Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 2.7s

Alternatives: 11

Speedup: 1.0×

• 34.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]
2. Add Preprocessing

Alternative 2: 82.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - t\right) \cdot z\\ \mathbf{if}\;z \leq -4.1 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+99}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x t) z)))
   (if (<= z -4.1e+29) t_1 (if (<= z 3.7e+99) (fma (- t x) y x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - t) * z;
	double tmp;
	if (z <= -4.1e+29) {
		tmp = t_1;
	} else if (z <= 3.7e+99) {
		tmp = fma((t - x), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - t) * z)
	tmp = 0.0
	if (z <= -4.1e+29)
		tmp = t_1;
	elseif (z <= 3.7e+99)
		tmp = fma(Float64(t - x), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -4.1e+29], t$95$1, If[LessEqual[z, 3.7e+99], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.1000000000000003e29 or 3.7000000000000001e99 < z

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

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

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

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

      10. +-commutative N/A

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

      11. distribute-rgt-out N/A

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

      12. associate-*r* N/A

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

      13. +-commutative N/A

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

      14. associate-+l+ N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lift--.f64 N/A

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

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

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

      20. lower--.f64 N/A

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x - t\right)} \]
   5. Step-by-step derivation

      1. associate-+r- N/A

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

      2. +-commutative N/A

         \[\leadsto z \cdot \left(x - t\right) \]

      3. *-commutative N/A

         \[\leadsto z \cdot \left(x - t\right) \]

      4. *-commutative N/A

         \[\leadsto z \cdot \left(x - t\right) \]

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

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

      6. *-commutative N/A

         \[\leadsto z \cdot \left(x - t\right) \]

      7. +-commutative N/A

         \[\leadsto z \cdot \left(x - t\right) \]

      8. distribute-lft-neg-out N/A

         \[\leadsto z \cdot \left(x - t\right) \]

      9. *-commutative N/A

         \[\leadsto z \cdot \left(x - t\right) \]

      10. distribute-rgt-neg-out N/A

          \[\leadsto z \cdot \left(x - t\right) \]

      11. lift-neg.f64 N/A

          \[\leadsto z \cdot \left(x - t\right) \]

      12. +-commutative N/A

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

      13. lift-neg.f64 N/A

          \[\leadsto z \cdot \left(x - t\right) \]

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower--.f64 83.5

          \[\leadsto \left(x - t\right) \cdot z \]

   6. Applied rewrites 83.5%

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

   if -4.1000000000000003e29 < z < 3.7000000000000001e99

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

         \[\leadsto \left(t - x\right) \cdot y + x \]

      3. lower-fma.f64 N/A

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

      4. lift--.f64 82.3

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

   4. Applied rewrites 82.3%

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

Alternative 3: 71.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot y\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-21}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-292}:\\ \;\;\;\;x - t \cdot z\\ \mathbf{elif}\;y \leq 54000000000000:\\ \;\;\;\;\left(x - t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t x) y)))
   (if (<= y -2.2e+81)
     t_1
     (if (<= y -5.5e-21)
       (* (- y z) t)
       (if (<= y 5.6e-292)
         (- x (* t z))
         (if (<= y 54000000000000.0) (* (- x t) z) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * y;
	double tmp;
	if (y <= -2.2e+81) {
		tmp = t_1;
	} else if (y <= -5.5e-21) {
		tmp = (y - z) * t;
	} else if (y <= 5.6e-292) {
		tmp = x - (t * z);
	} else if (y <= 54000000000000.0) {
		tmp = (x - t) * 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)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - x) * y
    if (y <= (-2.2d+81)) then
        tmp = t_1
    else if (y <= (-5.5d-21)) then
        tmp = (y - z) * t
    else if (y <= 5.6d-292) then
        tmp = x - (t * z)
    else if (y <= 54000000000000.0d0) then
        tmp = (x - t) * 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 t_1 = (t - x) * y;
	double tmp;
	if (y <= -2.2e+81) {
		tmp = t_1;
	} else if (y <= -5.5e-21) {
		tmp = (y - z) * t;
	} else if (y <= 5.6e-292) {
		tmp = x - (t * z);
	} else if (y <= 54000000000000.0) {
		tmp = (x - t) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t - x) * y
	tmp = 0
	if y <= -2.2e+81:
		tmp = t_1
	elif y <= -5.5e-21:
		tmp = (y - z) * t
	elif y <= 5.6e-292:
		tmp = x - (t * z)
	elif y <= 54000000000000.0:
		tmp = (x - t) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t - x) * y)
	tmp = 0.0
	if (y <= -2.2e+81)
		tmp = t_1;
	elseif (y <= -5.5e-21)
		tmp = Float64(Float64(y - z) * t);
	elseif (y <= 5.6e-292)
		tmp = Float64(x - Float64(t * z));
	elseif (y <= 54000000000000.0)
		tmp = Float64(Float64(x - t) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t - x) * y;
	tmp = 0.0;
	if (y <= -2.2e+81)
		tmp = t_1;
	elseif (y <= -5.5e-21)
		tmp = (y - z) * t;
	elseif (y <= 5.6e-292)
		tmp = x - (t * z);
	elseif (y <= 54000000000000.0)
		tmp = (x - t) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -2.2e+81], t$95$1, If[LessEqual[y, -5.5e-21], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 5.6e-292], N[(x - N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 54000000000000.0], N[(N[(x - t), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.19999999999999987e81 or 5.4e13 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 81.5

         \[\leadsto \left(t - x\right) \cdot y \]

   4. Applied rewrites 81.5%

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

   if -2.19999999999999987e81 < y < -5.49999999999999977e-21

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 49.1

         \[\leadsto \left(y - z\right) \cdot t \]

   4. Applied rewrites 49.1%

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

   if -5.49999999999999977e-21 < y < 5.6000000000000003e-292

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 92.0

         \[\leadsto x - \left(t - x\right) \cdot z \]

   4. Applied rewrites 92.0%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 68.8%

      \[\leadsto x - t \cdot z \]

   if 5.6000000000000003e-292 < y < 5.4e13

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

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

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

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

      10. +-commutative N/A

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

      11. distribute-rgt-out N/A

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

      12. associate-*r* N/A

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

      13. +-commutative N/A

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

      14. associate-+l+ N/A

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

      15. +-commutative N/A

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

      16. *-commutative N/A

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

      17. lower-fma.f64 N/A

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

      18. lift--.f64 N/A

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

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

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

      20. lower--.f64 N/A

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

   3. Applied rewrites 100.0%

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

   4. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x - t\right)} \]
   5. Step-by-step derivation

      1. associate-+r- N/A

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

      2. +-commutative N/A

         \[\leadsto z \cdot \left(x - t\right) \]

      3. *-commutative N/A

         \[\leadsto z \cdot \left(x - t\right) \]

      4. *-commutative N/A

         \[\leadsto z \cdot \left(x - t\right) \]

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

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

      6. *-commutative N/A

         \[\leadsto z \cdot \left(x - t\right) \]

      7. +-commutative N/A

         \[\leadsto z \cdot \left(x - t\right) \]

      8. distribute-lft-neg-out N/A

         \[\leadsto z \cdot \left(x - t\right) \]

      9. *-commutative N/A

         \[\leadsto z \cdot \left(x - t\right) \]

      10. distribute-rgt-neg-out N/A

          \[\leadsto z \cdot \left(x - t\right) \]

      11. lift-neg.f64 N/A

          \[\leadsto z \cdot \left(x - t\right) \]

      12. +-commutative N/A

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

      13. lift-neg.f64 N/A

          \[\leadsto z \cdot \left(x - t\right) \]

      14. *-commutative N/A

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

      15. lower-*.f64 N/A

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

      16. lower--.f64 58.2

          \[\leadsto \left(x - t\right) \cdot z \]

   6. Applied rewrites 58.2%

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

Alternative 4: 69.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot y\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-21}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-119}:\\ \;\;\;\;x - t \cdot z\\ \mathbf{elif}\;y \leq 2500000000000:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t x) y)))
   (if (<= y -2.2e+81)
     t_1
     (if (<= y -5.5e-21)
       (* (- y z) t)
       (if (<= y 1.5e-119)
         (- x (* t z))
         (if (<= y 2500000000000.0) (fma z x x) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * y;
	double tmp;
	if (y <= -2.2e+81) {
		tmp = t_1;
	} else if (y <= -5.5e-21) {
		tmp = (y - z) * t;
	} else if (y <= 1.5e-119) {
		tmp = x - (t * z);
	} else if (y <= 2500000000000.0) {
		tmp = fma(z, x, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t - x) * y)
	tmp = 0.0
	if (y <= -2.2e+81)
		tmp = t_1;
	elseif (y <= -5.5e-21)
		tmp = Float64(Float64(y - z) * t);
	elseif (y <= 1.5e-119)
		tmp = Float64(x - Float64(t * z));
	elseif (y <= 2500000000000.0)
		tmp = fma(z, x, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -2.2e+81], t$95$1, If[LessEqual[y, -5.5e-21], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 1.5e-119], N[(x - N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2500000000000.0], N[(z * x + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.19999999999999987e81 or 2.5e12 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 81.5

         \[\leadsto \left(t - x\right) \cdot y \]

   4. Applied rewrites 81.5%

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

   if -2.19999999999999987e81 < y < -5.49999999999999977e-21

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 49.1

         \[\leadsto \left(y - z\right) \cdot t \]

   4. Applied rewrites 49.1%

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

   if -5.49999999999999977e-21 < y < 1.5000000000000001e-119

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 93.1

         \[\leadsto x - \left(t - x\right) \cdot z \]

   4. Applied rewrites 93.1%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 70.4%

      \[\leadsto x - t \cdot z \]

   if 1.5000000000000001e-119 < y < 2.5e12

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 76.8

         \[\leadsto x - \left(t - x\right) \cdot z \]

   4. Applied rewrites 76.8%

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

   5. Taylor expanded in x around -inf

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

      1. *-commutative N/A

         \[\leadsto \left(1 + z\right) \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \left(1 + z\right) \cdot x \]

      3. lower-+.f64 48.4

         \[\leadsto \left(1 + z\right) \cdot x \]

   7. Applied rewrites 48.4%

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

   8. Taylor expanded in t around 0

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

      1. associate-*r* N/A

         \[\leadsto x - \left(-1 \cdot x\right) \cdot z \]

      2. mul-1-neg N/A

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

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

         \[\leadsto x + x \cdot \color{blue}{z} \]

      4. +-commutative N/A

         \[\leadsto x \cdot z + x \]

      5. *-commutative N/A

         \[\leadsto z \cdot x + x \]

      6. lower-fma.f64 48.4

         \[\leadsto \mathsf{fma}\left(z, x, x\right) \]

   10. Applied rewrites 48.4%

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

Alternative 5: 66.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot y\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-138}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 2500000000000:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t x) y)))
   (if (<= y -2.2e+81)
     t_1
     (if (<= y -1.85e-138)
       (* (- y z) t)
       (if (<= y 2500000000000.0) (fma z x x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * y;
	double tmp;
	if (y <= -2.2e+81) {
		tmp = t_1;
	} else if (y <= -1.85e-138) {
		tmp = (y - z) * t;
	} else if (y <= 2500000000000.0) {
		tmp = fma(z, x, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t - x) * y)
	tmp = 0.0
	if (y <= -2.2e+81)
		tmp = t_1;
	elseif (y <= -1.85e-138)
		tmp = Float64(Float64(y - z) * t);
	elseif (y <= 2500000000000.0)
		tmp = fma(z, x, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -2.2e+81], t$95$1, If[LessEqual[y, -1.85e-138], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 2500000000000.0], N[(z * x + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.19999999999999987e81 or 2.5e12 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 81.5

         \[\leadsto \left(t - x\right) \cdot y \]

   4. Applied rewrites 81.5%

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

   if -2.19999999999999987e81 < y < -1.84999999999999995e-138

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 48.9

         \[\leadsto \left(y - z\right) \cdot t \]

   4. Applied rewrites 48.9%

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

   if -1.84999999999999995e-138 < y < 2.5e12

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 91.1

         \[\leadsto x - \left(t - x\right) \cdot z \]

   4. Applied rewrites 91.1%

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

   5. Taylor expanded in x around -inf

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

      1. *-commutative N/A

         \[\leadsto \left(1 + z\right) \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \left(1 + z\right) \cdot x \]

      3. lower-+.f64 56.8

         \[\leadsto \left(1 + z\right) \cdot x \]

   7. Applied rewrites 56.8%

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

   8. Taylor expanded in t around 0

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

      1. associate-*r* N/A

         \[\leadsto x - \left(-1 \cdot x\right) \cdot z \]

      2. mul-1-neg N/A

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

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

         \[\leadsto x + x \cdot \color{blue}{z} \]

      4. +-commutative N/A

         \[\leadsto x \cdot z + x \]

      5. *-commutative N/A

         \[\leadsto z \cdot x + x \]

      6. lower-fma.f64 56.8

         \[\leadsto \mathsf{fma}\left(z, x, x\right) \]

   10. Applied rewrites 56.8%

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

Alternative 6: 65.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot y\\ \mathbf{if}\;y \leq -0.05:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2500000000000:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t x) y)))
   (if (<= y -0.05) t_1 (if (<= y 2500000000000.0) (fma z x x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * y;
	double tmp;
	if (y <= -0.05) {
		tmp = t_1;
	} else if (y <= 2500000000000.0) {
		tmp = fma(z, x, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t - x) * y)
	tmp = 0.0
	if (y <= -0.05)
		tmp = t_1;
	elseif (y <= 2500000000000.0)
		tmp = fma(z, x, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -0.05], t$95$1, If[LessEqual[y, 2500000000000.0], N[(z * x + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.050000000000000003 or 2.5e12 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 78.2

         \[\leadsto \left(t - x\right) \cdot y \]

   4. Applied rewrites 78.2%

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

   if -0.050000000000000003 < y < 2.5e12

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 89.0

         \[\leadsto x - \left(t - x\right) \cdot z \]

   4. Applied rewrites 89.0%

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

   5. Taylor expanded in x around -inf

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

      1. *-commutative N/A

         \[\leadsto \left(1 + z\right) \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \left(1 + z\right) \cdot x \]

      3. lower-+.f64 55.9

         \[\leadsto \left(1 + z\right) \cdot x \]

   7. Applied rewrites 55.9%

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

   8. Taylor expanded in t around 0

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

      1. associate-*r* N/A

         \[\leadsto x - \left(-1 \cdot x\right) \cdot z \]

      2. mul-1-neg N/A

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

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

         \[\leadsto x + x \cdot \color{blue}{z} \]

      4. +-commutative N/A

         \[\leadsto x \cdot z + x \]

      5. *-commutative N/A

         \[\leadsto z \cdot x + x \]

      6. lower-fma.f64 55.9

         \[\leadsto \mathsf{fma}\left(z, x, x\right) \]

   10. Applied rewrites 55.9%

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

Alternative 7: 49.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.4:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;y \leq 50000000000000:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.4) (* t y) (if (<= y 50000000000000.0) (fma z x x) (* t y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.4) {
		tmp = t * y;
	} else if (y <= 50000000000000.0) {
		tmp = fma(z, x, x);
	} else {
		tmp = t * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.4)
		tmp = Float64(t * y);
	elseif (y <= 50000000000000.0)
		tmp = fma(z, x, x);
	else
		tmp = Float64(t * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.4], N[(t * y), $MachinePrecision], If[LessEqual[y, 50000000000000.0], N[(z * x + x), $MachinePrecision], N[(t * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.40000000000000002 or 5e13 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 78.3

         \[\leadsto \left(t - x\right) \cdot y \]

   4. Applied rewrites 78.3%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 42.8%

      \[\leadsto t \cdot y \]

   if -0.40000000000000002 < y < 5e13

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 88.9

         \[\leadsto x - \left(t - x\right) \cdot z \]

   4. Applied rewrites 88.9%

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

   5. Taylor expanded in x around -inf

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

      1. *-commutative N/A

         \[\leadsto \left(1 + z\right) \cdot x \]

      2. lower-*.f64 N/A

         \[\leadsto \left(1 + z\right) \cdot x \]

      3. lower-+.f64 55.8

         \[\leadsto \left(1 + z\right) \cdot x \]

   7. Applied rewrites 55.8%

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

   8. Taylor expanded in t around 0

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

      1. associate-*r* N/A

         \[\leadsto x - \left(-1 \cdot x\right) \cdot z \]

      2. mul-1-neg N/A

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

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

         \[\leadsto x + x \cdot \color{blue}{z} \]

      4. +-commutative N/A

         \[\leadsto x \cdot z + x \]

      5. *-commutative N/A

         \[\leadsto z \cdot x + x \]

      6. lower-fma.f64 55.8

         \[\leadsto \mathsf{fma}\left(z, x, x\right) \]

   10. Applied rewrites 55.8%

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

Alternative 8: 38.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{+267}:\\ \;\;\;\;\left(-z\right) \cdot t\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+46}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+60}:\\ \;\;\;\;t \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.9e+267)
   (* (- z) t)
   (if (<= z -6e+46) (* z x) (if (<= z 1.36e+60) (* t y) (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.9e+267) {
		tmp = -z * t;
	} else if (z <= -6e+46) {
		tmp = z * x;
	} else if (z <= 1.36e+60) {
		tmp = t * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.9d+267)) then
        tmp = -z * t
    else if (z <= (-6d+46)) then
        tmp = z * x
    else if (z <= 1.36d+60) then
        tmp = t * y
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.9e+267) {
		tmp = -z * t;
	} else if (z <= -6e+46) {
		tmp = z * x;
	} else if (z <= 1.36e+60) {
		tmp = t * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.9e+267:
		tmp = -z * t
	elif z <= -6e+46:
		tmp = z * x
	elif z <= 1.36e+60:
		tmp = t * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.9e+267)
		tmp = Float64(Float64(-z) * t);
	elseif (z <= -6e+46)
		tmp = Float64(z * x);
	elseif (z <= 1.36e+60)
		tmp = Float64(t * y);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.9e+267)
		tmp = -z * t;
	elseif (z <= -6e+46)
		tmp = z * x;
	elseif (z <= 1.36e+60)
		tmp = t * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.9e+267], N[((-z) * t), $MachinePrecision], If[LessEqual[z, -6e+46], N[(z * x), $MachinePrecision], If[LessEqual[z, 1.36e+60], N[(t * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.90000000000000021e267

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 97.6

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

   4. Applied rewrites 97.6%

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

   5. Taylor expanded in x around 0

      \[\leadsto \left(-z\right) \cdot t \]
   6. Step-by-step derivation

   7. Applied rewrites 51.4%

      \[\leadsto \left(-z\right) \cdot t \]

   if -5.90000000000000021e267 < z < -6.00000000000000047e46 or 1.36000000000000002e60 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 81.7

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

   4. Applied rewrites 81.7%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto z \cdot x \]

      2. lower-*.f64 42.2

         \[\leadsto z \cdot x \]

   7. Applied rewrites 42.2%

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

   if -6.00000000000000047e46 < z < 1.36000000000000002e60

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 56.6

         \[\leadsto \left(t - x\right) \cdot y \]

   4. Applied rewrites 56.6%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 34.5%

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

Alternative 9: 38.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+46}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+60}:\\ \;\;\;\;t \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6e+46) (* z x) (if (<= z 1.36e+60) (* t y) (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6e+46) {
		tmp = z * x;
	} else if (z <= 1.36e+60) {
		tmp = t * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6d+46)) then
        tmp = z * x
    else if (z <= 1.36d+60) then
        tmp = t * y
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6e+46) {
		tmp = z * x;
	} else if (z <= 1.36e+60) {
		tmp = t * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6e+46:
		tmp = z * x
	elif z <= 1.36e+60:
		tmp = t * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6e+46)
		tmp = Float64(z * x);
	elseif (z <= 1.36e+60)
		tmp = Float64(t * y);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6e+46)
		tmp = z * x;
	elseif (z <= 1.36e+60)
		tmp = t * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6e+46], N[(z * x), $MachinePrecision], If[LessEqual[z, 1.36e+60], N[(t * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.00000000000000047e46 or 1.36000000000000002e60 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 82.9

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

   4. Applied rewrites 82.9%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto z \cdot x \]

      2. lower-*.f64 43.4

         \[\leadsto z \cdot x \]

   7. Applied rewrites 43.4%

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

   if -6.00000000000000047e46 < z < 1.36000000000000002e60

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 56.6

         \[\leadsto \left(t - x\right) \cdot y \]

   4. Applied rewrites 56.6%

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

   5. Taylor expanded in x around 0

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

   7. Applied rewrites 34.5%

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

Alternative 10: 36.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00075:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 580:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.00075) (* z x) (if (<= z 580.0) x (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.00075) {
		tmp = z * x;
	} else if (z <= 580.0) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-0.00075d0)) then
        tmp = z * x
    else if (z <= 580.0d0) then
        tmp = x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.00075) {
		tmp = z * x;
	} else if (z <= 580.0) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -0.00075:
		tmp = z * x
	elif z <= 580.0:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.00075)
		tmp = Float64(z * x);
	elseif (z <= 580.0)
		tmp = x;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.00075)
		tmp = z * x;
	elseif (z <= 580.0)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.00075], N[(z * x), $MachinePrecision], If[LessEqual[z, 580.0], x, N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.5000000000000002e-4 or 580 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lift--.f64 78.4

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

   4. Applied rewrites 78.4%

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

   5. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto z \cdot x \]

      2. lower-*.f64 40.6

         \[\leadsto z \cdot x \]

   7. Applied rewrites 40.6%

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

   if -7.5000000000000002e-4 < z < 580

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0

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

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

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

      2. lower--.f64 N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 42.6

         \[\leadsto x - \left(t - x\right) \cdot z \]

   4. Applied rewrites 42.6%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 33.2%

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

Alternative 11: 18.0% accurate, 11.9× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around 0

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

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

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

   2. lower--.f64 N/A

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

   3. metadata-eval N/A

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

   4. *-lft-identity N/A

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

   5. *-commutative N/A

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

   6. lower-*.f64 N/A

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

   7. lift--.f64 60.7

      \[\leadsto x - \left(t - x\right) \cdot z \]

4. Applied rewrites 60.7%

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

5. Taylor expanded in z around 0

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

7. Applied rewrites 18.0%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025114 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64
  (+ x (* (- y z) (- t x))))