Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.4s

Alternatives: 12

Speedup: 1.0×

• 33.8% 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
3. Add Preprocessing

Alternative 2: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-59} \lor \neg \left(x \leq 1.4 \cdot 10^{-34}\right):\\ \;\;\;\;\left(1 - \left(y - z\right)\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -6.5e-59) (not (<= x 1.4e-34)))
   (* (- 1.0 (- y z)) x)
   (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6.5e-59) || !(x <= 1.4e-34)) {
		tmp = (1.0 - (y - z)) * x;
	} else {
		tmp = (y - z) * t;
	}
	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 ((x <= (-6.5d-59)) .or. (.not. (x <= 1.4d-34))) then
        tmp = (1.0d0 - (y - z)) * x
    else
        tmp = (y - z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -6.5e-59) || !(x <= 1.4e-34)) {
		tmp = (1.0 - (y - z)) * x;
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -6.5e-59) or not (x <= 1.4e-34):
		tmp = (1.0 - (y - z)) * x
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -6.5e-59) || !(x <= 1.4e-34))
		tmp = Float64(Float64(1.0 - Float64(y - z)) * x);
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -6.5e-59) || ~((x <= 1.4e-34)))
		tmp = (1.0 - (y - z)) * x;
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -6.5e-59], N[Not[LessEqual[x, 1.4e-34]], $MachinePrecision]], N[(N[(1.0 - N[(y - z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.50000000000000017e-59 or 1.39999999999999998e-34 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

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

      5. *-lft-identity N/A

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

      6. lower--.f64 N/A

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

      7. lift--.f64 86.8

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

   5. Applied rewrites 86.8%

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

   if -6.50000000000000017e-59 < x < 1.39999999999999998e-34

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t \cdot \left(y - z\right)} \]
   4. 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 85.3

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

   5. Applied rewrites 85.3%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-59} \lor \neg \left(x \leq 1.4 \cdot 10^{-34}\right):\\ \;\;\;\;\left(1 - \left(y - z\right)\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 37.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -980000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-163}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -980000.0)
   (* z x)
   (if (<= z -1.06e-163) (* y t) (if (<= z 6e-15) x (* z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -980000.0) {
		tmp = z * x;
	} else if (z <= -1.06e-163) {
		tmp = y * t;
	} else if (z <= 6e-15) {
		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 <= (-980000.0d0)) then
        tmp = z * x
    else if (z <= (-1.06d-163)) then
        tmp = y * t
    else if (z <= 6d-15) 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 <= -980000.0) {
		tmp = z * x;
	} else if (z <= -1.06e-163) {
		tmp = y * t;
	} else if (z <= 6e-15) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -980000.0:
		tmp = z * x
	elif z <= -1.06e-163:
		tmp = y * t
	elif z <= 6e-15:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -980000.0)
		tmp = Float64(z * x);
	elseif (z <= -1.06e-163)
		tmp = Float64(y * t);
	elseif (z <= 6e-15)
		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 <= -980000.0)
		tmp = z * x;
	elseif (z <= -1.06e-163)
		tmp = y * t;
	elseif (z <= 6e-15)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -980000.0], N[(z * x), $MachinePrecision], If[LessEqual[z, -1.06e-163], N[(y * t), $MachinePrecision], If[LessEqual[z, 6e-15], x, N[(z * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.8e5 or 6e-15 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(t - x\right)\right)} \]
   4. 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 73.4

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto z \cdot x \]

      2. lower-*.f64 41.2

         \[\leadsto z \cdot x \]

   8. Applied rewrites 41.2%

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

   if -9.8e5 < z < -1.06000000000000006e-163

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t \cdot \left(y - z\right)} \]
   4. 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 51.5

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

   5. Applied rewrites 51.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 42.5%

      \[\leadsto y \cdot t \]

   if -1.06000000000000006e-163 < z < 6e-15

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + y \cdot \left(t - x\right)} \]
   4. 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 91.7

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

   5. Applied rewrites 91.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 41.5%

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

Alternative 4: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+15}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(-z, t - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.5e+15)
   (fma (- t x) y x)
   (if (<= y 1.3e-5) (fma (- z) (- t x) x) (* (- t x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e+15) {
		tmp = fma((t - x), y, x);
	} else if (y <= 1.3e-5) {
		tmp = fma(-z, (t - x), x);
	} else {
		tmp = (t - x) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.5e+15)
		tmp = fma(Float64(t - x), y, x);
	elseif (y <= 1.3e-5)
		tmp = fma(Float64(-z), Float64(t - x), x);
	else
		tmp = Float64(Float64(t - x) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.5e+15], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[y, 1.3e-5], N[((-z) * N[(t - x), $MachinePrecision] + x), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5e15

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + y \cdot \left(t - x\right)} \]
   4. 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 83.1

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

   5. Applied rewrites 83.1%

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

   if -6.5e15 < y < 1.29999999999999992e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-fma.f64 N/A

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

      4. mul-1-neg N/A

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

      5. lower-neg.f64 N/A

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

      6. lift--.f64 91.5

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

   5. Applied rewrites 91.5%

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

   if 1.29999999999999992e-5 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(t - x\right)} \]
   4. 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 85.6

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

   5. Applied rewrites 85.6%

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

Alternative 5: 83.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1700000 \lor \neg \left(z \leq 2.35 \cdot 10^{+54}\right):\\ \;\;\;\;\left(-z\right) \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1700000.0) (not (<= z 2.35e+54)))
   (* (- z) (- t x))
   (fma (- t x) y x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1700000.0) || !(z <= 2.35e+54)) {
		tmp = -z * (t - x);
	} else {
		tmp = fma((t - x), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1700000.0) || !(z <= 2.35e+54))
		tmp = Float64(Float64(-z) * Float64(t - x));
	else
		tmp = fma(Float64(t - x), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1700000.0], N[Not[LessEqual[z, 2.35e+54]], $MachinePrecision]], N[((-z) * N[(t - x), $MachinePrecision]), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e6 or 2.34999999999999996e54 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(t - x\right)\right)} \]
   4. 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 77.7

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

   5. Applied rewrites 77.7%

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

   if -1.7e6 < z < 2.34999999999999996e54

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + y \cdot \left(t - x\right)} \]
   4. 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 87.8

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

   5. Applied rewrites 87.8%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1700000 \lor \neg \left(z \leq 2.35 \cdot 10^{+54}\right):\\ \;\;\;\;\left(-z\right) \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.024 \lor \neg \left(y \leq 1.3 \cdot 10^{-5}\right):\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -0.024) (not (<= y 1.3e-5))) (* (- t x) y) (fma z x x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.024) || !(y <= 1.3e-5)) {
		tmp = (t - x) * y;
	} else {
		tmp = fma(z, x, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -0.024) || !(y <= 1.3e-5))
		tmp = Float64(Float64(t - x) * y);
	else
		tmp = fma(z, x, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -0.024], N[Not[LessEqual[y, 1.3e-5]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision], N[(z * x + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.024 or 1.29999999999999992e-5 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(t - x\right)} \]
   4. 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 82.0

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

   5. Applied rewrites 82.0%

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

   if -0.024 < y < 1.29999999999999992e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(t - x\right)} \]
   4. 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 8.8

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

   5. Applied rewrites 8.8%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lift--.f64 65.7

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

   8. Applied rewrites 65.7%

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

   9. Taylor expanded in y around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 65.7

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

   11. Applied rewrites 65.7%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.024 \lor \neg \left(y \leq 1.3 \cdot 10^{-5}\right):\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-5}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.7e-5)
   (fma (- t x) y x)
   (if (<= y 1.3e-5) (fma z x x) (* (- t x) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.7e-5) {
		tmp = fma((t - x), y, x);
	} else if (y <= 1.3e-5) {
		tmp = fma(z, x, x);
	} else {
		tmp = (t - x) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.7e-5)
		tmp = fma(Float64(t - x), y, x);
	elseif (y <= 1.3e-5)
		tmp = fma(z, x, x);
	else
		tmp = Float64(Float64(t - x) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.7e-5], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision], If[LessEqual[y, 1.3e-5], N[(z * x + x), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6999999999999999e-5

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + y \cdot \left(t - x\right)} \]
   4. 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 80.6

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

   5. Applied rewrites 80.6%

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

   if -2.6999999999999999e-5 < y < 1.29999999999999992e-5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(t - x\right)} \]
   4. 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 8.8

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

   5. Applied rewrites 8.8%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lift--.f64 65.7

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

   8. Applied rewrites 65.7%

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

   9. Taylor expanded in y around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 65.7

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

   11. Applied rewrites 65.7%

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

   if 1.29999999999999992e-5 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(t - x\right)} \]
   4. 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 85.6

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

   5. Applied rewrites 85.6%

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

Alternative 8: 49.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -900000000 \lor \neg \left(y \leq 1550000000\right):\\ \;\;\;\;\left(-x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -900000000.0) (not (<= y 1550000000.0)))
   (* (- x) y)
   (fma z x x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -900000000.0) || !(y <= 1550000000.0)) {
		tmp = -x * y;
	} else {
		tmp = fma(z, x, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -900000000.0) || !(y <= 1550000000.0))
		tmp = Float64(Float64(-x) * y);
	else
		tmp = fma(z, x, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -900000000.0], N[Not[LessEqual[y, 1550000000.0]], $MachinePrecision]], N[((-x) * y), $MachinePrecision], N[(z * x + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9e8 or 1.55e9 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(t - x\right)} \]
   4. 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 83.4

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

   5. Applied rewrites 83.4%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(-1 \cdot x\right) \cdot y \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 51.2

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

   8. Applied rewrites 51.2%

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

   if -9e8 < y < 1.55e9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(t - x\right)} \]
   4. 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 10.2

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

   5. Applied rewrites 10.2%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lift--.f64 65.5

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

   8. Applied rewrites 65.5%

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

   9. Taylor expanded in y around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 64.9

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

   11. Applied rewrites 64.9%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -900000000 \lor \neg \left(y \leq 1550000000\right):\\ \;\;\;\;\left(-x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-56} \lor \neg \left(x \leq 380000000000\right):\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.95e-56) (not (<= x 380000000000.0)))
   (fma z x x)
   (fma t y x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.95e-56) || !(x <= 380000000000.0)) {
		tmp = fma(z, x, x);
	} else {
		tmp = fma(t, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.95e-56) || !(x <= 380000000000.0))
		tmp = fma(z, x, x);
	else
		tmp = fma(t, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.95e-56], N[Not[LessEqual[x, 380000000000.0]], $MachinePrecision]], N[(z * x + x), $MachinePrecision], N[(t * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.95e-56 or 3.8e11 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(t - x\right)} \]
   4. 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 41.9

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

   5. Applied rewrites 41.9%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lift--.f64 87.4

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

   8. Applied rewrites 87.4%

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

   9. Taylor expanded in y around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 56.6

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

   11. Applied rewrites 56.6%

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

   if -1.95e-56 < x < 3.8e11

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + y \cdot \left(t - x\right)} \]
   4. 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 57.7

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

   5. Applied rewrites 57.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 47.8%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{-56} \lor \neg \left(x \leq 380000000000\right):\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 49.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+65} \lor \neg \left(y \leq 16000\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.8e+65) (not (<= y 16000.0))) (* y t) (fma z x x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.8e+65) || !(y <= 16000.0)) {
		tmp = y * t;
	} else {
		tmp = fma(z, x, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.8e+65) || !(y <= 16000.0))
		tmp = Float64(y * t);
	else
		tmp = fma(z, x, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.8e+65], N[Not[LessEqual[y, 16000.0]], $MachinePrecision]], N[(y * t), $MachinePrecision], N[(z * x + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.79999999999999989e65 or 16000 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t \cdot \left(y - z\right)} \]
   4. 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 50.5

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

   5. Applied rewrites 50.5%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 39.4%

      \[\leadsto y \cdot t \]

   if -1.79999999999999989e65 < y < 16000

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(t - x\right)} \]
   4. 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 14.8

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

   5. Applied rewrites 14.8%

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

   6. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-*r* N/A

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

      3. mul-1-neg N/A

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

      4. lower-fma.f64 N/A

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

      5. lower-neg.f64 N/A

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

      6. lift--.f64 65.2

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

   8. Applied rewrites 65.2%

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

   9. Taylor expanded in y around 0

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

       1. +-commutative N/A

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

       2. *-commutative N/A

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

       3. lower-fma.f64 60.9

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

   11. Applied rewrites 60.9%

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

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+65} \lor \neg \left(y \leq 16000\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 6 \cdot 10^{-15}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 6e-15))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 6e-15)) {
		tmp = z * x;
	} else {
		tmp = 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 <= (-1.0d0)) .or. (.not. (z <= 6d-15))) then
        tmp = z * x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 6e-15)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 6e-15):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 6e-15))
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 6e-15)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 6e-15]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 6e-15 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(t - x\right)\right)} \]
   4. 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 73.4

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

   5. Applied rewrites 73.4%

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

   6. Taylor expanded in x around inf

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

      1. *-commutative N/A

         \[\leadsto z \cdot x \]

      2. lower-*.f64 41.2

         \[\leadsto z \cdot x \]

   8. Applied rewrites 41.2%

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

   if -1 < z < 6e-15

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x + y \cdot \left(t - x\right)} \]
   4. 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 91.5

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

   5. Applied rewrites 91.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 35.2%

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

4. Final simplification 38.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 6 \cdot 10^{-15}\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 17.3% accurate, 15.0× 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. Add Preprocessing

3. Taylor expanded in z around 0

   \[\leadsto \color{blue}{x + y \cdot \left(t - x\right)} \]
4. 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 60.5

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

5. Applied rewrites 60.5%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 17.6%

   \[\leadsto x \]
9. Add Preprocessing

Developer Target 1: 96.1% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2025064 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

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

  (+ x (* (- y z) (- t x))))