Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A

Percentage Accurate: 84.9% → 92.0%

Time: 6.1s

Alternatives: 8

Speedup: 0.7×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y \cdot z}{t - a \cdot z} \end{array} \]

FPCore

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

C

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

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 - (a * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y \cdot z}{t - a \cdot z} \end{array} \]

FPCore

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

C

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

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 - (a * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+151}:\\ \;\;\;\;\frac{x - y \cdot z}{\mathsf{fma}\left(-a, z, t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -1.95e+101)
     t_1
     (if (<= z 2.6e+151) (/ (- x (* y z)) (fma (- a) z t)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.95e+101) {
		tmp = t_1;
	} else if (z <= 2.6e+151) {
		tmp = (x - (y * z)) / fma(-a, z, t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.95e+101)
		tmp = t_1;
	elseif (z <= 2.6e+151)
		tmp = Float64(Float64(x - Float64(y * z)) / fma(Float64(-a), z, t));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -1.95e+101], t$95$1, If[LessEqual[z, 2.6e+151], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[((-a) * z + t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e101 or 2.60000000000000013e151 < z

   1. Initial program 59.2%

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

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z} + \frac{y}{a}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z} + \color{blue}{\frac{y}{a}} \]

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      5. lower--.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      6. lower-/.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      7. associate-/l* N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - t \cdot \frac{y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - t \cdot \frac{y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - t \cdot \frac{y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      10. unpow2 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 64.3

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

   4. Applied rewrites 64.3%

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

   5. Taylor expanded in a around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 80.8

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

   7. Applied rewrites 80.8%

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

   if -1.95e101 < z < 2.60000000000000013e151

   1. Initial program 95.6%

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

      1. lift-*.f64 N/A

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

      2. lift--.f64 N/A

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

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

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

      4. mul-1-neg N/A

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

      5. associate-*r* N/A

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

      6. +-commutative N/A

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

      7. associate-*r* N/A

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

      8. mul-1-neg N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-neg.f64 95.6

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

   3. Applied rewrites 95.6%

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

Alternative 2: 91.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+151}:\\ \;\;\;\;\frac{x - y \cdot z}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -1.95e+101)
     t_1
     (if (<= z 2.6e+151) (/ (- x (* y z)) (- t (* a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.95e+101) {
		tmp = t_1;
	} else if (z <= 2.6e+151) {
		tmp = (x - (y * z)) / (t - (a * z));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (y - (x / z)) / a
    if (z <= (-1.95d+101)) then
        tmp = t_1
    else if (z <= 2.6d+151) then
        tmp = (x - (y * z)) / (t - (a * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.95e+101) {
		tmp = t_1;
	} else if (z <= 2.6e+151) {
		tmp = (x - (y * z)) / (t - (a * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -1.95e+101:
		tmp = t_1
	elif z <= 2.6e+151:
		tmp = (x - (y * z)) / (t - (a * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.95e+101)
		tmp = t_1;
	elseif (z <= 2.6e+151)
		tmp = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(a * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -1.95e+101)
		tmp = t_1;
	elseif (z <= 2.6e+151)
		tmp = (x - (y * z)) / (t - (a * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -1.95e+101], t$95$1, If[LessEqual[z, 2.6e+151], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e101 or 2.60000000000000013e151 < z

   1. Initial program 59.2%

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

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z} + \frac{y}{a}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z} + \color{blue}{\frac{y}{a}} \]

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      5. lower--.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      6. lower-/.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      7. associate-/l* N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - t \cdot \frac{y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - t \cdot \frac{y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - t \cdot \frac{y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      10. unpow2 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 64.3

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

   4. Applied rewrites 64.3%

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

   5. Taylor expanded in a around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 80.8

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

   7. Applied rewrites 80.8%

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

   if -1.95e101 < z < 2.60000000000000013e151

   1. Initial program 95.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 91.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ \mathbf{if}\;\frac{x - y \cdot z}{t\_1} \leq \infty:\\ \;\;\;\;\frac{x}{t\_1} - y \cdot \frac{z}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 89.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. div-sub N/A

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

      7. lower--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift-*.f64 N/A

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

      11. associate-/l* N/A

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

      12. lower-*.f64 N/A

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

      13. lower-/.f64 N/A

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

      14. lift--.f64 N/A

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

      15. lift-*.f64 91.6

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

   3. Applied rewrites 91.6%

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

   if +inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 0.0%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{y}{a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 100.0

         \[\leadsto \frac{y}{\color{blue}{a}} \]

   4. Applied rewrites 100.0%

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

Alternative 4: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -30000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+151}:\\ \;\;\;\;-y \cdot \frac{z}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z))) (t_2 (/ (- y (/ x z)) a)))
   (if (<= z -30000000.0)
     t_2
     (if (<= z 1.02e+52)
       (/ x t_1)
       (if (<= z 1.75e+151) (- (* y (/ z t_1))) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -30000000.0) {
		tmp = t_2;
	} else if (z <= 1.02e+52) {
		tmp = x / t_1;
	} else if (z <= 1.75e+151) {
		tmp = -(y * (z / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - (a * z)
    t_2 = (y - (x / z)) / a
    if (z <= (-30000000.0d0)) then
        tmp = t_2
    else if (z <= 1.02d+52) then
        tmp = x / t_1
    else if (z <= 1.75d+151) then
        tmp = -(y * (z / t_1))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -30000000.0) {
		tmp = t_2;
	} else if (z <= 1.02e+52) {
		tmp = x / t_1;
	} else if (z <= 1.75e+151) {
		tmp = -(y * (z / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * z)
	t_2 = (y - (x / z)) / a
	tmp = 0
	if z <= -30000000.0:
		tmp = t_2
	elif z <= 1.02e+52:
		tmp = x / t_1
	elif z <= 1.75e+151:
		tmp = -(y * (z / t_1))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * z))
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -30000000.0)
		tmp = t_2;
	elseif (z <= 1.02e+52)
		tmp = Float64(x / t_1);
	elseif (z <= 1.75e+151)
		tmp = Float64(-Float64(y * Float64(z / t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * z);
	t_2 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -30000000.0)
		tmp = t_2;
	elseif (z <= 1.02e+52)
		tmp = x / t_1;
	elseif (z <= 1.75e+151)
		tmp = -(y * (z / t_1));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -30000000.0], t$95$2, If[LessEqual[z, 1.02e+52], N[(x / t$95$1), $MachinePrecision], If[LessEqual[z, 1.75e+151], (-N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3e7 or 1.7500000000000001e151 < z

   1. Initial program 64.9%

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

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z} + \frac{y}{a}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z} + \color{blue}{\frac{y}{a}} \]

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      5. lower--.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      6. lower-/.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      7. associate-/l* N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - t \cdot \frac{y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - t \cdot \frac{y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - t \cdot \frac{y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      10. unpow2 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 62.6

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

   4. Applied rewrites 62.6%

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

   5. Taylor expanded in a around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 77.2

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

   7. Applied rewrites 77.2%

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

   if -3e7 < z < 1.02000000000000002e52

   1. Initial program 99.4%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 71.9%

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

   if 1.02000000000000002e52 < z < 1.7500000000000001e151

   1. Initial program 79.1%

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

   2. Taylor expanded in x around -inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 N/A

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

      5. associate-/r* N/A

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

      6. sub-div N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lift-*.f64 68.4

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

   4. Applied rewrites 68.4%

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

   5. Taylor expanded in x around 0

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 59.6

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

   7. Applied rewrites 59.6%

      \[\leadsto -y \cdot \frac{z}{t - a \cdot z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 70.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -30000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+164}:\\ \;\;\;\;\frac{x}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -30000000.0) t_1 (if (<= z 2.25e+164) (/ x (- t (* a z))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -30000000.0) {
		tmp = t_1;
	} else if (z <= 2.25e+164) {
		tmp = x / (t - (a * z));
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (y - (x / z)) / a
    if (z <= (-30000000.0d0)) then
        tmp = t_1
    else if (z <= 2.25d+164) then
        tmp = x / (t - (a * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -30000000.0) {
		tmp = t_1;
	} else if (z <= 2.25e+164) {
		tmp = x / (t - (a * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -30000000.0:
		tmp = t_1
	elif z <= 2.25e+164:
		tmp = x / (t - (a * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -30000000.0)
		tmp = t_1;
	elseif (z <= 2.25e+164)
		tmp = Float64(x / Float64(t - Float64(a * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -30000000.0)
		tmp = t_1;
	elseif (z <= 2.25e+164)
		tmp = x / (t - (a * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -30000000.0], t$95$1, If[LessEqual[z, 2.25e+164], N[(x / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3e7 or 2.24999999999999988e164 < z

   1. Initial program 65.0%

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

   2. Taylor expanded in z around -inf

      \[\leadsto \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z} + \frac{y}{a}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto -1 \cdot \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z} + \color{blue}{\frac{y}{a}} \]

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      5. lower--.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      6. lower-/.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      7. associate-/l* N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - t \cdot \frac{y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      8. lower-*.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - t \cdot \frac{y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      9. lower-/.f64 N/A

         \[\leadsto \left(-\frac{\frac{x}{a} - t \cdot \frac{y}{{a}^{2}}}{z}\right) + \frac{y}{a} \]

      10. unpow2 N/A

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

      11. lower-*.f64 N/A

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

      12. lower-/.f64 62.6

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

   4. Applied rewrites 62.6%

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

   5. Taylor expanded in a around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 N/A

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

      3. lower-/.f64 77.3

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

   7. Applied rewrites 77.3%

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

   if -3e7 < z < 2.24999999999999988e164

   1. Initial program 96.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 67.0%

      \[\leadsto \frac{\color{blue}{x}}{t - a \cdot z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 65.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -330000000:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+164}:\\ \;\;\;\;\frac{x}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -330000000.0)
   (/ y a)
   (if (<= z 2.3e+164) (/ x (- t (* a z))) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -330000000.0) {
		tmp = y / a;
	} else if (z <= 2.3e+164) {
		tmp = x / (t - (a * z));
	} else {
		tmp = y / 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 <= (-330000000.0d0)) then
        tmp = y / a
    else if (z <= 2.3d+164) then
        tmp = x / (t - (a * z))
    else
        tmp = y / 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 <= -330000000.0) {
		tmp = y / a;
	} else if (z <= 2.3e+164) {
		tmp = x / (t - (a * z));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -330000000.0:
		tmp = y / a
	elif z <= 2.3e+164:
		tmp = x / (t - (a * z))
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -330000000.0)
		tmp = Float64(y / a);
	elseif (z <= 2.3e+164)
		tmp = Float64(x / Float64(t - Float64(a * z)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -330000000.0)
		tmp = y / a;
	elseif (z <= 2.3e+164)
		tmp = x / (t - (a * z));
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -330000000.0], N[(y / a), $MachinePrecision], If[LessEqual[z, 2.3e+164], N[(x / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.3e8 or 2.3e164 < z

   1. Initial program 64.8%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{y}{a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 61.9

         \[\leadsto \frac{y}{\color{blue}{a}} \]

   4. Applied rewrites 61.9%

      \[\leadsto \color{blue}{\frac{y}{a}} \]

   if -3.3e8 < z < 2.3e164

   1. Initial program 96.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 66.9%

      \[\leadsto \frac{\color{blue}{x}}{t - a \cdot z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 54.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-37}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8e-37) (/ y a) (if (<= z 9.2e+131) (/ x t) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e-37) {
		tmp = y / a;
	} else if (z <= 9.2e+131) {
		tmp = x / t;
	} else {
		tmp = y / 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 <= (-2.8d-37)) then
        tmp = y / a
    else if (z <= 9.2d+131) then
        tmp = x / t
    else
        tmp = y / 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 <= -2.8e-37) {
		tmp = y / a;
	} else if (z <= 9.2e+131) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.8e-37:
		tmp = y / a
	elif z <= 9.2e+131:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.8e-37)
		tmp = Float64(y / a);
	elseif (z <= 9.2e+131)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.8e-37)
		tmp = y / a;
	elseif (z <= 9.2e+131)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.8e-37], N[(y / a), $MachinePrecision], If[LessEqual[z, 9.2e+131], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8000000000000001e-37 or 9.19999999999999966e131 < z

   1. Initial program 67.9%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{y}{a}} \]
   3. Step-by-step derivation

      1. lower-/.f64 58.7

         \[\leadsto \frac{y}{\color{blue}{a}} \]

   4. Applied rewrites 58.7%

      \[\leadsto \color{blue}{\frac{y}{a}} \]

   if -2.8000000000000001e-37 < z < 9.19999999999999966e131

   1. Initial program 97.3%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 51.4

         \[\leadsto \frac{x}{\color{blue}{t}} \]

   4. Applied rewrites 51.4%

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

Alternative 8: 35.8% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \frac{x}{t} \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, 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 / t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 84.9%

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

2. Taylor expanded in z around 0

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

   1. lower-/.f64 35.8

      \[\leadsto \frac{x}{\color{blue}{t}} \]

4. Applied rewrites 35.8%

   \[\leadsto \color{blue}{\frac{x}{t}} \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2025115 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64
  (/ (- x (* y z)) (- t (* a z))))