001e58 < z

   1. Initial program 95.8%

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

   3. Taylor expanded in z around inf

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

      1. lower--.f64 76.4

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

   5. Applied rewrites 76.4%

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

   if -7.3000000000000002e-13 < z < 3.4000000000000001e58

   1. Initial program 97.8%

      \[x - \frac{y - z}{\frac{\left(t - z\right) + 1}{a}} \]
   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 64.7

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

   5. Applied rewrites 64.7%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 28.3%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 64.3%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.3 \cdot 10^{-13} \lor \neg \left(z \leq 3.4 \cdot 10^{+58}\right):\\ \;\;\;\;x - a\\ \mathbf{else}:\\ \;\;\;\;x - a \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.0% 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 96.9%

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

3. Taylor expanded in z around inf

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

   1. lower--.f64 56.0

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

5. Applied rewrites 56.0%

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

Alternative 13: 16.5% 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 96.9%

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

3. Taylor expanded in z around inf

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

   1. lower--.f64 56.0

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

5. Applied rewrites 56.0%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 15.9%

   \[\leadsto -a \]
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 2024352 
(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))))