Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.7s

Alternatives: 13

Speedup: 1.0×

• 34.0% 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: 63.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ t_2 := \left(t - x\right) \cdot y\\ \mathbf{if}\;y \leq -0.0022:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-137}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 0.0054:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+67}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)) (t_2 (* (- t x) y)))
   (if (<= y -0.0022)
     t_2
     (if (<= y -1.75e-137)
       (fma z x x)
       (if (<= y 9.8e-141)
         t_1
         (if (<= y 0.0054) (fma z x x) (if (<= y 6.8e+67) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double t_2 = (t - x) * y;
	double tmp;
	if (y <= -0.0022) {
		tmp = t_2;
	} else if (y <= -1.75e-137) {
		tmp = fma(z, x, x);
	} else if (y <= 9.8e-141) {
		tmp = t_1;
	} else if (y <= 0.0054) {
		tmp = fma(z, x, x);
	} else if (y <= 6.8e+67) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	t_2 = Float64(Float64(t - x) * y)
	tmp = 0.0
	if (y <= -0.0022)
		tmp = t_2;
	elseif (y <= -1.75e-137)
		tmp = fma(z, x, x);
	elseif (y <= 9.8e-141)
		tmp = t_1;
	elseif (y <= 0.0054)
		tmp = fma(z, x, x);
	elseif (y <= 6.8e+67)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -0.0022], t$95$2, If[LessEqual[y, -1.75e-137], N[(z * x + x), $MachinePrecision], If[LessEqual[y, 9.8e-141], t$95$1, If[LessEqual[y, 0.0054], N[(z * x + x), $MachinePrecision], If[LessEqual[y, 6.8e+67], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.00220000000000000013 or 6.8000000000000003e67 < 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 81.6

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

   5. Applied rewrites 81.6%

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

   if -0.00220000000000000013 < y < -1.7500000000000001e-137 or 9.80000000000000012e-141 < y < 0.0054000000000000003

   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 68.1

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

   5. Applied rewrites 68.1%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 25.9%

      \[\leadsto z \cdot x \]

   9. Taylor expanded in y around 0

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

       1. *-commutative N/A

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

       2. +-commutative N/A

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

       3. distribute-lft1-in N/A

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

       4. lower-fma.f64 64.4

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

   11. Applied rewrites 64.4%

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

   if -1.7500000000000001e-137 < y < 9.80000000000000012e-141 or 0.0054000000000000003 < y < 6.8000000000000003e67

   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 66.1

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

   5. Applied rewrites 66.1%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0022:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-137}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-141}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 0.0054:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+67}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 38.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y - z \leq -2 \cdot 10^{+191}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y - z \leq -1 \cdot 10^{-6} \lor \neg \left(y - z \leq 5 \cdot 10^{-6}\right):\\ \;\;\;\;t \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (- y z) -2e+191)
   (* z x)
   (if (or (<= (- y z) -1e-6) (not (<= (- y z) 5e-6))) (* t y) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y - z) <= -2e+191) {
		tmp = z * x;
	} else if (((y - z) <= -1e-6) || !((y - z) <= 5e-6)) {
		tmp = t * y;
	} 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 ((y - z) <= (-2d+191)) then
        tmp = z * x
    else if (((y - z) <= (-1d-6)) .or. (.not. ((y - z) <= 5d-6))) then
        tmp = t * y
    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 ((y - z) <= -2e+191) {
		tmp = z * x;
	} else if (((y - z) <= -1e-6) || !((y - z) <= 5e-6)) {
		tmp = t * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y - z) <= -2e+191:
		tmp = z * x
	elif ((y - z) <= -1e-6) or not ((y - z) <= 5e-6):
		tmp = t * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(y - z) <= -2e+191)
		tmp = Float64(z * x);
	elseif ((Float64(y - z) <= -1e-6) || !(Float64(y - z) <= 5e-6))
		tmp = Float64(t * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y - z) <= -2e+191)
		tmp = z * x;
	elseif (((y - z) <= -1e-6) || ~(((y - z) <= 5e-6)))
		tmp = t * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(y - z), $MachinePrecision], -2e+191], N[(z * x), $MachinePrecision], If[Or[LessEqual[N[(y - z), $MachinePrecision], -1e-6], N[Not[LessEqual[N[(y - z), $MachinePrecision], 5e-6]], $MachinePrecision]], N[(t * y), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 y z) < -2.00000000000000015e191

   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 61.4

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

   5. Applied rewrites 61.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 36.3%

      \[\leadsto z \cdot x \]

   if -2.00000000000000015e191 < (-.f64 y z) < -9.99999999999999955e-7 or 5.00000000000000041e-6 < (-.f64 y z)

   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 54.9

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

   5. Applied rewrites 54.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 37.6%

      \[\leadsto t \cdot y \]

   if -9.99999999999999955e-7 < (-.f64 y z) < 5.00000000000000041e-6

   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 78.5

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

   5. Applied rewrites 78.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 67.6%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \leq -2 \cdot 10^{+191}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y - z \leq -1 \cdot 10^{-6} \lor \neg \left(y - z \leq 5 \cdot 10^{-6}\right):\\ \;\;\;\;t \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8500 \lor \neg \left(z \leq 2.5 \cdot 10^{+108}\right):\\ \;\;\;\;\left(-z\right) \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8500.0) (not (<= z 2.5e+108)))
   (* (- z) (- t x))
   (fma (- t x) y x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8500.0) || !(z <= 2.5e+108)) {
		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 <= -8500.0) || !(z <= 2.5e+108))
		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, -8500.0], N[Not[LessEqual[z, 2.5e+108]], $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 < -8500 or 2.49999999999999995e108 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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 86.8

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

   5. Applied rewrites 86.8%

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

   if -8500 < z < 2.49999999999999995e108

   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 88.0

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

   5. Applied rewrites 88.0%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8500 \lor \neg \left(z \leq 2.5 \cdot 10^{+108}\right):\\ \;\;\;\;\left(-z\right) \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6200:\\ \;\;\;\;\mathsf{fma}\left(-z, t - x, x\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+108}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6200.0)
   (fma (- z) (- t x) x)
   (if (<= z 2.5e+108) (fma (- t x) y x) (* (- z) (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6200.0) {
		tmp = fma(-z, (t - x), x);
	} else if (z <= 2.5e+108) {
		tmp = fma((t - x), y, x);
	} else {
		tmp = -z * (t - x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6200.0)
		tmp = fma(Float64(-z), Float64(t - x), x);
	elseif (z <= 2.5e+108)
		tmp = fma(Float64(t - x), y, x);
	else
		tmp = Float64(Float64(-z) * Float64(t - x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6200.0], N[((-z) * N[(t - x), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[z, 2.5e+108], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision], N[((-z) * N[(t - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6200

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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 81.6

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

   5. Applied rewrites 81.6%

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

   if -6200 < z < 2.49999999999999995e108

   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 88.0

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

   5. Applied rewrites 88.0%

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

   if 2.49999999999999995e108 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   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 95.6

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

   5. Applied rewrites 95.6%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6200:\\ \;\;\;\;\mathsf{fma}\left(-z, t - x, x\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+108}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1350 \lor \neg \left(z \leq 5.8 \cdot 10^{+74}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1350.0) (not (<= z 5.8e+74))) (* (- y z) t) (fma (- t x) y x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1350.0) || !(z <= 5.8e+74)) {
		tmp = (y - z) * t;
	} else {
		tmp = fma((t - x), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1350.0) || !(z <= 5.8e+74))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = fma(Float64(t - x), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1350.0], N[Not[LessEqual[z, 5.8e+74]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1350 or 5.8000000000000005e74 < z

   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 62.1

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

   5. Applied rewrites 62.1%

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

   if -1350 < z < 5.8000000000000005e74

   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 89.5

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

   5. Applied rewrites 89.5%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1350 \lor \neg \left(z \leq 5.8 \cdot 10^{+74}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+53} \lor \neg \left(x \leq 8.5 \cdot 10^{+87}\right):\\ \;\;\;\;\mathsf{fma}\left(-x, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.4e+53) (not (<= x 8.5e+87))) (fma (- x) y x) (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.4e+53) || !(x <= 8.5e+87)) {
		tmp = fma(-x, y, x);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.4e+53) || !(x <= 8.5e+87))
		tmp = fma(Float64(-x), y, x);
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.4e+53], N[Not[LessEqual[x, 8.5e+87]], $MachinePrecision]], N[((-x) * y + x), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.40000000000000039e53 or 8.5000000000000001e87 < x

   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 69.1

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

   5. Applied rewrites 69.1%

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

   6. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. lift-neg.f64 62.6

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

   8. Applied rewrites 62.6%

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

   if -5.40000000000000039e53 < x < 8.5000000000000001e87

   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 73.9

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

   5. Applied rewrites 73.9%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+53} \lor \neg \left(x \leq 8.5 \cdot 10^{+87}\right):\\ \;\;\;\;\mathsf{fma}\left(-x, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0022 \lor \neg \left(y \leq 0.01\right):\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -0.0022) (not (<= y 0.01))) (* (- t x) y) (fma z x x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.0022) || !(y <= 0.01)) {
		tmp = (t - x) * y;
	} else {
		tmp = fma(z, x, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -0.0022) || !(y <= 0.01))
		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, -0.0022], N[Not[LessEqual[y, 0.01]], $MachinePrecision]], N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision], N[(z * x + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00220000000000000013 or 0.0100000000000000002 < 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 77.9

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

   5. Applied rewrites 77.9%

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

   if -0.00220000000000000013 < y < 0.0100000000000000002

   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 55.8

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

   5. Applied rewrites 55.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 24.1%

      \[\leadsto z \cdot x \]

   9. Taylor expanded in y around 0

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

       1. *-commutative N/A

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

       2. +-commutative N/A

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

       3. distribute-lft1-in N/A

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

       4. lower-fma.f64 54.1

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

   11. Applied rewrites 54.1%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0022 \lor \neg \left(y \leq 0.01\right):\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1020 \lor \neg \left(z \leq 6.5 \cdot 10^{+74}\right):\\ \;\;\;\;\left(-z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1020.0) (not (<= z 6.5e+74))) (* (- z) t) (fma t y x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1020.0) || !(z <= 6.5e+74)) {
		tmp = -z * t;
	} else {
		tmp = fma(t, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1020.0) || !(z <= 6.5e+74))
		tmp = Float64(Float64(-z) * t);
	else
		tmp = fma(t, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1020.0], N[Not[LessEqual[z, 6.5e+74]], $MachinePrecision]], N[((-z) * t), $MachinePrecision], N[(t * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1020 or 6.49999999999999962e74 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing
   3. 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

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

      4. lift-*.f64 N/A

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

      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. distribute-rgt-out N/A

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

      11. associate-*r* N/A

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

      12. associate-+l+ N/A

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

      13. *-commutative N/A

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

      14. +-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lift--.f64 N/A

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

      17. +-commutative N/A

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

      18. associate-*r* N/A

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

      19. lower-fma.f64 N/A

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

      20. mul-1-neg N/A

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

      21. lower-neg.f64 N/A

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

      22. lift--.f64 99.1

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

   4. Applied rewrites 99.1%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot \left(t - x\right)\right)} \]
   6. 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. lift-neg.f64 N/A

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

      5. lift--.f64 84.9

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

   7. Applied rewrites 84.9%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 53.5%

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

   if -1020 < z < 6.49999999999999962e74

   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 89.5

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

   5. Applied rewrites 89.5%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 64.3%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1020 \lor \neg \left(z \leq 6.5 \cdot 10^{+74}\right):\\ \;\;\;\;\left(-z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-6} \lor \neg \left(z \leq 1.05 \cdot 10^{+115}\right):\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.6e-6) (not (<= z 1.05e+115))) (fma z x x) (fma t y x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.6e-6) || !(z <= 1.05e+115)) {
		tmp = fma(z, x, x);
	} else {
		tmp = fma(t, y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.6e-6) || !(z <= 1.05e+115))
		tmp = fma(z, x, x);
	else
		tmp = fma(t, y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.6e-6], N[Not[LessEqual[z, 1.05e+115]], $MachinePrecision]], N[(z * x + x), $MachinePrecision], N[(t * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.59999999999999984e-6 or 1.05000000000000002e115 < z

   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 48.8

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

   5. Applied rewrites 48.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 40.9%

      \[\leadsto z \cdot x \]

   9. Taylor expanded in y around 0

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

       1. *-commutative N/A

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

       2. +-commutative N/A

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

       3. distribute-lft1-in N/A

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

       4. lower-fma.f64 42.4

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

   11. Applied rewrites 42.4%

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

   if -3.59999999999999984e-6 < z < 1.05000000000000002e115

   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 87.7

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

   5. Applied rewrites 87.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 63.5%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-6} \lor \neg \left(z \leq 1.05 \cdot 10^{+115}\right):\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0022 \lor \neg \left(y \leq 0.01\right):\\ \;\;\;\;t \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -0.0022) (not (<= y 0.01))) (* t y) (fma z x x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.0022) || !(y <= 0.01)) {
		tmp = t * y;
	} else {
		tmp = fma(z, x, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -0.0022) || !(y <= 0.01))
		tmp = Float64(t * y);
	else
		tmp = fma(z, x, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -0.0022], N[Not[LessEqual[y, 0.01]], $MachinePrecision]], N[(t * y), $MachinePrecision], N[(z * x + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.00220000000000000013 or 0.0100000000000000002 < 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 77.9

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

   5. Applied rewrites 77.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 46.9%

      \[\leadsto t \cdot y \]

   if -0.00220000000000000013 < y < 0.0100000000000000002

   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 55.8

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

   5. Applied rewrites 55.8%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 24.1%

      \[\leadsto z \cdot x \]

   9. Taylor expanded in y around 0

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

       1. *-commutative N/A

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

       2. +-commutative N/A

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

       3. distribute-lft1-in N/A

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

       4. lower-fma.f64 54.1

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

   11. Applied rewrites 54.1%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0022 \lor \neg \left(y \leq 0.01\right):\\ \;\;\;\;t \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z, x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -125 \lor \neg \left(z \leq 0.0015\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -125.0) (not (<= z 0.0015))) (* z x) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -125.0) || !(z <= 0.0015)) {
		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 <= (-125.0d0)) .or. (.not. (z <= 0.0015d0))) 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 <= -125.0) || !(z <= 0.0015)) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -125.0) or not (z <= 0.0015):
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -125.0) || !(z <= 0.0015))
		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 <= -125.0) || ~((z <= 0.0015)))
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -125.0], N[Not[LessEqual[z, 0.0015]], $MachinePrecision]], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -125 or 0.0015 < z

   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 46.0

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

   5. Applied rewrites 46.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 34.7%

      \[\leadsto z \cdot x \]

   if -125 < z < 0.0015

   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 91.4

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

   5. Applied rewrites 91.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 29.4%

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

4. Final simplification 32.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -125 \lor \neg \left(z \leq 0.0015\right):\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 18.3% 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 60.3

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

5. Applied rewrites 60.3%

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

6. Taylor expanded in y around 0

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

8. Applied rewrites 15.5%

   \[\leadsto x \]

9. Final simplification 15.5%

   \[\leadsto x \]
10. Add Preprocessing

Developer Target 1: 96.2% 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 2025057 
(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))))