FastMath dist4

Percentage Accurate: 88.8% → 98.5%

Time: 7.3s

Alternatives: 12

Speedup: 1.7×

• 32.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)))

C

double code(double d1, double d2, double d3, double d4) {
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
}

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(d1, d2, d3, d4)
use fmin_fmax_functions
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    code = (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
}

Python

def code(d1, d2, d3, d4):
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)

Julia

function code(d1, d2, d3, d4)
	return Float64(Float64(Float64(Float64(d1 * d2) - Float64(d1 * d3)) + Float64(d4 * d1)) - Float64(d1 * d1))
end

MATLAB

function tmp = code(d1, d2, d3, d4)
	tmp = (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
end

Wolfram

code[d1_, d2_, d3_, d4_] := N[(N[(N[(N[(d1 * d2), $MachinePrecision] - N[(d1 * d3), $MachinePrecision]), $MachinePrecision] + N[(d4 * d1), $MachinePrecision]), $MachinePrecision] - N[(d1 * d1), $MachinePrecision]), $MachinePrecision]

Initial Program: 88.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)))

C

double code(double d1, double d2, double d3, double d4) {
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
}

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(d1, d2, d3, d4)
use fmin_fmax_functions
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    code = (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
}

Python

def code(d1, d2, d3, d4):
	return (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)

Julia

function code(d1, d2, d3, d4)
	return Float64(Float64(Float64(Float64(d1 * d2) - Float64(d1 * d3)) + Float64(d4 * d1)) - Float64(d1 * d1))
end

MATLAB

function tmp = code(d1, d2, d3, d4)
	tmp = (((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1);
end

Wolfram

code[d1_, d2_, d3_, d4_] := N[(N[(N[(N[(d1 * d2), $MachinePrecision] - N[(d1 * d3), $MachinePrecision]), $MachinePrecision] + N[(d4 * d1), $MachinePrecision]), $MachinePrecision] - N[(d1 * d1), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [d1, d2, d3, d4] = \mathsf{sort}([d1, d2, d3, d4])\\ \\ \begin{array}{l} \mathbf{if}\;\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(d1, d4 - d1, \left(d2 - d3\right) \cdot d1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(d2 - d3\right) - d1\right) \cdot d1\\ \end{array} \end{array} \]

FPCore

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)) INFINITY)
   (fma d1 (- d4 d1) (* (- d2 d3) d1))
   (* (- (- d2 d3) d1) d1)))

C

assert(d1 < d2 && d2 < d3 && d3 < d4);
double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (((((d1 * d2) - (d1 * d3)) + (d4 * d1)) - (d1 * d1)) <= ((double) INFINITY)) {
		tmp = fma(d1, (d4 - d1), ((d2 - d3) * d1));
	} else {
		tmp = ((d2 - d3) - d1) * d1;
	}
	return tmp;
}

Julia

d1, d2, d3, d4 = sort([d1, d2, d3, d4])
function code(d1, d2, d3, d4)
	tmp = 0.0
	if (Float64(Float64(Float64(Float64(d1 * d2) - Float64(d1 * d3)) + Float64(d4 * d1)) - Float64(d1 * d1)) <= Inf)
		tmp = fma(d1, Float64(d4 - d1), Float64(Float64(d2 - d3) * d1));
	else
		tmp = Float64(Float64(Float64(d2 - d3) - d1) * d1);
	end
	return tmp
end

Wolfram

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
code[d1_, d2_, d3_, d4_] := If[LessEqual[N[(N[(N[(N[(d1 * d2), $MachinePrecision] - N[(d1 * d3), $MachinePrecision]), $MachinePrecision] + N[(d4 * d1), $MachinePrecision]), $MachinePrecision] - N[(d1 * d1), $MachinePrecision]), $MachinePrecision], Infinity], N[(d1 * N[(d4 - d1), $MachinePrecision] + N[(N[(d2 - d3), $MachinePrecision] * d1), $MachinePrecision]), $MachinePrecision], N[(N[(N[(d2 - d3), $MachinePrecision] - d1), $MachinePrecision] * d1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 d1 d2) (*.f64 d1 d3)) (*.f64 d4 d1)) (*.f64 d1 d1)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right)} - d1 \cdot d1 \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{\left(d1 \cdot d2 - d1 \cdot d3\right) + \left(d4 \cdot d1 - d1 \cdot d1\right)} \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(d4 \cdot d1 - d1 \cdot d1\right) + \left(d1 \cdot d2 - d1 \cdot d3\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{d4 \cdot d1} - d1 \cdot d1\right) + \left(d1 \cdot d2 - d1 \cdot d3\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(d4 \cdot d1 - \color{blue}{d1 \cdot d1}\right) + \left(d1 \cdot d2 - d1 \cdot d3\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(d4 - d1\right)} + \left(d1 \cdot d2 - d1 \cdot d3\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(d1, d4 - d1, d1 \cdot d2 - d1 \cdot d3\right)} \]

      9. lower--.f64 100.0

         \[\leadsto \mathsf{fma}\left(d1, \color{blue}{d4 - d1}, d1 \cdot d2 - d1 \cdot d3\right) \]

      10. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{d1 \cdot d2 - d1 \cdot d3}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{d1 \cdot d2} - d1 \cdot d3\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, d1 \cdot d2 - \color{blue}{d1 \cdot d3}\right) \]

      13. distribute-lft-out-- N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{\left(d2 - d3\right) \cdot d1}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{\left(d2 - d3\right) \cdot d1}\right) \]

      16. lower--.f64 100.0

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{\left(d2 - d3\right)} \cdot d1\right) \]

   4. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(d1, d4 - d1, \left(d2 - d3\right) \cdot d1\right)} \]

   if +inf.0 < (-.f64 (+.f64 (-.f64 (*.f64 d1 d2) (*.f64 d1 d3)) (*.f64 d4 d1)) (*.f64 d1 d1))

   1. Initial program 0.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot d2 - \left(d1 \cdot d3 + {d1}^{2}\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(d1 \cdot d2 - d1 \cdot d3\right) - {d1}^{2}} \]

      2. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(d2 - d3\right)} - {d1}^{2} \]

      3. unpow2 N/A

         \[\leadsto d1 \cdot \left(d2 - d3\right) - \color{blue}{d1 \cdot d1} \]

      4. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - d3\right) - d1\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      7. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right)} \cdot d1 \]

      8. lower--.f64 84.6

         \[\leadsto \left(\color{blue}{\left(d2 - d3\right)} - d1\right) \cdot d1 \]

   5. Applied rewrites 84.6%

      \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 51.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} [d1, d2, d3, d4] = \mathsf{sort}([d1, d2, d3, d4])\\ \\ \begin{array}{l} \mathbf{if}\;d4 \leq -2.3 \cdot 10^{-163}:\\ \;\;\;\;d2 \cdot d1\\ \mathbf{elif}\;d4 \leq 5.2 \cdot 10^{+50}:\\ \;\;\;\;\left(-d3\right) \cdot d1\\ \mathbf{elif}\;d4 \leq 1.6 \cdot 10^{+129}:\\ \;\;\;\;\left(-d1\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;d4 \cdot d1\\ \end{array} \end{array} \]

FPCore

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 -2.3e-163)
   (* d2 d1)
   (if (<= d4 5.2e+50)
     (* (- d3) d1)
     (if (<= d4 1.6e+129) (* (- d1) d1) (* d4 d1)))))

C

assert(d1 < d2 && d2 < d3 && d3 < d4);
double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= -2.3e-163) {
		tmp = d2 * d1;
	} else if (d4 <= 5.2e+50) {
		tmp = -d3 * d1;
	} else if (d4 <= 1.6e+129) {
		tmp = -d1 * d1;
	} else {
		tmp = d4 * d1;
	}
	return tmp;
}

Fortran

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
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(d1, d2, d3, d4)
use fmin_fmax_functions
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d4 <= (-2.3d-163)) then
        tmp = d2 * d1
    else if (d4 <= 5.2d+50) then
        tmp = -d3 * d1
    else if (d4 <= 1.6d+129) then
        tmp = -d1 * d1
    else
        tmp = d4 * d1
    end if
    code = tmp
end function

Java

assert d1 < d2 && d2 < d3 && d3 < d4;
public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= -2.3e-163) {
		tmp = d2 * d1;
	} else if (d4 <= 5.2e+50) {
		tmp = -d3 * d1;
	} else if (d4 <= 1.6e+129) {
		tmp = -d1 * d1;
	} else {
		tmp = d4 * d1;
	}
	return tmp;
}

Python

[d1, d2, d3, d4] = sort([d1, d2, d3, d4])
def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= -2.3e-163:
		tmp = d2 * d1
	elif d4 <= 5.2e+50:
		tmp = -d3 * d1
	elif d4 <= 1.6e+129:
		tmp = -d1 * d1
	else:
		tmp = d4 * d1
	return tmp

Julia

d1, d2, d3, d4 = sort([d1, d2, d3, d4])
function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= -2.3e-163)
		tmp = Float64(d2 * d1);
	elseif (d4 <= 5.2e+50)
		tmp = Float64(Float64(-d3) * d1);
	elseif (d4 <= 1.6e+129)
		tmp = Float64(Float64(-d1) * d1);
	else
		tmp = Float64(d4 * d1);
	end
	return tmp
end

MATLAB

d1, d2, d3, d4 = num2cell(sort([d1, d2, d3, d4])){:}
function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d4 <= -2.3e-163)
		tmp = d2 * d1;
	elseif (d4 <= 5.2e+50)
		tmp = -d3 * d1;
	elseif (d4 <= 1.6e+129)
		tmp = -d1 * d1;
	else
		tmp = d4 * d1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, -2.3e-163], N[(d2 * d1), $MachinePrecision], If[LessEqual[d4, 5.2e+50], N[((-d3) * d1), $MachinePrecision], If[LessEqual[d4, 1.6e+129], N[((-d1) * d1), $MachinePrecision], N[(d4 * d1), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if d4 < -2.2999999999999999e-163

   1. Initial program 92.3%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right)} - d1 \cdot d1 \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{\left(d1 \cdot d2 - d1 \cdot d3\right) + \left(d4 \cdot d1 - d1 \cdot d1\right)} \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(d4 \cdot d1 - d1 \cdot d1\right) + \left(d1 \cdot d2 - d1 \cdot d3\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{d4 \cdot d1} - d1 \cdot d1\right) + \left(d1 \cdot d2 - d1 \cdot d3\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(d4 \cdot d1 - \color{blue}{d1 \cdot d1}\right) + \left(d1 \cdot d2 - d1 \cdot d3\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(d4 - d1\right)} + \left(d1 \cdot d2 - d1 \cdot d3\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(d1, d4 - d1, d1 \cdot d2 - d1 \cdot d3\right)} \]

      9. lower--.f64 97.1

         \[\leadsto \mathsf{fma}\left(d1, \color{blue}{d4 - d1}, d1 \cdot d2 - d1 \cdot d3\right) \]

      10. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{d1 \cdot d2 - d1 \cdot d3}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{d1 \cdot d2} - d1 \cdot d3\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, d1 \cdot d2 - \color{blue}{d1 \cdot d3}\right) \]

      13. distribute-lft-out-- N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{\left(d2 - d3\right) \cdot d1}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{\left(d2 - d3\right) \cdot d1}\right) \]

      16. lower--.f64 97.1

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{\left(d2 - d3\right)} \cdot d1\right) \]

   4. Applied rewrites 97.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(d1, d4 - d1, \left(d2 - d3\right) \cdot d1\right)} \]

   5. Taylor expanded in d2 around inf

      \[\leadsto \color{blue}{d1 \cdot d2} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{d2 \cdot d1} \]

      2. lower-*.f64 22.8

         \[\leadsto \color{blue}{d2 \cdot d1} \]

   7. Applied rewrites 22.8%

      \[\leadsto \color{blue}{d2 \cdot d1} \]

   if -2.2999999999999999e-163 < d4 < 5.2000000000000004e50

   1. Initial program 90.7%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot d2 - \left(d1 \cdot d3 + {d1}^{2}\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(d1 \cdot d2 - d1 \cdot d3\right) - {d1}^{2}} \]

      2. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(d2 - d3\right)} - {d1}^{2} \]

      3. unpow2 N/A

         \[\leadsto d1 \cdot \left(d2 - d3\right) - \color{blue}{d1 \cdot d1} \]

      4. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - d3\right) - d1\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      7. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right)} \cdot d1 \]

      8. lower--.f64 92.4

         \[\leadsto \left(\color{blue}{\left(d2 - d3\right)} - d1\right) \cdot d1 \]

   5. Applied rewrites 92.4%

      \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

   6. Taylor expanded in d1 around 0

      \[\leadsto \left(d2 - d3\right) \cdot d1 \]
   7. Step-by-step derivation

   8. Applied rewrites 67.1%

      \[\leadsto \left(d2 - d3\right) \cdot d1 \]

   9. Taylor expanded in d2 around 0

      \[\leadsto \left(-1 \cdot d3\right) \cdot d1 \]
   10. Step-by-step derivation

   11. Applied rewrites 46.4%

       \[\leadsto \left(-d3\right) \cdot d1 \]

   if 5.2000000000000004e50 < d4 < 1.6000000000000001e129

   1. Initial program 94.7%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d1 around inf

      \[\leadsto \color{blue}{-1 \cdot {d1}^{2}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

         \[\leadsto -1 \cdot \color{blue}{\left(d1 \cdot d1\right)} \]

      2. associate-*r* N/A

         \[\leadsto \color{blue}{\left(-1 \cdot d1\right) \cdot d1} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(-1 \cdot d1\right) \cdot d1} \]

      4. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(d1\right)\right)} \cdot d1 \]

      5. lower-neg.f64 34.1

         \[\leadsto \color{blue}{\left(-d1\right)} \cdot d1 \]

   5. Applied rewrites 34.1%

      \[\leadsto \color{blue}{\left(-d1\right) \cdot d1} \]

   if 1.6000000000000001e129 < d4

   1. Initial program 80.8%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d4 around inf

      \[\leadsto \color{blue}{d1 \cdot d4} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{d4 \cdot d1} \]

      2. lower-*.f64 72.8

         \[\leadsto \color{blue}{d4 \cdot d1} \]

   5. Applied rewrites 72.8%

      \[\leadsto \color{blue}{d4 \cdot d1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d4 \leq -2.3 \cdot 10^{-163}:\\ \;\;\;\;d2 \cdot d1\\ \mathbf{elif}\;d4 \leq 5.2 \cdot 10^{+50}:\\ \;\;\;\;\left(-d3\right) \cdot d1\\ \mathbf{elif}\;d4 \leq 1.6 \cdot 10^{+129}:\\ \;\;\;\;\left(-d1\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;d4 \cdot d1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} [d1, d2, d3, d4] = \mathsf{sort}([d1, d2, d3, d4])\\ \\ \begin{array}{l} \mathbf{if}\;d1 \leq -1.5 \cdot 10^{+151}:\\ \;\;\;\;\left(\left(-d3\right) - d1\right) \cdot d1\\ \mathbf{elif}\;d1 \leq 8 \cdot 10^{+93}:\\ \;\;\;\;\left(\left(d4 + d2\right) - d3\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(d2 - d1\right) \cdot d1\\ \end{array} \end{array} \]

FPCore

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d1 -1.5e+151)
   (* (- (- d3) d1) d1)
   (if (<= d1 8e+93) (* (- (+ d4 d2) d3) d1) (* (- d2 d1) d1))))

C

assert(d1 < d2 && d2 < d3 && d3 < d4);
double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d1 <= -1.5e+151) {
		tmp = (-d3 - d1) * d1;
	} else if (d1 <= 8e+93) {
		tmp = ((d4 + d2) - d3) * d1;
	} else {
		tmp = (d2 - d1) * d1;
	}
	return tmp;
}

Fortran

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
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(d1, d2, d3, d4)
use fmin_fmax_functions
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d1 <= (-1.5d+151)) then
        tmp = (-d3 - d1) * d1
    else if (d1 <= 8d+93) then
        tmp = ((d4 + d2) - d3) * d1
    else
        tmp = (d2 - d1) * d1
    end if
    code = tmp
end function

Java

assert d1 < d2 && d2 < d3 && d3 < d4;
public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d1 <= -1.5e+151) {
		tmp = (-d3 - d1) * d1;
	} else if (d1 <= 8e+93) {
		tmp = ((d4 + d2) - d3) * d1;
	} else {
		tmp = (d2 - d1) * d1;
	}
	return tmp;
}

Python

[d1, d2, d3, d4] = sort([d1, d2, d3, d4])
def code(d1, d2, d3, d4):
	tmp = 0
	if d1 <= -1.5e+151:
		tmp = (-d3 - d1) * d1
	elif d1 <= 8e+93:
		tmp = ((d4 + d2) - d3) * d1
	else:
		tmp = (d2 - d1) * d1
	return tmp

Julia

d1, d2, d3, d4 = sort([d1, d2, d3, d4])
function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d1 <= -1.5e+151)
		tmp = Float64(Float64(Float64(-d3) - d1) * d1);
	elseif (d1 <= 8e+93)
		tmp = Float64(Float64(Float64(d4 + d2) - d3) * d1);
	else
		tmp = Float64(Float64(d2 - d1) * d1);
	end
	return tmp
end

MATLAB

d1, d2, d3, d4 = num2cell(sort([d1, d2, d3, d4])){:}
function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d1 <= -1.5e+151)
		tmp = (-d3 - d1) * d1;
	elseif (d1 <= 8e+93)
		tmp = ((d4 + d2) - d3) * d1;
	else
		tmp = (d2 - d1) * d1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
code[d1_, d2_, d3_, d4_] := If[LessEqual[d1, -1.5e+151], N[(N[((-d3) - d1), $MachinePrecision] * d1), $MachinePrecision], If[LessEqual[d1, 8e+93], N[(N[(N[(d4 + d2), $MachinePrecision] - d3), $MachinePrecision] * d1), $MachinePrecision], N[(N[(d2 - d1), $MachinePrecision] * d1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d1 < -1.5e151

   1. Initial program 67.6%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot d2 - \left(d1 \cdot d3 + {d1}^{2}\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(d1 \cdot d2 - d1 \cdot d3\right) - {d1}^{2}} \]

      2. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(d2 - d3\right)} - {d1}^{2} \]

      3. unpow2 N/A

         \[\leadsto d1 \cdot \left(d2 - d3\right) - \color{blue}{d1 \cdot d1} \]

      4. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - d3\right) - d1\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      7. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right)} \cdot d1 \]

      8. lower--.f64 97.1

         \[\leadsto \left(\color{blue}{\left(d2 - d3\right)} - d1\right) \cdot d1 \]

   5. Applied rewrites 97.1%

      \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

   6. Taylor expanded in d2 around 0

      \[\leadsto \left(-1 \cdot d3 - d1\right) \cdot d1 \]
   7. Step-by-step derivation

   8. Applied rewrites 97.1%

      \[\leadsto \left(\left(-d3\right) - d1\right) \cdot d1 \]

   if -1.5e151 < d1 < 8.00000000000000035e93

   1. Initial program 98.8%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right) \cdot d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right) \cdot d1} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right)} \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(d4 + d2\right)} - d3\right) \cdot d1 \]

      5. lower-+.f64 91.9

         \[\leadsto \left(\color{blue}{\left(d4 + d2\right)} - d3\right) \cdot d1 \]

   5. Applied rewrites 91.9%

      \[\leadsto \color{blue}{\left(\left(d4 + d2\right) - d3\right) \cdot d1} \]

   if 8.00000000000000035e93 < d1

   1. Initial program 67.5%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot d2 - \left(d1 \cdot d3 + {d1}^{2}\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(d1 \cdot d2 - d1 \cdot d3\right) - {d1}^{2}} \]

      2. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(d2 - d3\right)} - {d1}^{2} \]

      3. unpow2 N/A

         \[\leadsto d1 \cdot \left(d2 - d3\right) - \color{blue}{d1 \cdot d1} \]

      4. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - d3\right) - d1\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      7. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right)} \cdot d1 \]

      8. lower--.f64 88.2

         \[\leadsto \left(\color{blue}{\left(d2 - d3\right)} - d1\right) \cdot d1 \]

   5. Applied rewrites 88.2%

      \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

   6. Taylor expanded in d3 around 0

      \[\leadsto \left(d2 - d1\right) \cdot d1 \]
   7. Step-by-step derivation

   8. Applied rewrites 83.2%

      \[\leadsto \left(d2 - d1\right) \cdot d1 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 74.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [d1, d2, d3, d4] = \mathsf{sort}([d1, d2, d3, d4])\\ \\ \begin{array}{l} \mathbf{if}\;d4 \leq -2.3 \cdot 10^{-163}:\\ \;\;\;\;\left(d2 - d1\right) \cdot d1\\ \mathbf{elif}\;d4 \leq 1.6 \cdot 10^{+129}:\\ \;\;\;\;\left(\left(-d3\right) - d1\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(d4 - d3\right) \cdot d1\\ \end{array} \end{array} \]

FPCore

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 -2.3e-163)
   (* (- d2 d1) d1)
   (if (<= d4 1.6e+129) (* (- (- d3) d1) d1) (* (- d4 d3) d1))))

C

assert(d1 < d2 && d2 < d3 && d3 < d4);
double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= -2.3e-163) {
		tmp = (d2 - d1) * d1;
	} else if (d4 <= 1.6e+129) {
		tmp = (-d3 - d1) * d1;
	} else {
		tmp = (d4 - d3) * d1;
	}
	return tmp;
}

Fortran

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
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(d1, d2, d3, d4)
use fmin_fmax_functions
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d4 <= (-2.3d-163)) then
        tmp = (d2 - d1) * d1
    else if (d4 <= 1.6d+129) then
        tmp = (-d3 - d1) * d1
    else
        tmp = (d4 - d3) * d1
    end if
    code = tmp
end function

Java

assert d1 < d2 && d2 < d3 && d3 < d4;
public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= -2.3e-163) {
		tmp = (d2 - d1) * d1;
	} else if (d4 <= 1.6e+129) {
		tmp = (-d3 - d1) * d1;
	} else {
		tmp = (d4 - d3) * d1;
	}
	return tmp;
}

Python

[d1, d2, d3, d4] = sort([d1, d2, d3, d4])
def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= -2.3e-163:
		tmp = (d2 - d1) * d1
	elif d4 <= 1.6e+129:
		tmp = (-d3 - d1) * d1
	else:
		tmp = (d4 - d3) * d1
	return tmp

Julia

d1, d2, d3, d4 = sort([d1, d2, d3, d4])
function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= -2.3e-163)
		tmp = Float64(Float64(d2 - d1) * d1);
	elseif (d4 <= 1.6e+129)
		tmp = Float64(Float64(Float64(-d3) - d1) * d1);
	else
		tmp = Float64(Float64(d4 - d3) * d1);
	end
	return tmp
end

MATLAB

d1, d2, d3, d4 = num2cell(sort([d1, d2, d3, d4])){:}
function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d4 <= -2.3e-163)
		tmp = (d2 - d1) * d1;
	elseif (d4 <= 1.6e+129)
		tmp = (-d3 - d1) * d1;
	else
		tmp = (d4 - d3) * d1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, -2.3e-163], N[(N[(d2 - d1), $MachinePrecision] * d1), $MachinePrecision], If[LessEqual[d4, 1.6e+129], N[(N[((-d3) - d1), $MachinePrecision] * d1), $MachinePrecision], N[(N[(d4 - d3), $MachinePrecision] * d1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d4 < -2.2999999999999999e-163

   1. Initial program 92.3%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot d2 - \left(d1 \cdot d3 + {d1}^{2}\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(d1 \cdot d2 - d1 \cdot d3\right) - {d1}^{2}} \]

      2. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(d2 - d3\right)} - {d1}^{2} \]

      3. unpow2 N/A

         \[\leadsto d1 \cdot \left(d2 - d3\right) - \color{blue}{d1 \cdot d1} \]

      4. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - d3\right) - d1\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      7. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right)} \cdot d1 \]

      8. lower--.f64 72.0

         \[\leadsto \left(\color{blue}{\left(d2 - d3\right)} - d1\right) \cdot d1 \]

   5. Applied rewrites 72.0%

      \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

   6. Taylor expanded in d3 around 0

      \[\leadsto \left(d2 - d1\right) \cdot d1 \]
   7. Step-by-step derivation

   8. Applied rewrites 51.3%

      \[\leadsto \left(d2 - d1\right) \cdot d1 \]

   if -2.2999999999999999e-163 < d4 < 1.6000000000000001e129

   1. Initial program 91.4%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot d2 - \left(d1 \cdot d3 + {d1}^{2}\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(d1 \cdot d2 - d1 \cdot d3\right) - {d1}^{2}} \]

      2. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(d2 - d3\right)} - {d1}^{2} \]

      3. unpow2 N/A

         \[\leadsto d1 \cdot \left(d2 - d3\right) - \color{blue}{d1 \cdot d1} \]

      4. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - d3\right) - d1\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      7. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right)} \cdot d1 \]

      8. lower--.f64 90.1

         \[\leadsto \left(\color{blue}{\left(d2 - d3\right)} - d1\right) \cdot d1 \]

   5. Applied rewrites 90.1%

      \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

   6. Taylor expanded in d2 around 0

      \[\leadsto \left(-1 \cdot d3 - d1\right) \cdot d1 \]
   7. Step-by-step derivation

   8. Applied rewrites 65.5%

      \[\leadsto \left(\left(-d3\right) - d1\right) \cdot d1 \]

   if 1.6000000000000001e129 < d4

   1. Initial program 80.8%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right) \cdot d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right) \cdot d1} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right)} \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(d4 + d2\right)} - d3\right) \cdot d1 \]

      5. lower-+.f64 93.6

         \[\leadsto \left(\color{blue}{\left(d4 + d2\right)} - d3\right) \cdot d1 \]

   5. Applied rewrites 93.6%

      \[\leadsto \color{blue}{\left(\left(d4 + d2\right) - d3\right) \cdot d1} \]

   6. Taylor expanded in d2 around 0

      \[\leadsto \left(d4 - d3\right) \cdot d1 \]
   7. Step-by-step derivation

   8. Applied rewrites 87.2%

      \[\leadsto \left(d4 - d3\right) \cdot d1 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 68.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [d1, d2, d3, d4] = \mathsf{sort}([d1, d2, d3, d4])\\ \\ \begin{array}{l} \mathbf{if}\;d3 \leq -5.2 \cdot 10^{+110} \lor \neg \left(d3 \leq 6.5 \cdot 10^{+155}\right):\\ \;\;\;\;\left(-d3\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(d2 + d4\right) \cdot d1\\ \end{array} \end{array} \]

FPCore

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (or (<= d3 -5.2e+110) (not (<= d3 6.5e+155)))
   (* (- d3) d1)
   (* (+ d2 d4) d1)))

C

assert(d1 < d2 && d2 < d3 && d3 < d4);
double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if ((d3 <= -5.2e+110) || !(d3 <= 6.5e+155)) {
		tmp = -d3 * d1;
	} else {
		tmp = (d2 + d4) * d1;
	}
	return tmp;
}

Fortran

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
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(d1, d2, d3, d4)
use fmin_fmax_functions
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if ((d3 <= (-5.2d+110)) .or. (.not. (d3 <= 6.5d+155))) then
        tmp = -d3 * d1
    else
        tmp = (d2 + d4) * d1
    end if
    code = tmp
end function

Java

assert d1 < d2 && d2 < d3 && d3 < d4;
public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if ((d3 <= -5.2e+110) || !(d3 <= 6.5e+155)) {
		tmp = -d3 * d1;
	} else {
		tmp = (d2 + d4) * d1;
	}
	return tmp;
}

Python

[d1, d2, d3, d4] = sort([d1, d2, d3, d4])
def code(d1, d2, d3, d4):
	tmp = 0
	if (d3 <= -5.2e+110) or not (d3 <= 6.5e+155):
		tmp = -d3 * d1
	else:
		tmp = (d2 + d4) * d1
	return tmp

Julia

d1, d2, d3, d4 = sort([d1, d2, d3, d4])
function code(d1, d2, d3, d4)
	tmp = 0.0
	if ((d3 <= -5.2e+110) || !(d3 <= 6.5e+155))
		tmp = Float64(Float64(-d3) * d1);
	else
		tmp = Float64(Float64(d2 + d4) * d1);
	end
	return tmp
end

MATLAB

d1, d2, d3, d4 = num2cell(sort([d1, d2, d3, d4])){:}
function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if ((d3 <= -5.2e+110) || ~((d3 <= 6.5e+155)))
		tmp = -d3 * d1;
	else
		tmp = (d2 + d4) * d1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
code[d1_, d2_, d3_, d4_] := If[Or[LessEqual[d3, -5.2e+110], N[Not[LessEqual[d3, 6.5e+155]], $MachinePrecision]], N[((-d3) * d1), $MachinePrecision], N[(N[(d2 + d4), $MachinePrecision] * d1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d3 < -5.2e110 or 6.50000000000000046e155 < d3

   1. Initial program 87.3%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot d2 - \left(d1 \cdot d3 + {d1}^{2}\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(d1 \cdot d2 - d1 \cdot d3\right) - {d1}^{2}} \]

      2. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(d2 - d3\right)} - {d1}^{2} \]

      3. unpow2 N/A

         \[\leadsto d1 \cdot \left(d2 - d3\right) - \color{blue}{d1 \cdot d1} \]

      4. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - d3\right) - d1\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      7. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right)} \cdot d1 \]

      8. lower--.f64 88.1

         \[\leadsto \left(\color{blue}{\left(d2 - d3\right)} - d1\right) \cdot d1 \]

   5. Applied rewrites 88.1%

      \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

   6. Taylor expanded in d1 around 0

      \[\leadsto \left(d2 - d3\right) \cdot d1 \]
   7. Step-by-step derivation

   8. Applied rewrites 86.7%

      \[\leadsto \left(d2 - d3\right) \cdot d1 \]

   9. Taylor expanded in d2 around 0

      \[\leadsto \left(-1 \cdot d3\right) \cdot d1 \]
   10. Step-by-step derivation

   11. Applied rewrites 81.6%

       \[\leadsto \left(-d3\right) \cdot d1 \]

   if -5.2e110 < d3 < 6.50000000000000046e155

   1. Initial program 90.8%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right) \cdot d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right) \cdot d1} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right)} \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(d4 + d2\right)} - d3\right) \cdot d1 \]

      5. lower-+.f64 72.6

         \[\leadsto \left(\color{blue}{\left(d4 + d2\right)} - d3\right) \cdot d1 \]

   5. Applied rewrites 72.6%

      \[\leadsto \color{blue}{\left(\left(d4 + d2\right) - d3\right) \cdot d1} \]

   6. Taylor expanded in d3 around 0

      \[\leadsto d1 \cdot \color{blue}{\left(d2 + d4\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 65.9%

      \[\leadsto \left(d2 + d4\right) \cdot \color{blue}{d1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq -5.2 \cdot 10^{+110} \lor \neg \left(d3 \leq 6.5 \cdot 10^{+155}\right):\\ \;\;\;\;\left(-d3\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(d2 + d4\right) \cdot d1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} [d1, d2, d3, d4] = \mathsf{sort}([d1, d2, d3, d4])\\ \\ \begin{array}{l} \mathbf{if}\;d2 \leq -1 \cdot 10^{+35}:\\ \;\;\;\;\left(d2 - d3\right) \cdot d1\\ \mathbf{elif}\;d2 \leq -1.85 \cdot 10^{-24}:\\ \;\;\;\;\left(d2 - d1\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(d4 - d3\right) \cdot d1\\ \end{array} \end{array} \]

FPCore

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -1e+35)
   (* (- d2 d3) d1)
   (if (<= d2 -1.85e-24) (* (- d2 d1) d1) (* (- d4 d3) d1))))

C

assert(d1 < d2 && d2 < d3 && d3 < d4);
double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -1e+35) {
		tmp = (d2 - d3) * d1;
	} else if (d2 <= -1.85e-24) {
		tmp = (d2 - d1) * d1;
	} else {
		tmp = (d4 - d3) * d1;
	}
	return tmp;
}

Fortran

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
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(d1, d2, d3, d4)
use fmin_fmax_functions
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d2 <= (-1d+35)) then
        tmp = (d2 - d3) * d1
    else if (d2 <= (-1.85d-24)) then
        tmp = (d2 - d1) * d1
    else
        tmp = (d4 - d3) * d1
    end if
    code = tmp
end function

Java

assert d1 < d2 && d2 < d3 && d3 < d4;
public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -1e+35) {
		tmp = (d2 - d3) * d1;
	} else if (d2 <= -1.85e-24) {
		tmp = (d2 - d1) * d1;
	} else {
		tmp = (d4 - d3) * d1;
	}
	return tmp;
}

Python

[d1, d2, d3, d4] = sort([d1, d2, d3, d4])
def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -1e+35:
		tmp = (d2 - d3) * d1
	elif d2 <= -1.85e-24:
		tmp = (d2 - d1) * d1
	else:
		tmp = (d4 - d3) * d1
	return tmp

Julia

d1, d2, d3, d4 = sort([d1, d2, d3, d4])
function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -1e+35)
		tmp = Float64(Float64(d2 - d3) * d1);
	elseif (d2 <= -1.85e-24)
		tmp = Float64(Float64(d2 - d1) * d1);
	else
		tmp = Float64(Float64(d4 - d3) * d1);
	end
	return tmp
end

MATLAB

d1, d2, d3, d4 = num2cell(sort([d1, d2, d3, d4])){:}
function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d2 <= -1e+35)
		tmp = (d2 - d3) * d1;
	elseif (d2 <= -1.85e-24)
		tmp = (d2 - d1) * d1;
	else
		tmp = (d4 - d3) * d1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -1e+35], N[(N[(d2 - d3), $MachinePrecision] * d1), $MachinePrecision], If[LessEqual[d2, -1.85e-24], N[(N[(d2 - d1), $MachinePrecision] * d1), $MachinePrecision], N[(N[(d4 - d3), $MachinePrecision] * d1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d2 < -9.9999999999999997e34

   1. Initial program 91.4%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot d2 - \left(d1 \cdot d3 + {d1}^{2}\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(d1 \cdot d2 - d1 \cdot d3\right) - {d1}^{2}} \]

      2. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(d2 - d3\right)} - {d1}^{2} \]

      3. unpow2 N/A

         \[\leadsto d1 \cdot \left(d2 - d3\right) - \color{blue}{d1 \cdot d1} \]

      4. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - d3\right) - d1\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      7. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right)} \cdot d1 \]

      8. lower--.f64 81.6

         \[\leadsto \left(\color{blue}{\left(d2 - d3\right)} - d1\right) \cdot d1 \]

   5. Applied rewrites 81.6%

      \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

   6. Taylor expanded in d1 around 0

      \[\leadsto \left(d2 - d3\right) \cdot d1 \]
   7. Step-by-step derivation

   8. Applied rewrites 61.0%

      \[\leadsto \left(d2 - d3\right) \cdot d1 \]

   if -9.9999999999999997e34 < d2 < -1.8499999999999999e-24

   1. Initial program 99.8%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot d2 - \left(d1 \cdot d3 + {d1}^{2}\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(d1 \cdot d2 - d1 \cdot d3\right) - {d1}^{2}} \]

      2. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(d2 - d3\right)} - {d1}^{2} \]

      3. unpow2 N/A

         \[\leadsto d1 \cdot \left(d2 - d3\right) - \color{blue}{d1 \cdot d1} \]

      4. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - d3\right) - d1\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      7. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right)} \cdot d1 \]

      8. lower--.f64 76.0

         \[\leadsto \left(\color{blue}{\left(d2 - d3\right)} - d1\right) \cdot d1 \]

   5. Applied rewrites 76.0%

      \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

   6. Taylor expanded in d3 around 0

      \[\leadsto \left(d2 - d1\right) \cdot d1 \]
   7. Step-by-step derivation

   8. Applied rewrites 63.9%

      \[\leadsto \left(d2 - d1\right) \cdot d1 \]

   if -1.8499999999999999e-24 < d2

   1. Initial program 89.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right) \cdot d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right) \cdot d1} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right)} \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(d4 + d2\right)} - d3\right) \cdot d1 \]

      5. lower-+.f64 79.3

         \[\leadsto \left(\color{blue}{\left(d4 + d2\right)} - d3\right) \cdot d1 \]

   5. Applied rewrites 79.3%

      \[\leadsto \color{blue}{\left(\left(d4 + d2\right) - d3\right) \cdot d1} \]

   6. Taylor expanded in d2 around 0

      \[\leadsto \left(d4 - d3\right) \cdot d1 \]
   7. Step-by-step derivation

   8. Applied rewrites 66.1%

      \[\leadsto \left(d4 - d3\right) \cdot d1 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 73.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} [d1, d2, d3, d4] = \mathsf{sort}([d1, d2, d3, d4])\\ \\ \begin{array}{l} \mathbf{if}\;d2 \leq -3.4 \cdot 10^{+153}:\\ \;\;\;\;\left(d2 + d4\right) \cdot d1\\ \mathbf{elif}\;d2 \leq -1.85 \cdot 10^{-24}:\\ \;\;\;\;\left(d2 - d1\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(d4 - d3\right) \cdot d1\\ \end{array} \end{array} \]

FPCore

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -3.4e+153)
   (* (+ d2 d4) d1)
   (if (<= d2 -1.85e-24) (* (- d2 d1) d1) (* (- d4 d3) d1))))

C

assert(d1 < d2 && d2 < d3 && d3 < d4);
double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -3.4e+153) {
		tmp = (d2 + d4) * d1;
	} else if (d2 <= -1.85e-24) {
		tmp = (d2 - d1) * d1;
	} else {
		tmp = (d4 - d3) * d1;
	}
	return tmp;
}

Fortran

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
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(d1, d2, d3, d4)
use fmin_fmax_functions
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d2 <= (-3.4d+153)) then
        tmp = (d2 + d4) * d1
    else if (d2 <= (-1.85d-24)) then
        tmp = (d2 - d1) * d1
    else
        tmp = (d4 - d3) * d1
    end if
    code = tmp
end function

Java

assert d1 < d2 && d2 < d3 && d3 < d4;
public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -3.4e+153) {
		tmp = (d2 + d4) * d1;
	} else if (d2 <= -1.85e-24) {
		tmp = (d2 - d1) * d1;
	} else {
		tmp = (d4 - d3) * d1;
	}
	return tmp;
}

Python

[d1, d2, d3, d4] = sort([d1, d2, d3, d4])
def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -3.4e+153:
		tmp = (d2 + d4) * d1
	elif d2 <= -1.85e-24:
		tmp = (d2 - d1) * d1
	else:
		tmp = (d4 - d3) * d1
	return tmp

Julia

d1, d2, d3, d4 = sort([d1, d2, d3, d4])
function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -3.4e+153)
		tmp = Float64(Float64(d2 + d4) * d1);
	elseif (d2 <= -1.85e-24)
		tmp = Float64(Float64(d2 - d1) * d1);
	else
		tmp = Float64(Float64(d4 - d3) * d1);
	end
	return tmp
end

MATLAB

d1, d2, d3, d4 = num2cell(sort([d1, d2, d3, d4])){:}
function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d2 <= -3.4e+153)
		tmp = (d2 + d4) * d1;
	elseif (d2 <= -1.85e-24)
		tmp = (d2 - d1) * d1;
	else
		tmp = (d4 - d3) * d1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -3.4e+153], N[(N[(d2 + d4), $MachinePrecision] * d1), $MachinePrecision], If[LessEqual[d2, -1.85e-24], N[(N[(d2 - d1), $MachinePrecision] * d1), $MachinePrecision], N[(N[(d4 - d3), $MachinePrecision] * d1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d2 < -3.3999999999999997e153

   1. Initial program 90.8%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right) \cdot d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right) \cdot d1} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right)} \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(d4 + d2\right)} - d3\right) \cdot d1 \]

      5. lower-+.f64 95.5

         \[\leadsto \left(\color{blue}{\left(d4 + d2\right)} - d3\right) \cdot d1 \]

   5. Applied rewrites 95.5%

      \[\leadsto \color{blue}{\left(\left(d4 + d2\right) - d3\right) \cdot d1} \]

   6. Taylor expanded in d3 around 0

      \[\leadsto d1 \cdot \color{blue}{\left(d2 + d4\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 82.8%

      \[\leadsto \left(d2 + d4\right) \cdot \color{blue}{d1} \]

   if -3.3999999999999997e153 < d2 < -1.8499999999999999e-24

   1. Initial program 93.9%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot d2 - \left(d1 \cdot d3 + {d1}^{2}\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(d1 \cdot d2 - d1 \cdot d3\right) - {d1}^{2}} \]

      2. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(d2 - d3\right)} - {d1}^{2} \]

      3. unpow2 N/A

         \[\leadsto d1 \cdot \left(d2 - d3\right) - \color{blue}{d1 \cdot d1} \]

      4. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - d3\right) - d1\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      7. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right)} \cdot d1 \]

      8. lower--.f64 79.5

         \[\leadsto \left(\color{blue}{\left(d2 - d3\right)} - d1\right) \cdot d1 \]

   5. Applied rewrites 79.5%

      \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

   6. Taylor expanded in d3 around 0

      \[\leadsto \left(d2 - d1\right) \cdot d1 \]
   7. Step-by-step derivation

   8. Applied rewrites 57.4%

      \[\leadsto \left(d2 - d1\right) \cdot d1 \]

   if -1.8499999999999999e-24 < d2

   1. Initial program 89.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right) \cdot d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right) \cdot d1} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right)} \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(d4 + d2\right)} - d3\right) \cdot d1 \]

      5. lower-+.f64 79.3

         \[\leadsto \left(\color{blue}{\left(d4 + d2\right)} - d3\right) \cdot d1 \]

   5. Applied rewrites 79.3%

      \[\leadsto \color{blue}{\left(\left(d4 + d2\right) - d3\right) \cdot d1} \]

   6. Taylor expanded in d2 around 0

      \[\leadsto \left(d4 - d3\right) \cdot d1 \]
   7. Step-by-step derivation

   8. Applied rewrites 66.1%

      \[\leadsto \left(d4 - d3\right) \cdot d1 \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 53.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} [d1, d2, d3, d4] = \mathsf{sort}([d1, d2, d3, d4])\\ \\ \begin{array}{l} \mathbf{if}\;d4 \leq -2.3 \cdot 10^{-163}:\\ \;\;\;\;d2 \cdot d1\\ \mathbf{elif}\;d4 \leq 1.6 \cdot 10^{+60}:\\ \;\;\;\;\left(-d3\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;d4 \cdot d1\\ \end{array} \end{array} \]

FPCore

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 -2.3e-163) (* d2 d1) (if (<= d4 1.6e+60) (* (- d3) d1) (* d4 d1))))

C

assert(d1 < d2 && d2 < d3 && d3 < d4);
double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= -2.3e-163) {
		tmp = d2 * d1;
	} else if (d4 <= 1.6e+60) {
		tmp = -d3 * d1;
	} else {
		tmp = d4 * d1;
	}
	return tmp;
}

Fortran

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
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(d1, d2, d3, d4)
use fmin_fmax_functions
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d4 <= (-2.3d-163)) then
        tmp = d2 * d1
    else if (d4 <= 1.6d+60) then
        tmp = -d3 * d1
    else
        tmp = d4 * d1
    end if
    code = tmp
end function

Java

assert d1 < d2 && d2 < d3 && d3 < d4;
public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= -2.3e-163) {
		tmp = d2 * d1;
	} else if (d4 <= 1.6e+60) {
		tmp = -d3 * d1;
	} else {
		tmp = d4 * d1;
	}
	return tmp;
}

Python

[d1, d2, d3, d4] = sort([d1, d2, d3, d4])
def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= -2.3e-163:
		tmp = d2 * d1
	elif d4 <= 1.6e+60:
		tmp = -d3 * d1
	else:
		tmp = d4 * d1
	return tmp

Julia

d1, d2, d3, d4 = sort([d1, d2, d3, d4])
function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= -2.3e-163)
		tmp = Float64(d2 * d1);
	elseif (d4 <= 1.6e+60)
		tmp = Float64(Float64(-d3) * d1);
	else
		tmp = Float64(d4 * d1);
	end
	return tmp
end

MATLAB

d1, d2, d3, d4 = num2cell(sort([d1, d2, d3, d4])){:}
function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d4 <= -2.3e-163)
		tmp = d2 * d1;
	elseif (d4 <= 1.6e+60)
		tmp = -d3 * d1;
	else
		tmp = d4 * d1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, -2.3e-163], N[(d2 * d1), $MachinePrecision], If[LessEqual[d4, 1.6e+60], N[((-d3) * d1), $MachinePrecision], N[(d4 * d1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d4 < -2.2999999999999999e-163

   1. Initial program 92.3%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right)} - d1 \cdot d1 \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{\left(d1 \cdot d2 - d1 \cdot d3\right) + \left(d4 \cdot d1 - d1 \cdot d1\right)} \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(d4 \cdot d1 - d1 \cdot d1\right) + \left(d1 \cdot d2 - d1 \cdot d3\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{d4 \cdot d1} - d1 \cdot d1\right) + \left(d1 \cdot d2 - d1 \cdot d3\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(d4 \cdot d1 - \color{blue}{d1 \cdot d1}\right) + \left(d1 \cdot d2 - d1 \cdot d3\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(d4 - d1\right)} + \left(d1 \cdot d2 - d1 \cdot d3\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(d1, d4 - d1, d1 \cdot d2 - d1 \cdot d3\right)} \]

      9. lower--.f64 97.1

         \[\leadsto \mathsf{fma}\left(d1, \color{blue}{d4 - d1}, d1 \cdot d2 - d1 \cdot d3\right) \]

      10. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{d1 \cdot d2 - d1 \cdot d3}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{d1 \cdot d2} - d1 \cdot d3\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, d1 \cdot d2 - \color{blue}{d1 \cdot d3}\right) \]

      13. distribute-lft-out-- N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{\left(d2 - d3\right) \cdot d1}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{\left(d2 - d3\right) \cdot d1}\right) \]

      16. lower--.f64 97.1

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{\left(d2 - d3\right)} \cdot d1\right) \]

   4. Applied rewrites 97.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(d1, d4 - d1, \left(d2 - d3\right) \cdot d1\right)} \]

   5. Taylor expanded in d2 around inf

      \[\leadsto \color{blue}{d1 \cdot d2} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{d2 \cdot d1} \]

      2. lower-*.f64 22.8

         \[\leadsto \color{blue}{d2 \cdot d1} \]

   7. Applied rewrites 22.8%

      \[\leadsto \color{blue}{d2 \cdot d1} \]

   if -2.2999999999999999e-163 < d4 < 1.59999999999999995e60

   1. Initial program 90.1%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot d2 - \left(d1 \cdot d3 + {d1}^{2}\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(d1 \cdot d2 - d1 \cdot d3\right) - {d1}^{2}} \]

      2. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(d2 - d3\right)} - {d1}^{2} \]

      3. unpow2 N/A

         \[\leadsto d1 \cdot \left(d2 - d3\right) - \color{blue}{d1 \cdot d1} \]

      4. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - d3\right) - d1\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      7. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right)} \cdot d1 \]

      8. lower--.f64 92.7

         \[\leadsto \left(\color{blue}{\left(d2 - d3\right)} - d1\right) \cdot d1 \]

   5. Applied rewrites 92.7%

      \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

   6. Taylor expanded in d1 around 0

      \[\leadsto \left(d2 - d3\right) \cdot d1 \]
   7. Step-by-step derivation

   8. Applied rewrites 67.7%

      \[\leadsto \left(d2 - d3\right) \cdot d1 \]

   9. Taylor expanded in d2 around 0

      \[\leadsto \left(-1 \cdot d3\right) \cdot d1 \]
   10. Step-by-step derivation

   11. Applied rewrites 47.1%

       \[\leadsto \left(-d3\right) \cdot d1 \]

   if 1.59999999999999995e60 < d4

   1. Initial program 85.2%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d4 around inf

      \[\leadsto \color{blue}{d1 \cdot d4} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{d4 \cdot d1} \]

      2. lower-*.f64 66.6

         \[\leadsto \color{blue}{d4 \cdot d1} \]

   5. Applied rewrites 66.6%

      \[\leadsto \color{blue}{d4 \cdot d1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d4 \leq -2.3 \cdot 10^{-163}:\\ \;\;\;\;d2 \cdot d1\\ \mathbf{elif}\;d4 \leq 1.6 \cdot 10^{+60}:\\ \;\;\;\;\left(-d3\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;d4 \cdot d1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 92.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} [d1, d2, d3, d4] = \mathsf{sort}([d1, d2, d3, d4])\\ \\ \begin{array}{l} \mathbf{if}\;d4 \leq 1.8 \cdot 10^{+129}:\\ \;\;\;\;\left(\left(d2 - d3\right) - d1\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(d4 + d2\right) - d3\right) \cdot d1\\ \end{array} \end{array} \]

FPCore

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 1.8e+129) (* (- (- d2 d3) d1) d1) (* (- (+ d4 d2) d3) d1)))

C

assert(d1 < d2 && d2 < d3 && d3 < d4);
double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 1.8e+129) {
		tmp = ((d2 - d3) - d1) * d1;
	} else {
		tmp = ((d4 + d2) - d3) * d1;
	}
	return tmp;
}

Fortran

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
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(d1, d2, d3, d4)
use fmin_fmax_functions
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d4 <= 1.8d+129) then
        tmp = ((d2 - d3) - d1) * d1
    else
        tmp = ((d4 + d2) - d3) * d1
    end if
    code = tmp
end function

Java

assert d1 < d2 && d2 < d3 && d3 < d4;
public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 1.8e+129) {
		tmp = ((d2 - d3) - d1) * d1;
	} else {
		tmp = ((d4 + d2) - d3) * d1;
	}
	return tmp;
}

Python

[d1, d2, d3, d4] = sort([d1, d2, d3, d4])
def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 1.8e+129:
		tmp = ((d2 - d3) - d1) * d1
	else:
		tmp = ((d4 + d2) - d3) * d1
	return tmp

Julia

d1, d2, d3, d4 = sort([d1, d2, d3, d4])
function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 1.8e+129)
		tmp = Float64(Float64(Float64(d2 - d3) - d1) * d1);
	else
		tmp = Float64(Float64(Float64(d4 + d2) - d3) * d1);
	end
	return tmp
end

MATLAB

d1, d2, d3, d4 = num2cell(sort([d1, d2, d3, d4])){:}
function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d4 <= 1.8e+129)
		tmp = ((d2 - d3) - d1) * d1;
	else
		tmp = ((d4 + d2) - d3) * d1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 1.8e+129], N[(N[(N[(d2 - d3), $MachinePrecision] - d1), $MachinePrecision] * d1), $MachinePrecision], N[(N[(N[(d4 + d2), $MachinePrecision] - d3), $MachinePrecision] * d1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d4 < 1.8000000000000001e129

   1. Initial program 91.8%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d4 around 0

      \[\leadsto \color{blue}{d1 \cdot d2 - \left(d1 \cdot d3 + {d1}^{2}\right)} \]
   4. Step-by-step derivation

      1. associate--r+ N/A

         \[\leadsto \color{blue}{\left(d1 \cdot d2 - d1 \cdot d3\right) - {d1}^{2}} \]

      2. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(d2 - d3\right)} - {d1}^{2} \]

      3. unpow2 N/A

         \[\leadsto d1 \cdot \left(d2 - d3\right) - \color{blue}{d1 \cdot d1} \]

      4. distribute-lft-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 - d3\right) - d1\right)} \]

      5. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      6. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

      7. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right)} \cdot d1 \]

      8. lower--.f64 81.1

         \[\leadsto \left(\color{blue}{\left(d2 - d3\right)} - d1\right) \cdot d1 \]

   5. Applied rewrites 81.1%

      \[\leadsto \color{blue}{\left(\left(d2 - d3\right) - d1\right) \cdot d1} \]

   if 1.8000000000000001e129 < d4

   1. Initial program 80.8%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right) \cdot d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right) \cdot d1} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right)} \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(d4 + d2\right)} - d3\right) \cdot d1 \]

      5. lower-+.f64 93.6

         \[\leadsto \left(\color{blue}{\left(d4 + d2\right)} - d3\right) \cdot d1 \]

   5. Applied rewrites 93.6%

      \[\leadsto \color{blue}{\left(\left(d4 + d2\right) - d3\right) \cdot d1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 72.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} [d1, d2, d3, d4] = \mathsf{sort}([d1, d2, d3, d4])\\ \\ \begin{array}{l} \mathbf{if}\;d2 \leq -4.2 \cdot 10^{+78}:\\ \;\;\;\;\left(d2 + d4\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(d4 - d3\right) \cdot d1\\ \end{array} \end{array} \]

FPCore

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -4.2e+78) (* (+ d2 d4) d1) (* (- d4 d3) d1)))

C

assert(d1 < d2 && d2 < d3 && d3 < d4);
double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -4.2e+78) {
		tmp = (d2 + d4) * d1;
	} else {
		tmp = (d4 - d3) * d1;
	}
	return tmp;
}

Fortran

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
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(d1, d2, d3, d4)
use fmin_fmax_functions
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d2 <= (-4.2d+78)) then
        tmp = (d2 + d4) * d1
    else
        tmp = (d4 - d3) * d1
    end if
    code = tmp
end function

Java

assert d1 < d2 && d2 < d3 && d3 < d4;
public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -4.2e+78) {
		tmp = (d2 + d4) * d1;
	} else {
		tmp = (d4 - d3) * d1;
	}
	return tmp;
}

Python

[d1, d2, d3, d4] = sort([d1, d2, d3, d4])
def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -4.2e+78:
		tmp = (d2 + d4) * d1
	else:
		tmp = (d4 - d3) * d1
	return tmp

Julia

d1, d2, d3, d4 = sort([d1, d2, d3, d4])
function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -4.2e+78)
		tmp = Float64(Float64(d2 + d4) * d1);
	else
		tmp = Float64(Float64(d4 - d3) * d1);
	end
	return tmp
end

MATLAB

d1, d2, d3, d4 = num2cell(sort([d1, d2, d3, d4])){:}
function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d2 <= -4.2e+78)
		tmp = (d2 + d4) * d1;
	else
		tmp = (d4 - d3) * d1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -4.2e+78], N[(N[(d2 + d4), $MachinePrecision] * d1), $MachinePrecision], N[(N[(d4 - d3), $MachinePrecision] * d1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -4.2000000000000002e78

   1. Initial program 89.9%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right) \cdot d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right) \cdot d1} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right)} \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(d4 + d2\right)} - d3\right) \cdot d1 \]

      5. lower-+.f64 85.5

         \[\leadsto \left(\color{blue}{\left(d4 + d2\right)} - d3\right) \cdot d1 \]

   5. Applied rewrites 85.5%

      \[\leadsto \color{blue}{\left(\left(d4 + d2\right) - d3\right) \cdot d1} \]

   6. Taylor expanded in d3 around 0

      \[\leadsto d1 \cdot \color{blue}{\left(d2 + d4\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 73.8%

      \[\leadsto \left(d2 + d4\right) \cdot \color{blue}{d1} \]

   if -4.2000000000000002e78 < d2

   1. Initial program 89.8%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + d4\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right) \cdot d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right) \cdot d1} \]

      3. lower--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d2 + d4\right) - d3\right)} \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\color{blue}{\left(d4 + d2\right)} - d3\right) \cdot d1 \]

      5. lower-+.f64 78.7

         \[\leadsto \left(\color{blue}{\left(d4 + d2\right)} - d3\right) \cdot d1 \]

   5. Applied rewrites 78.7%

      \[\leadsto \color{blue}{\left(\left(d4 + d2\right) - d3\right) \cdot d1} \]

   6. Taylor expanded in d2 around 0

      \[\leadsto \left(d4 - d3\right) \cdot d1 \]
   7. Step-by-step derivation

   8. Applied rewrites 65.4%

      \[\leadsto \left(d4 - d3\right) \cdot d1 \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 50.8% accurate, 2.5× speedup

Math

\[\begin{array}{l} [d1, d2, d3, d4] = \mathsf{sort}([d1, d2, d3, d4])\\ \\ \begin{array}{l} \mathbf{if}\;d2 \leq -3.4 \cdot 10^{+20}:\\ \;\;\;\;d2 \cdot d1\\ \mathbf{else}:\\ \;\;\;\;d4 \cdot d1\\ \end{array} \end{array} \]

FPCore

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -3.4e+20) (* d2 d1) (* d4 d1)))

C

assert(d1 < d2 && d2 < d3 && d3 < d4);
double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -3.4e+20) {
		tmp = d2 * d1;
	} else {
		tmp = d4 * d1;
	}
	return tmp;
}

Fortran

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
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(d1, d2, d3, d4)
use fmin_fmax_functions
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    real(8) :: tmp
    if (d2 <= (-3.4d+20)) then
        tmp = d2 * d1
    else
        tmp = d4 * d1
    end if
    code = tmp
end function

Java

assert d1 < d2 && d2 < d3 && d3 < d4;
public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -3.4e+20) {
		tmp = d2 * d1;
	} else {
		tmp = d4 * d1;
	}
	return tmp;
}

Python

[d1, d2, d3, d4] = sort([d1, d2, d3, d4])
def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -3.4e+20:
		tmp = d2 * d1
	else:
		tmp = d4 * d1
	return tmp

Julia

d1, d2, d3, d4 = sort([d1, d2, d3, d4])
function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -3.4e+20)
		tmp = Float64(d2 * d1);
	else
		tmp = Float64(d4 * d1);
	end
	return tmp
end

MATLAB

d1, d2, d3, d4 = num2cell(sort([d1, d2, d3, d4])){:}
function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d2 <= -3.4e+20)
		tmp = d2 * d1;
	else
		tmp = d4 * d1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -3.4e+20], N[(d2 * d1), $MachinePrecision], N[(d4 * d1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -3.4e20

   1. Initial program 92.1%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1} \]

      2. lift-+.f64 N/A

         \[\leadsto \color{blue}{\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right)} - d1 \cdot d1 \]

      3. associate--l+ N/A

         \[\leadsto \color{blue}{\left(d1 \cdot d2 - d1 \cdot d3\right) + \left(d4 \cdot d1 - d1 \cdot d1\right)} \]

      4. +-commutative N/A

         \[\leadsto \color{blue}{\left(d4 \cdot d1 - d1 \cdot d1\right) + \left(d1 \cdot d2 - d1 \cdot d3\right)} \]

      5. lift-*.f64 N/A

         \[\leadsto \left(\color{blue}{d4 \cdot d1} - d1 \cdot d1\right) + \left(d1 \cdot d2 - d1 \cdot d3\right) \]

      6. lift-*.f64 N/A

         \[\leadsto \left(d4 \cdot d1 - \color{blue}{d1 \cdot d1}\right) + \left(d1 \cdot d2 - d1 \cdot d3\right) \]

      7. distribute-rgt-out-- N/A

         \[\leadsto \color{blue}{d1 \cdot \left(d4 - d1\right)} + \left(d1 \cdot d2 - d1 \cdot d3\right) \]

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(d1, d4 - d1, d1 \cdot d2 - d1 \cdot d3\right)} \]

      9. lower--.f64 92.1

         \[\leadsto \mathsf{fma}\left(d1, \color{blue}{d4 - d1}, d1 \cdot d2 - d1 \cdot d3\right) \]

      10. lift--.f64 N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{d1 \cdot d2 - d1 \cdot d3}\right) \]

      11. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{d1 \cdot d2} - d1 \cdot d3\right) \]

      12. lift-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, d1 \cdot d2 - \color{blue}{d1 \cdot d3}\right) \]

      13. distribute-lft-out-- N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{\left(d2 - d3\right) \cdot d1}\right) \]

      15. lower-*.f64 N/A

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{\left(d2 - d3\right) \cdot d1}\right) \]

      16. lower--.f64 92.1

          \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{\left(d2 - d3\right)} \cdot d1\right) \]

   4. Applied rewrites 92.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(d1, d4 - d1, \left(d2 - d3\right) \cdot d1\right)} \]

   5. Taylor expanded in d2 around inf

      \[\leadsto \color{blue}{d1 \cdot d2} \]
   6. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{d2 \cdot d1} \]

      2. lower-*.f64 42.7

         \[\leadsto \color{blue}{d2 \cdot d1} \]

   7. Applied rewrites 42.7%

      \[\leadsto \color{blue}{d2 \cdot d1} \]

   if -3.4e20 < d2

   1. Initial program 89.2%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   2. Add Preprocessing

   3. Taylor expanded in d4 around inf

      \[\leadsto \color{blue}{d1 \cdot d4} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{d4 \cdot d1} \]

      2. lower-*.f64 36.2

         \[\leadsto \color{blue}{d4 \cdot d1} \]

   5. Applied rewrites 36.2%

      \[\leadsto \color{blue}{d4 \cdot d1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d2 \leq -3.4 \cdot 10^{+20}:\\ \;\;\;\;d2 \cdot d1\\ \mathbf{else}:\\ \;\;\;\;d4 \cdot d1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 31.1% accurate, 5.0× speedup

Math

\[\begin{array}{l} [d1, d2, d3, d4] = \mathsf{sort}([d1, d2, d3, d4])\\ \\ d2 \cdot d1 \end{array} \]

FPCore

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
(FPCore (d1 d2 d3 d4) :precision binary64 (* d2 d1))

C

assert(d1 < d2 && d2 < d3 && d3 < d4);
double code(double d1, double d2, double d3, double d4) {
	return d2 * d1;
}

Fortran

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
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(d1, d2, d3, d4)
use fmin_fmax_functions
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    code = d2 * d1
end function

Java

assert d1 < d2 && d2 < d3 && d3 < d4;
public static double code(double d1, double d2, double d3, double d4) {
	return d2 * d1;
}

Python

[d1, d2, d3, d4] = sort([d1, d2, d3, d4])
def code(d1, d2, d3, d4):
	return d2 * d1

Julia

d1, d2, d3, d4 = sort([d1, d2, d3, d4])
function code(d1, d2, d3, d4)
	return Float64(d2 * d1)
end

MATLAB

d1, d2, d3, d4 = num2cell(sort([d1, d2, d3, d4])){:}
function tmp = code(d1, d2, d3, d4)
	tmp = d2 * d1;
end

Wolfram

NOTE: d1, d2, d3, and d4 should be sorted in increasing order before calling this function.
code[d1_, d2_, d3_, d4_] := N[(d2 * d1), $MachinePrecision]

Derivation

1. Initial program 89.8%

   \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift--.f64 N/A

      \[\leadsto \color{blue}{\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1} \]

   2. lift-+.f64 N/A

      \[\leadsto \color{blue}{\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right)} - d1 \cdot d1 \]

   3. associate--l+ N/A

      \[\leadsto \color{blue}{\left(d1 \cdot d2 - d1 \cdot d3\right) + \left(d4 \cdot d1 - d1 \cdot d1\right)} \]

   4. +-commutative N/A

      \[\leadsto \color{blue}{\left(d4 \cdot d1 - d1 \cdot d1\right) + \left(d1 \cdot d2 - d1 \cdot d3\right)} \]

   5. lift-*.f64 N/A

      \[\leadsto \left(\color{blue}{d4 \cdot d1} - d1 \cdot d1\right) + \left(d1 \cdot d2 - d1 \cdot d3\right) \]

   6. lift-*.f64 N/A

      \[\leadsto \left(d4 \cdot d1 - \color{blue}{d1 \cdot d1}\right) + \left(d1 \cdot d2 - d1 \cdot d3\right) \]

   7. distribute-rgt-out-- N/A

      \[\leadsto \color{blue}{d1 \cdot \left(d4 - d1\right)} + \left(d1 \cdot d2 - d1 \cdot d3\right) \]

   8. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(d1, d4 - d1, d1 \cdot d2 - d1 \cdot d3\right)} \]

   9. lower--.f64 95.3

      \[\leadsto \mathsf{fma}\left(d1, \color{blue}{d4 - d1}, d1 \cdot d2 - d1 \cdot d3\right) \]

   10. lift--.f64 N/A

       \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{d1 \cdot d2 - d1 \cdot d3}\right) \]

   11. lift-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{d1 \cdot d2} - d1 \cdot d3\right) \]

   12. lift-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(d1, d4 - d1, d1 \cdot d2 - \color{blue}{d1 \cdot d3}\right) \]

   13. distribute-lft-out-- N/A

       \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{d1 \cdot \left(d2 - d3\right)}\right) \]

   14. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{\left(d2 - d3\right) \cdot d1}\right) \]

   15. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{\left(d2 - d3\right) \cdot d1}\right) \]

   16. lower--.f64 95.3

       \[\leadsto \mathsf{fma}\left(d1, d4 - d1, \color{blue}{\left(d2 - d3\right)} \cdot d1\right) \]

4. Applied rewrites 95.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(d1, d4 - d1, \left(d2 - d3\right) \cdot d1\right)} \]

5. Taylor expanded in d2 around inf

   \[\leadsto \color{blue}{d1 \cdot d2} \]
6. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \color{blue}{d2 \cdot d1} \]

   2. lower-*.f64 24.4

      \[\leadsto \color{blue}{d2 \cdot d1} \]

7. Applied rewrites 24.4%

   \[\leadsto \color{blue}{d2 \cdot d1} \]

8. Final simplification 24.4%

   \[\leadsto d2 \cdot d1 \]
9. Add Preprocessing

Developer Target 1: 100.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ d1 \cdot \left(\left(\left(d2 - d3\right) + d4\right) - d1\right) \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4) :precision binary64 (* d1 (- (+ (- d2 d3) d4) d1)))

C

double code(double d1, double d2, double d3, double d4) {
	return d1 * (((d2 - d3) + d4) - d1);
}

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(d1, d2, d3, d4)
use fmin_fmax_functions
    real(8), intent (in) :: d1
    real(8), intent (in) :: d2
    real(8), intent (in) :: d3
    real(8), intent (in) :: d4
    code = d1 * (((d2 - d3) + d4) - d1)
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	return d1 * (((d2 - d3) + d4) - d1);
}

Python

def code(d1, d2, d3, d4):
	return d1 * (((d2 - d3) + d4) - d1)

Julia

function code(d1, d2, d3, d4)
	return Float64(d1 * Float64(Float64(Float64(d2 - d3) + d4) - d1))
end

MATLAB

function tmp = code(d1, d2, d3, d4)
	tmp = d1 * (((d2 - d3) + d4) - d1);
end

Wolfram

code[d1_, d2_, d3_, d4_] := N[(d1 * N[(N[(N[(d2 - d3), $MachinePrecision] + d4), $MachinePrecision] - d1), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024346 
(FPCore (d1 d2 d3 d4)
  :name "FastMath dist4"
  :precision binary64

  :alt
  (! :herbie-platform default (* d1 (- (+ (- d2 d3) d4) d1)))

  (- (+ (- (* d1 d2) (* d1 d3)) (* d4 d1)) (* d1 d1)))