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

Percentage Accurate: 84.8% → 95.8%

Time: 3.8s

Alternatives: 10

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: 84.8% 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: 95.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := t - a \cdot z\\ t_3 := \frac{z}{t\_2}\\ t_4 := \frac{t\_1}{t\_2}\\ \mathbf{if}\;t\_4 \leq -5 \cdot 10^{-307}:\\ \;\;\;\;\frac{x}{t\_2} - y \cdot t\_3\\ \mathbf{elif}\;t\_4 \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(-1, \frac{x}{a}, \frac{y \cdot z}{a}\right)}{z}\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+303}:\\ \;\;\;\;\frac{t\_1}{\mathsf{fma}\left(-a, z, t\right)}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(t\_3, -1, \frac{x}{t\_2 \cdot y}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* y z)))
        (t_2 (- t (* a z)))
        (t_3 (/ z t_2))
        (t_4 (/ t_1 t_2)))
   (if (<= t_4 -5e-307)
     (- (/ x t_2) (* y t_3))
     (if (<= t_4 0.0)
       (/ (fma -1.0 (/ x a) (/ (* y z) a)) z)
       (if (<= t_4 2e+303)
         (/ t_1 (fma (- a) z t))
         (if (<= t_4 INFINITY)
           (* (fma t_3 -1.0 (/ x (* t_2 y))) y)
           (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (y * z);
	double t_2 = t - (a * z);
	double t_3 = z / t_2;
	double t_4 = t_1 / t_2;
	double tmp;
	if (t_4 <= -5e-307) {
		tmp = (x / t_2) - (y * t_3);
	} else if (t_4 <= 0.0) {
		tmp = fma(-1.0, (x / a), ((y * z) / a)) / z;
	} else if (t_4 <= 2e+303) {
		tmp = t_1 / fma(-a, z, t);
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = fma(t_3, -1.0, (x / (t_2 * y))) * y;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(t - Float64(a * z))
	t_3 = Float64(z / t_2)
	t_4 = Float64(t_1 / t_2)
	tmp = 0.0
	if (t_4 <= -5e-307)
		tmp = Float64(Float64(x / t_2) - Float64(y * t_3));
	elseif (t_4 <= 0.0)
		tmp = Float64(fma(-1.0, Float64(x / a), Float64(Float64(y * z) / a)) / z);
	elseif (t_4 <= 2e+303)
		tmp = Float64(t_1 / fma(Float64(-a), z, t));
	elseif (t_4 <= Inf)
		tmp = Float64(fma(t_3, -1.0, Float64(x / Float64(t_2 * y))) * y);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$4, -5e-307], N[(N[(x / t$95$2), $MachinePrecision] - N[(y * t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 0.0], N[(N[(-1.0 * N[(x / a), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$4, 2e+303], N[(t$95$1 / N[((-a) * z + t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], N[(N[(t$95$3 * -1.0 + N[(x / N[(t$95$2 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -5.00000000000000014e-307

   1. Initial program 93.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing
   3. 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

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      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

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

      10. lift--.f64 N/A

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

      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

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

      15. lift--.f64 97.2

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

   4. Applied rewrites 97.2%

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

   if -5.00000000000000014e-307 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 59.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing
   3. 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

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      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

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

      10. lift--.f64 N/A

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

      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

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

      15. lift--.f64 58.9

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

   4. Applied rewrites 58.9%

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

   5. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 72.8

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

   7. Applied rewrites 72.8%

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

   8. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift-*.f64 77.8

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

   10. Applied rewrites 77.8%

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

   if 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 2e303

   1. Initial program 99.7%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      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 99.7

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

   4. Applied rewrites 99.7%

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

   if 2e303 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 63.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. lift--.f64 99.2

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

   5. Applied rewrites 99.2%

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

   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. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 100.0

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

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\frac{y}{a}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 2: 94.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ t_2 := \frac{x}{t\_1} - y \cdot \frac{z}{t\_1}\\ t_3 := \frac{x - y \cdot z}{t\_1}\\ \mathbf{if}\;t\_3 \leq -5 \cdot 10^{-307}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(-1, \frac{x}{a}, \frac{y \cdot z}{a}\right)}{z}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z)))
        (t_2 (- (/ x t_1) (* y (/ z t_1))))
        (t_3 (/ (- x (* y z)) t_1)))
   (if (<= t_3 -5e-307)
     t_2
     (if (<= t_3 0.0)
       (/ (fma -1.0 (/ x a) (/ (* y z) a)) z)
       (if (<= t_3 INFINITY) t_2 (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y * (z / t_1));
	double t_3 = (x - (y * z)) / t_1;
	double tmp;
	if (t_3 <= -5e-307) {
		tmp = t_2;
	} else if (t_3 <= 0.0) {
		tmp = fma(-1.0, (x / a), ((y * z) / a)) / z;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * z))
	t_2 = Float64(Float64(x / t_1) - Float64(y * Float64(z / t_1)))
	t_3 = Float64(Float64(x - Float64(y * z)) / t_1)
	tmp = 0.0
	if (t_3 <= -5e-307)
		tmp = t_2;
	elseif (t_3 <= 0.0)
		tmp = Float64(fma(-1.0, Float64(x / a), Float64(Float64(y * z) / a)) / z);
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(y / a);
	end
	return 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[(x / t$95$1), $MachinePrecision] - N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, -5e-307], t$95$2, If[LessEqual[t$95$3, 0.0], N[(N[(-1.0 * N[(x / a), $MachinePrecision] + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$2, N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -5.00000000000000014e-307 or 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < +inf.0

   1. Initial program 93.3%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing
   3. 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

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      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

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

      10. lift--.f64 N/A

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

      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

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

      15. lift--.f64 97.3

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

   4. Applied rewrites 97.3%

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

   if -5.00000000000000014e-307 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 59.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing
   3. 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

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      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

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

      10. lift--.f64 N/A

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

      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

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

      15. lift--.f64 58.9

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

   4. Applied rewrites 58.9%

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

   5. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 72.8

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

   7. Applied rewrites 72.8%

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

   8. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift-*.f64 77.8

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

   10. Applied rewrites 77.8%

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

   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. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 100.0

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

   5. Applied rewrites 100.0%

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

Alternative 3: 89.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$1 / N[((-a) * z + t), $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 88.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      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 88.6

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

   4. Applied rewrites 88.6%

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

   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. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 100.0

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

   5. Applied rewrites 100.0%

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

Alternative 4: 89.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, 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 88.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   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. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 100.0

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

   5. Applied rewrites 100.0%

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

Alternative 5: 66.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+161}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+26}:\\ \;\;\;\;\frac{x - y \cdot z}{\left(-a\right) \cdot z}\\ \mathbf{elif}\;z \leq 420000000000:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+136}:\\ \;\;\;\;\frac{\left(-y\right) \cdot z}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z))))
   (if (<= z -3.2e+161)
     (/ y a)
     (if (<= z -1.4e+26)
       (/ (- x (* y z)) (* (- a) z))
       (if (<= z 420000000000.0)
         (/ x t_1)
         (if (<= z 3e+136) (/ (* (- 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 (z <= -3.2e+161) {
		tmp = y / a;
	} else if (z <= -1.4e+26) {
		tmp = (x - (y * z)) / (-a * z);
	} else if (z <= 420000000000.0) {
		tmp = x / t_1;
	} else if (z <= 3e+136) {
		tmp = (-y * z) / t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t - (a * z)
    if (z <= (-3.2d+161)) then
        tmp = y / a
    else if (z <= (-1.4d+26)) then
        tmp = (x - (y * z)) / (-a * z)
    else if (z <= 420000000000.0d0) then
        tmp = x / t_1
    else if (z <= 3d+136) then
        tmp = (-y * z) / t_1
    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 t_1 = t - (a * z);
	double tmp;
	if (z <= -3.2e+161) {
		tmp = y / a;
	} else if (z <= -1.4e+26) {
		tmp = (x - (y * z)) / (-a * z);
	} else if (z <= 420000000000.0) {
		tmp = x / t_1;
	} else if (z <= 3e+136) {
		tmp = (-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 z <= -3.2e+161:
		tmp = y / a
	elif z <= -1.4e+26:
		tmp = (x - (y * z)) / (-a * z)
	elif z <= 420000000000.0:
		tmp = x / t_1
	elif z <= 3e+136:
		tmp = (-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 (z <= -3.2e+161)
		tmp = Float64(y / a);
	elseif (z <= -1.4e+26)
		tmp = Float64(Float64(x - Float64(y * z)) / Float64(Float64(-a) * z));
	elseif (z <= 420000000000.0)
		tmp = Float64(x / t_1);
	elseif (z <= 3e+136)
		tmp = Float64(Float64(Float64(-y) * 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 (z <= -3.2e+161)
		tmp = y / a;
	elseif (z <= -1.4e+26)
		tmp = (x - (y * z)) / (-a * z);
	elseif (z <= 420000000000.0)
		tmp = x / t_1;
	elseif (z <= 3e+136)
		tmp = (-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[z, -3.2e+161], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.4e+26], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[((-a) * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 420000000000.0], N[(x / t$95$1), $MachinePrecision], If[LessEqual[z, 3e+136], N[(N[((-y) * z), $MachinePrecision] / t$95$1), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.20000000000000002e161 or 2.99999999999999979e136 < z

   1. Initial program 56.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 67.2

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

   5. Applied rewrites 67.2%

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

   if -3.20000000000000002e161 < z < -1.4e26

   1. Initial program 80.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. mul-1-neg N/A

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

      3. lower-*.f64 N/A

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

      4. lower-neg.f64 50.7

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

   5. Applied rewrites 50.7%

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

   if -1.4e26 < z < 4.2e11

   1. Initial program 99.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 72.3%

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

   if 4.2e11 < z < 2.99999999999999979e136

   1. Initial program 84.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 52.9

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

   5. Applied rewrites 52.9%

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

Alternative 6: 66.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+26}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 420000000000:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+136}:\\ \;\;\;\;\frac{\left(-y\right) \cdot z}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z))))
   (if (<= z -1.7e+26)
     (/ y a)
     (if (<= z 420000000000.0)
       (/ x t_1)
       (if (<= z 3e+136) (/ (* (- 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 (z <= -1.7e+26) {
		tmp = y / a;
	} else if (z <= 420000000000.0) {
		tmp = x / t_1;
	} else if (z <= 3e+136) {
		tmp = (-y * z) / t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t - (a * z)
    if (z <= (-1.7d+26)) then
        tmp = y / a
    else if (z <= 420000000000.0d0) then
        tmp = x / t_1
    else if (z <= 3d+136) then
        tmp = (-y * z) / t_1
    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 t_1 = t - (a * z);
	double tmp;
	if (z <= -1.7e+26) {
		tmp = y / a;
	} else if (z <= 420000000000.0) {
		tmp = x / t_1;
	} else if (z <= 3e+136) {
		tmp = (-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 z <= -1.7e+26:
		tmp = y / a
	elif z <= 420000000000.0:
		tmp = x / t_1
	elif z <= 3e+136:
		tmp = (-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 (z <= -1.7e+26)
		tmp = Float64(y / a);
	elseif (z <= 420000000000.0)
		tmp = Float64(x / t_1);
	elseif (z <= 3e+136)
		tmp = Float64(Float64(Float64(-y) * 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 (z <= -1.7e+26)
		tmp = y / a;
	elseif (z <= 420000000000.0)
		tmp = x / t_1;
	elseif (z <= 3e+136)
		tmp = (-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[z, -1.7e+26], N[(y / a), $MachinePrecision], If[LessEqual[z, 420000000000.0], N[(x / t$95$1), $MachinePrecision], If[LessEqual[z, 3e+136], N[(N[((-y) * z), $MachinePrecision] / t$95$1), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7000000000000001e26 or 2.99999999999999979e136 < z

   1. Initial program 63.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 61.0

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

   5. Applied rewrites 61.0%

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

   if -1.7000000000000001e26 < z < 4.2e11

   1. Initial program 99.7%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 72.3%

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

   if 4.2e11 < z < 2.99999999999999979e136

   1. Initial program 84.0%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 52.9

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

   5. Applied rewrites 52.9%

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

Alternative 7: 89.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -1 \cdot \frac{\frac{x}{z} - y}{a}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+136}:\\ \;\;\;\;\frac{x - y \cdot z}{\mathsf{fma}\left(-a, z, t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -1.0 (/ (- (/ x z) y) a))))
   (if (<= z -1.1e+46)
     t_1
     (if (<= z 3e+136) (/ (- 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 = -1.0 * (((x / z) - y) / a);
	double tmp;
	if (z <= -1.1e+46) {
		tmp = t_1;
	} else if (z <= 3e+136) {
		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(-1.0 * Float64(Float64(Float64(x / z) - y) / a))
	tmp = 0.0
	if (z <= -1.1e+46)
		tmp = t_1;
	elseif (z <= 3e+136)
		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[(-1.0 * N[(N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+46], t$95$1, If[LessEqual[z, 3e+136], 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 < -1.1e46 or 2.99999999999999979e136 < z

   1. Initial program 62.6%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing
   3. 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

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-*.f64 N/A

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

      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

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

      10. lift--.f64 N/A

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

      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

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

      15. lift--.f64 75.8

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

   4. Applied rewrites 75.8%

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

   5. Taylor expanded in a around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 76.2

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

   7. Applied rewrites 76.2%

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

   if -1.1e46 < z < 2.99999999999999979e136

   1. Initial program 97.0%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      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 97.0

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

   4. Applied rewrites 97.0%

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

Alternative 8: 64.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+26}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+136}:\\ \;\;\;\;\frac{x}{t - a \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.7e+26) (/ y a) (if (<= z 2.8e+136) (/ x (- t (* a z))) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.7e+26) {
		tmp = y / a;
	} else if (z <= 2.8e+136) {
		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 <= (-1.7d+26)) then
        tmp = y / a
    else if (z <= 2.8d+136) 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 <= -1.7e+26) {
		tmp = y / a;
	} else if (z <= 2.8e+136) {
		tmp = x / (t - (a * z));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.7e+26:
		tmp = y / a
	elif z <= 2.8e+136:
		tmp = x / (t - (a * z))
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.7e+26)
		tmp = Float64(y / a);
	elseif (z <= 2.8e+136)
		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 <= -1.7e+26)
		tmp = y / a;
	elseif (z <= 2.8e+136)
		tmp = x / (t - (a * z));
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.7e+26], N[(y / a), $MachinePrecision], If[LessEqual[z, 2.8e+136], N[(x / N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7000000000000001e26 or 2.8000000000000002e136 < z

   1. Initial program 63.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 61.0

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

   5. Applied rewrites 61.0%

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

   if -1.7000000000000001e26 < z < 2.8000000000000002e136

   1. Initial program 97.1%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 67.1%

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

Alternative 9: 55.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-26}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 90000000000000:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.35e-26) (/ y a) (if (<= z 90000000000000.0) (/ x t) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.35e-26) {
		tmp = y / a;
	} else if (z <= 90000000000000.0) {
		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 <= (-2.35d-26)) then
        tmp = y / a
    else if (z <= 90000000000000.0d0) 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 <= -2.35e-26) {
		tmp = y / a;
	} else if (z <= 90000000000000.0) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.35e-26:
		tmp = y / a
	elif z <= 90000000000000.0:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.35e-26)
		tmp = Float64(y / a);
	elseif (z <= 90000000000000.0)
		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 <= -2.35e-26)
		tmp = y / a;
	elseif (z <= 90000000000000.0)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.35e-26], N[(y / a), $MachinePrecision], If[LessEqual[z, 90000000000000.0], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.34999999999999995e-26 or 9e13 < z

   1. Initial program 70.5%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

      1. lower-/.f64 55.2

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

   5. Applied rewrites 55.2%

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

   if -2.34999999999999995e-26 < z < 9e13

   1. Initial program 99.8%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 56.1

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

   5. Applied rewrites 56.1%

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

Alternative 10: 35.8% accurate, 2.3× 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 84.8%

   \[\frac{x - y \cdot z}{t - a \cdot z} \]
2. Add Preprocessing

3. Taylor expanded in z around 0

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

   1. lower-/.f64 35.8

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

5. Applied rewrites 35.8%

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

Developer Target 1: 97.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ t_2 := \frac{x}{t\_1} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{if}\;z < -32113435955957344:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z < 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z))) (t_2 (- (/ x t_1) (/ y (- (/ t z) a)))))
   (if (< z -32113435955957344.0)
     t_2
     (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 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 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / 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 = (x / t_1) - (y / ((t / z) - a))
    if (z < (-32113435955957344.0d0)) then
        tmp = t_2
    else if (z < 3.5139522372978296d-86) then
        tmp = (x - (y * z)) * (1.0d0 / 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 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * z)
	t_2 = (x / t_1) - (y / ((t / z) - a))
	tmp = 0
	if z < -32113435955957344.0:
		tmp = t_2
	elif z < 3.5139522372978296e-86:
		tmp = (x - (y * z)) * (1.0 / 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(x / t_1) - Float64(y / Float64(Float64(t / z) - a)))
	tmp = 0.0
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = Float64(Float64(x - Float64(y * z)) * Float64(1.0 / 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 = (x / t_1) - (y / ((t / z) - a));
	tmp = 0.0;
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = (x - (y * z)) * (1.0 / 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[(x / t$95$1), $MachinePrecision] - N[(y / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -32113435955957344.0], t$95$2, If[Less[z, 3.5139522372978296e-86], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2025089 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -32113435955957344) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 4392440296622287/125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* (- x (* y z)) (/ 1 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))))))

  (/ (- x (* y z)) (- t (* a z))))