FastMath dist4

Percentage Accurate: 87.8% → 100.0%

Time: 2.4s

Alternatives: 11

Speedup: 1.7×

• 33.2% 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: 87.8% 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: 100.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1 \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (* (- (+ (fma -1.0 d1 d4) d2) d3) d1))

C

double code(double d1, double d2, double d3, double d4) {
	return ((fma(-1.0, d1, d4) + d2) - d3) * d1;
}

Julia

function code(d1, d2, d3, d4)
	return Float64(Float64(Float64(fma(-1.0, d1, d4) + d2) - d3) * d1)
end

Wolfram

code[d1_, d2_, d3_, d4_] := N[(N[(N[(N[(-1.0 * d1 + d4), $MachinePrecision] + d2), $MachinePrecision] - d3), $MachinePrecision] * d1), $MachinePrecision]

Derivation

1. Initial program 85.9%

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

3. Taylor expanded in d1 around 0

   \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right)} \]
4. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

   2. lower-*.f64 N/A

      \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

   3. lower--.f64 N/A

      \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot d1 \]

   4. +-commutative N/A

      \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

   5. lower-+.f64 N/A

      \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

   6. +-commutative N/A

      \[\leadsto \left(\left(\left(-1 \cdot d1 + d4\right) + d2\right) - d3\right) \cdot d1 \]

   7. lower-fma.f64 100.0

      \[\leadsto \left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1 \]

5. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1} \]
6. Add Preprocessing

Alternative 2: 62.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 1.9 \cdot 10^{-272}:\\ \;\;\;\;\left(d2 - d3\right) \cdot d1\\ \mathbf{elif}\;d4 \leq 1.4 \cdot 10^{+108}:\\ \;\;\;\;\left(\left(-d1\right) - d3\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(d4 - d3\right) \cdot d1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 1.9e-272)
   (* (- d2 d3) d1)
   (if (<= d4 1.4e+108) (* (- (- d1) d3) d1) (* (- d4 d3) d1))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 1.9e-272) {
		tmp = (d2 - d3) * d1;
	} else if (d4 <= 1.4e+108) {
		tmp = (-d1 - d3) * d1;
	} else {
		tmp = (d4 - d3) * d1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(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 <= 1.9d-272) then
        tmp = (d2 - d3) * d1
    else if (d4 <= 1.4d+108) then
        tmp = (-d1 - d3) * d1
    else
        tmp = (d4 - d3) * d1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 1.9e-272) {
		tmp = (d2 - d3) * d1;
	} else if (d4 <= 1.4e+108) {
		tmp = (-d1 - d3) * d1;
	} else {
		tmp = (d4 - d3) * d1;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 1.9e-272:
		tmp = (d2 - d3) * d1
	elif d4 <= 1.4e+108:
		tmp = (-d1 - d3) * d1
	else:
		tmp = (d4 - d3) * d1
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 1.9e-272)
		tmp = Float64(Float64(d2 - d3) * d1);
	elseif (d4 <= 1.4e+108)
		tmp = Float64(Float64(Float64(-d1) - d3) * d1);
	else
		tmp = Float64(Float64(d4 - d3) * d1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d4 <= 1.9e-272)
		tmp = (d2 - d3) * d1;
	elseif (d4 <= 1.4e+108)
		tmp = (-d1 - d3) * d1;
	else
		tmp = (d4 - d3) * d1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 1.9e-272], N[(N[(d2 - d3), $MachinePrecision] * d1), $MachinePrecision], If[LessEqual[d4, 1.4e+108], N[(N[((-d1) - d3), $MachinePrecision] * d1), $MachinePrecision], N[(N[(d4 - d3), $MachinePrecision] * d1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d4 < 1.89999999999999985e-272

   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

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      6. +-commutative N/A

         \[\leadsto \left(\left(\left(-1 \cdot d1 + d4\right) + d2\right) - d3\right) \cdot d1 \]

      7. lower-fma.f64 100.0

         \[\leadsto \left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1 \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1} \]

   6. Taylor expanded in d2 around inf

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

   8. Applied rewrites 55.5%

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

   if 1.89999999999999985e-272 < d4 < 1.3999999999999999e108

   1. Initial program 92.0%

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

   3. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      6. +-commutative N/A

         \[\leadsto \left(\left(\left(-1 \cdot d1 + d4\right) + d2\right) - d3\right) \cdot d1 \]

      7. lower-fma.f64 100.0

         \[\leadsto \left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1 \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1} \]

   6. Taylor expanded in d1 around inf

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

      1. mul-1-neg N/A

         \[\leadsto \left(\left(\mathsf{neg}\left(d1\right)\right) - d3\right) \cdot d1 \]

      2. lift-neg.f64 64.6

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

   8. Applied rewrites 64.6%

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

   if 1.3999999999999999e108 < d4

   1. Initial program 54.8%

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

   3. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      6. +-commutative N/A

         \[\leadsto \left(\left(\left(-1 \cdot d1 + d4\right) + d2\right) - d3\right) \cdot d1 \]

      7. lower-fma.f64 100.0

         \[\leadsto \left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1 \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1} \]

   6. Taylor expanded in d4 around inf

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

   8. Applied rewrites 81.0%

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

Alternative 3: 67.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d3 \leq -1.02 \cdot 10^{+103} \lor \neg \left(d3 \leq 6.5 \cdot 10^{+198}\right):\\ \;\;\;\;\left(-d3\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(d4 + d2\right) \cdot d1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (or (<= d3 -1.02e+103) (not (<= d3 6.5e+198)))
   (* (- d3) d1)
   (* (+ d4 d2) d1)))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if ((d3 <= -1.02e+103) || !(d3 <= 6.5e+198)) {
		tmp = -d3 * d1;
	} else {
		tmp = (d4 + d2) * d1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(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 <= (-1.02d+103)) .or. (.not. (d3 <= 6.5d+198))) then
        tmp = -d3 * d1
    else
        tmp = (d4 + d2) * d1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if ((d3 <= -1.02e+103) || !(d3 <= 6.5e+198)) {
		tmp = -d3 * d1;
	} else {
		tmp = (d4 + d2) * d1;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if (d3 <= -1.02e+103) or not (d3 <= 6.5e+198):
		tmp = -d3 * d1
	else:
		tmp = (d4 + d2) * d1
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if ((d3 <= -1.02e+103) || !(d3 <= 6.5e+198))
		tmp = Float64(Float64(-d3) * d1);
	else
		tmp = Float64(Float64(d4 + d2) * d1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if ((d3 <= -1.02e+103) || ~((d3 <= 6.5e+198)))
		tmp = -d3 * d1;
	else
		tmp = (d4 + d2) * d1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[Or[LessEqual[d3, -1.02e+103], N[Not[LessEqual[d3, 6.5e+198]], $MachinePrecision]], N[((-d3) * d1), $MachinePrecision], N[(N[(d4 + d2), $MachinePrecision] * d1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d3 < -1.01999999999999991e103 or 6.5000000000000003e198 < d3

   1. Initial program 71.2%

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

   3. Taylor expanded in d3 around inf

      \[\leadsto \color{blue}{-1 \cdot \left(d1 \cdot d3\right)} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(d1 \cdot d3\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{neg}\left(d3 \cdot d1\right) \]

      3. distribute-lft-neg-in N/A

         \[\leadsto \left(\mathsf{neg}\left(d3\right)\right) \cdot \color{blue}{d1} \]

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot d3\right) \cdot d1 \]

      5. lower-*.f64 N/A

         \[\leadsto \left(-1 \cdot d3\right) \cdot \color{blue}{d1} \]

      6. mul-1-neg N/A

         \[\leadsto \left(\mathsf{neg}\left(d3\right)\right) \cdot d1 \]

      7. lower-neg.f64 77.8

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

   5. Applied rewrites 77.8%

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

   if -1.01999999999999991e103 < d3 < 6.5000000000000003e198

   1. Initial program 91.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \left(\left(d2 + d4\right) - d3\right) \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\left(d4 + d2\right) - d3\right) \cdot d1 \]

      5. lower-+.f64 72.9

         \[\leadsto \left(\left(d4 + d2\right) - d3\right) \cdot d1 \]

   5. Applied rewrites 72.9%

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

   6. Taylor expanded in d3 around 0

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

      1. +-commutative N/A

         \[\leadsto \left(d4 + d2\right) \cdot d1 \]

      2. lift-+.f64 67.1

         \[\leadsto \left(d4 + d2\right) \cdot d1 \]

   8. Applied rewrites 67.1%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d3 \leq -1.02 \cdot 10^{+103} \lor \neg \left(d3 \leq 6.5 \cdot 10^{+198}\right):\\ \;\;\;\;\left(-d3\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(d4 + d2\right) \cdot d1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 38.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 1.9 \cdot 10^{-272}:\\ \;\;\;\;d2 \cdot d1\\ \mathbf{elif}\;d4 \leq 2.2 \cdot 10^{+118}:\\ \;\;\;\;\left(-d1\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;d4 \cdot d1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 1.9e-272) (* d2 d1) (if (<= d4 2.2e+118) (* (- d1) d1) (* d4 d1))))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 1.9e-272) {
		tmp = d2 * d1;
	} else if (d4 <= 2.2e+118) {
		tmp = -d1 * d1;
	} else {
		tmp = d4 * d1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(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 <= 1.9d-272) then
        tmp = d2 * d1
    else if (d4 <= 2.2d+118) then
        tmp = -d1 * d1
    else
        tmp = d4 * d1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 1.9e-272) {
		tmp = d2 * d1;
	} else if (d4 <= 2.2e+118) {
		tmp = -d1 * d1;
	} else {
		tmp = d4 * d1;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 1.9e-272:
		tmp = d2 * d1
	elif d4 <= 2.2e+118:
		tmp = -d1 * d1
	else:
		tmp = d4 * d1
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 1.9e-272)
		tmp = Float64(d2 * d1);
	elseif (d4 <= 2.2e+118)
		tmp = Float64(Float64(-d1) * d1);
	else
		tmp = Float64(d4 * d1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d4 <= 1.9e-272)
		tmp = d2 * d1;
	elseif (d4 <= 2.2e+118)
		tmp = -d1 * d1;
	else
		tmp = d4 * d1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 1.9e-272], N[(d2 * d1), $MachinePrecision], If[LessEqual[d4, 2.2e+118], N[((-d1) * d1), $MachinePrecision], N[(d4 * d1), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d4 < 1.89999999999999985e-272

   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 d2 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 32.0

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

   5. Applied rewrites 32.0%

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

   if 1.89999999999999985e-272 < d4 < 2.19999999999999986e118

   1. Initial program 91.1%

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

   3. Taylor expanded in d1 around inf

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left({d1}^{2}\right) \]

      2. pow2 N/A

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

      3. distribute-lft-neg-in N/A

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

      4. mul-1-neg N/A

         \[\leadsto \left(-1 \cdot d1\right) \cdot d1 \]

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 46.0

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

   5. Applied rewrites 46.0%

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

   if 2.19999999999999986e118 < d4

   1. Initial program 55.2%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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

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

      2. lift-*.f64 74.1

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

   5. Applied rewrites 74.1%

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

Alternative 5: 82.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 1.75 \cdot 10^{-59}:\\ \;\;\;\;\left(\left(\left(-d1\right) + d2\right) - d3\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(d4 - d1\right) - d3\right) \cdot d1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 1.75e-59) (* (- (+ (- d1) d2) d3) d1) (* (- (- d4 d1) d3) d1)))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 1.75e-59) {
		tmp = ((-d1 + d2) - d3) * d1;
	} else {
		tmp = ((d4 - d1) - d3) * d1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(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 <= 1.75d-59) then
        tmp = ((-d1 + d2) - d3) * d1
    else
        tmp = ((d4 - d1) - d3) * d1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 1.75e-59) {
		tmp = ((-d1 + d2) - d3) * d1;
	} else {
		tmp = ((d4 - d1) - d3) * d1;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 1.75e-59:
		tmp = ((-d1 + d2) - d3) * d1
	else:
		tmp = ((d4 - d1) - d3) * d1
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 1.75e-59)
		tmp = Float64(Float64(Float64(Float64(-d1) + d2) - d3) * d1);
	else
		tmp = Float64(Float64(Float64(d4 - d1) - d3) * d1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d4 <= 1.75e-59)
		tmp = ((-d1 + d2) - d3) * d1;
	else
		tmp = ((d4 - d1) - d3) * d1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 1.75e-59], N[(N[(N[((-d1) + d2), $MachinePrecision] - d3), $MachinePrecision] * d1), $MachinePrecision], N[(N[(N[(d4 - d1), $MachinePrecision] - d3), $MachinePrecision] * d1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d4 < 1.75e-59

   1. Initial program 89.1%

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

   3. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      6. +-commutative N/A

         \[\leadsto \left(\left(\left(-1 \cdot d1 + d4\right) + d2\right) - d3\right) \cdot d1 \]

      7. lower-fma.f64 100.0

         \[\leadsto \left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1 \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1} \]

   6. Taylor expanded in d1 around inf

      \[\leadsto \left(\left(-1 \cdot d1 + d2\right) - d3\right) \cdot d1 \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \left(\left(\left(\mathsf{neg}\left(d1\right)\right) + d2\right) - d3\right) \cdot d1 \]

      2. lift-neg.f64 80.6

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

   8. Applied rewrites 80.6%

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

   if 1.75e-59 < d4

   1. Initial program 78.1%

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

   3. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      6. +-commutative N/A

         \[\leadsto \left(\left(\left(-1 \cdot d1 + d4\right) + d2\right) - d3\right) \cdot d1 \]

      7. lower-fma.f64 100.0

         \[\leadsto \left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1 \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1} \]

   6. Taylor expanded in d2 around 0

      \[\leadsto \left(\left(d4 + -1 \cdot d1\right) - d3\right) \cdot d1 \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(-1 \cdot d1 + d4\right) - d3\right) \cdot d1 \]

      2. lift-fma.f64 83.0

         \[\leadsto \left(\mathsf{fma}\left(-1, d1, d4\right) - d3\right) \cdot d1 \]

   8. Applied rewrites 83.0%

      \[\leadsto \left(\mathsf{fma}\left(-1, d1, d4\right) - d3\right) \cdot d1 \]
   9. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \left(\left(-1 \cdot d1 + d4\right) - d3\right) \cdot d1 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(\left(-1 \cdot d1 + d4\right) - d3\right) \cdot d1 \]

      3. mul-1-neg N/A

         \[\leadsto \left(\left(\left(\mathsf{neg}\left(d1\right)\right) + d4\right) - d3\right) \cdot d1 \]

      4. lift-neg.f64 83.0

         \[\leadsto \left(\left(\left(-d1\right) + d4\right) - d3\right) \cdot d1 \]

   10. Applied rewrites 83.0%

       \[\leadsto \left(\left(\left(-d1\right) + d4\right) - d3\right) \cdot d1 \]

   11. Taylor expanded in d4 around 0

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

       1. lower--.f64 83.0

          \[\leadsto \left(\left(d4 - d1\right) - d3\right) \cdot d1 \]

   13. Applied rewrites 83.0%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d4 \leq 1.75 \cdot 10^{-59}:\\ \;\;\;\;\left(\left(\left(-d1\right) + d2\right) - d3\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(d4 - d1\right) - d3\right) \cdot d1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -5.3 \cdot 10^{-14}:\\ \;\;\;\;\left(\left(d4 + d2\right) - d3\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(d4 - d1\right) - d3\right) \cdot d1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -5.3e-14) (* (- (+ d4 d2) d3) d1) (* (- (- d4 d1) d3) d1)))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -5.3e-14) {
		tmp = ((d4 + d2) - d3) * d1;
	} else {
		tmp = ((d4 - d1) - d3) * d1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(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 <= (-5.3d-14)) then
        tmp = ((d4 + d2) - d3) * d1
    else
        tmp = ((d4 - d1) - d3) * d1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -5.3e-14) {
		tmp = ((d4 + d2) - d3) * d1;
	} else {
		tmp = ((d4 - d1) - d3) * d1;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -5.3e-14:
		tmp = ((d4 + d2) - d3) * d1
	else:
		tmp = ((d4 - d1) - d3) * d1
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -5.3e-14)
		tmp = Float64(Float64(Float64(d4 + d2) - d3) * d1);
	else
		tmp = Float64(Float64(Float64(d4 - d1) - d3) * d1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d2 <= -5.3e-14)
		tmp = ((d4 + d2) - d3) * d1;
	else
		tmp = ((d4 - d1) - d3) * d1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -5.3e-14], N[(N[(N[(d4 + d2), $MachinePrecision] - d3), $MachinePrecision] * d1), $MachinePrecision], N[(N[(N[(d4 - d1), $MachinePrecision] - d3), $MachinePrecision] * d1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -5.3000000000000001e-14

   1. Initial program 85.0%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \left(\left(d2 + d4\right) - d3\right) \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\left(d4 + d2\right) - d3\right) \cdot d1 \]

      5. lower-+.f64 89.1

         \[\leadsto \left(\left(d4 + d2\right) - d3\right) \cdot d1 \]

   5. Applied rewrites 89.1%

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

   if -5.3000000000000001e-14 < d2

   1. Initial program 86.2%

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

   3. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      6. +-commutative N/A

         \[\leadsto \left(\left(\left(-1 \cdot d1 + d4\right) + d2\right) - d3\right) \cdot d1 \]

      7. lower-fma.f64 100.0

         \[\leadsto \left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1 \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1} \]

   6. Taylor expanded in d2 around 0

      \[\leadsto \left(\left(d4 + -1 \cdot d1\right) - d3\right) \cdot d1 \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(-1 \cdot d1 + d4\right) - d3\right) \cdot d1 \]

      2. lift-fma.f64 82.5

         \[\leadsto \left(\mathsf{fma}\left(-1, d1, d4\right) - d3\right) \cdot d1 \]

   8. Applied rewrites 82.5%

      \[\leadsto \left(\mathsf{fma}\left(-1, d1, d4\right) - d3\right) \cdot d1 \]
   9. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \left(\left(-1 \cdot d1 + d4\right) - d3\right) \cdot d1 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(\left(-1 \cdot d1 + d4\right) - d3\right) \cdot d1 \]

      3. mul-1-neg N/A

         \[\leadsto \left(\left(\left(\mathsf{neg}\left(d1\right)\right) + d4\right) - d3\right) \cdot d1 \]

      4. lift-neg.f64 82.5

         \[\leadsto \left(\left(\left(-d1\right) + d4\right) - d3\right) \cdot d1 \]

   10. Applied rewrites 82.5%

       \[\leadsto \left(\left(\left(-d1\right) + d4\right) - d3\right) \cdot d1 \]

   11. Taylor expanded in d4 around 0

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

       1. lower--.f64 82.5

          \[\leadsto \left(\left(d4 - d1\right) - d3\right) \cdot d1 \]

   13. Applied rewrites 82.5%

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

Alternative 7: 82.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d2 \leq -3.45 \cdot 10^{+87}:\\ \;\;\;\;\left(d2 - d3\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(d4 - d1\right) - d3\right) \cdot d1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d2 -3.45e+87) (* (- d2 d3) d1) (* (- (- d4 d1) d3) d1)))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -3.45e+87) {
		tmp = (d2 - d3) * d1;
	} else {
		tmp = ((d4 - d1) - d3) * d1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(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 <= (-3.45d+87)) then
        tmp = (d2 - d3) * d1
    else
        tmp = ((d4 - d1) - d3) * d1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d2 <= -3.45e+87) {
		tmp = (d2 - d3) * d1;
	} else {
		tmp = ((d4 - d1) - d3) * d1;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d2 <= -3.45e+87:
		tmp = (d2 - d3) * d1
	else:
		tmp = ((d4 - d1) - d3) * d1
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d2 <= -3.45e+87)
		tmp = Float64(Float64(d2 - d3) * d1);
	else
		tmp = Float64(Float64(Float64(d4 - d1) - d3) * d1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d2 <= -3.45e+87)
		tmp = (d2 - d3) * d1;
	else
		tmp = ((d4 - d1) - d3) * d1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d2, -3.45e+87], N[(N[(d2 - d3), $MachinePrecision] * d1), $MachinePrecision], N[(N[(N[(d4 - d1), $MachinePrecision] - d3), $MachinePrecision] * d1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d2 < -3.44999999999999982e87

   1. Initial program 86.0%

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

   3. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      6. +-commutative N/A

         \[\leadsto \left(\left(\left(-1 \cdot d1 + d4\right) + d2\right) - d3\right) \cdot d1 \]

      7. lower-fma.f64 100.0

         \[\leadsto \left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1 \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1} \]

   6. Taylor expanded in d2 around inf

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

   8. Applied rewrites 75.0%

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

   if -3.44999999999999982e87 < d2

   1. Initial program 85.9%

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

   3. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      6. +-commutative N/A

         \[\leadsto \left(\left(\left(-1 \cdot d1 + d4\right) + d2\right) - d3\right) \cdot d1 \]

      7. lower-fma.f64 100.0

         \[\leadsto \left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1 \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1} \]

   6. Taylor expanded in d2 around 0

      \[\leadsto \left(\left(d4 + -1 \cdot d1\right) - d3\right) \cdot d1 \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \left(\left(-1 \cdot d1 + d4\right) - d3\right) \cdot d1 \]

      2. lift-fma.f64 81.7

         \[\leadsto \left(\mathsf{fma}\left(-1, d1, d4\right) - d3\right) \cdot d1 \]

   8. Applied rewrites 81.7%

      \[\leadsto \left(\mathsf{fma}\left(-1, d1, d4\right) - d3\right) \cdot d1 \]
   9. Step-by-step derivation

      1. lift-fma.f64 N/A

         \[\leadsto \left(\left(-1 \cdot d1 + d4\right) - d3\right) \cdot d1 \]

      2. lower-+.f64 N/A

         \[\leadsto \left(\left(-1 \cdot d1 + d4\right) - d3\right) \cdot d1 \]

      3. mul-1-neg N/A

         \[\leadsto \left(\left(\left(\mathsf{neg}\left(d1\right)\right) + d4\right) - d3\right) \cdot d1 \]

      4. lift-neg.f64 81.7

         \[\leadsto \left(\left(\left(-d1\right) + d4\right) - d3\right) \cdot d1 \]

   10. Applied rewrites 81.7%

       \[\leadsto \left(\left(\left(-d1\right) + d4\right) - d3\right) \cdot d1 \]

   11. Taylor expanded in d4 around 0

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

       1. lower--.f64 81.7

          \[\leadsto \left(\left(d4 - d1\right) - d3\right) \cdot d1 \]

   13. Applied rewrites 81.7%

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

Alternative 8: 63.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 5 \cdot 10^{-31}:\\ \;\;\;\;\left(d2 - d3\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(d4 - d3\right) \cdot d1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 5e-31) (* (- d2 d3) d1) (* (- d4 d3) d1)))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 5e-31) {
		tmp = (d2 - d3) * d1;
	} else {
		tmp = (d4 - d3) * d1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(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 <= 5d-31) then
        tmp = (d2 - d3) * d1
    else
        tmp = (d4 - d3) * d1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 5e-31) {
		tmp = (d2 - d3) * d1;
	} else {
		tmp = (d4 - d3) * d1;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 5e-31:
		tmp = (d2 - d3) * d1
	else:
		tmp = (d4 - d3) * d1
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 5e-31)
		tmp = Float64(Float64(d2 - d3) * d1);
	else
		tmp = Float64(Float64(d4 - d3) * d1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d4 <= 5e-31)
		tmp = (d2 - d3) * d1;
	else
		tmp = (d4 - d3) * d1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 5e-31], N[(N[(d2 - d3), $MachinePrecision] * d1), $MachinePrecision], N[(N[(d4 - d3), $MachinePrecision] * d1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d4 < 5e-31

   1. Initial program 89.6%

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

   3. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      6. +-commutative N/A

         \[\leadsto \left(\left(\left(-1 \cdot d1 + d4\right) + d2\right) - d3\right) \cdot d1 \]

      7. lower-fma.f64 100.0

         \[\leadsto \left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1 \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1} \]

   6. Taylor expanded in d2 around inf

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

   8. Applied rewrites 59.6%

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

   if 5e-31 < d4

   1. Initial program 74.6%

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

   3. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      6. +-commutative N/A

         \[\leadsto \left(\left(\left(-1 \cdot d1 + d4\right) + d2\right) - d3\right) \cdot d1 \]

      7. lower-fma.f64 100.0

         \[\leadsto \left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1 \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1} \]

   6. Taylor expanded in d4 around inf

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

   8. Applied rewrites 66.6%

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

Alternative 9: 64.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 2.2 \cdot 10^{+18}:\\ \;\;\;\;\left(d2 - d3\right) \cdot d1\\ \mathbf{else}:\\ \;\;\;\;\left(d4 + d2\right) \cdot d1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 2.2e+18) (* (- d2 d3) d1) (* (+ d4 d2) d1)))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 2.2e+18) {
		tmp = (d2 - d3) * d1;
	} else {
		tmp = (d4 + d2) * d1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(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 <= 2.2d+18) then
        tmp = (d2 - d3) * d1
    else
        tmp = (d4 + d2) * d1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 2.2e+18) {
		tmp = (d2 - d3) * d1;
	} else {
		tmp = (d4 + d2) * d1;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 2.2e+18:
		tmp = (d2 - d3) * d1
	else:
		tmp = (d4 + d2) * d1
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 2.2e+18)
		tmp = Float64(Float64(d2 - d3) * d1);
	else
		tmp = Float64(Float64(d4 + d2) * d1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d4 <= 2.2e+18)
		tmp = (d2 - d3) * d1;
	else
		tmp = (d4 + d2) * d1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 2.2e+18], N[(N[(d2 - d3), $MachinePrecision] * d1), $MachinePrecision], N[(N[(d4 + d2), $MachinePrecision] * d1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d4 < 2.2e18

   1. Initial program 89.7%

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

   3. Taylor expanded in d1 around 0

      \[\leadsto \color{blue}{d1 \cdot \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot \color{blue}{d1} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\left(d2 + \left(d4 + -1 \cdot d1\right)\right) - d3\right) \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      5. lower-+.f64 N/A

         \[\leadsto \left(\left(\left(d4 + -1 \cdot d1\right) + d2\right) - d3\right) \cdot d1 \]

      6. +-commutative N/A

         \[\leadsto \left(\left(\left(-1 \cdot d1 + d4\right) + d2\right) - d3\right) \cdot d1 \]

      7. lower-fma.f64 100.0

         \[\leadsto \left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1 \]

   5. Applied rewrites 100.0%

      \[\leadsto \color{blue}{\left(\left(\mathsf{fma}\left(-1, d1, d4\right) + d2\right) - d3\right) \cdot d1} \]

   6. Taylor expanded in d2 around inf

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

   8. Applied rewrites 59.6%

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

   if 2.2e18 < d4

   1. Initial program 70.6%

      \[\left(\left(d1 \cdot d2 - d1 \cdot d3\right) + d4 \cdot d1\right) - d1 \cdot d1 \]
   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

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

         \[\leadsto \left(\left(d2 + d4\right) - d3\right) \cdot d1 \]

      4. +-commutative N/A

         \[\leadsto \left(\left(d4 + d2\right) - d3\right) \cdot d1 \]

      5. lower-+.f64 81.3

         \[\leadsto \left(\left(d4 + d2\right) - d3\right) \cdot d1 \]

   5. Applied rewrites 81.3%

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

   6. Taylor expanded in d3 around 0

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

      1. +-commutative N/A

         \[\leadsto \left(d4 + d2\right) \cdot d1 \]

      2. lift-+.f64 68.1

         \[\leadsto \left(d4 + d2\right) \cdot d1 \]

   8. Applied rewrites 68.1%

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

Alternative 10: 37.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d4 \leq 1.1 \cdot 10^{-57}:\\ \;\;\;\;d2 \cdot d1\\ \mathbf{else}:\\ \;\;\;\;d4 \cdot d1\\ \end{array} \end{array} \]

FPCore

(FPCore (d1 d2 d3 d4)
 :precision binary64
 (if (<= d4 1.1e-57) (* d2 d1) (* d4 d1)))

C

double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 1.1e-57) {
		tmp = d2 * d1;
	} else {
		tmp = d4 * d1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(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 <= 1.1d-57) then
        tmp = d2 * d1
    else
        tmp = d4 * d1
    end if
    code = tmp
end function

Java

public static double code(double d1, double d2, double d3, double d4) {
	double tmp;
	if (d4 <= 1.1e-57) {
		tmp = d2 * d1;
	} else {
		tmp = d4 * d1;
	}
	return tmp;
}

Python

def code(d1, d2, d3, d4):
	tmp = 0
	if d4 <= 1.1e-57:
		tmp = d2 * d1
	else:
		tmp = d4 * d1
	return tmp

Julia

function code(d1, d2, d3, d4)
	tmp = 0.0
	if (d4 <= 1.1e-57)
		tmp = Float64(d2 * d1);
	else
		tmp = Float64(d4 * d1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(d1, d2, d3, d4)
	tmp = 0.0;
	if (d4 <= 1.1e-57)
		tmp = d2 * d1;
	else
		tmp = d4 * d1;
	end
	tmp_2 = tmp;
end

Wolfram

code[d1_, d2_, d3_, d4_] := If[LessEqual[d4, 1.1e-57], N[(d2 * d1), $MachinePrecision], N[(d4 * d1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d4 < 1.09999999999999999e-57

   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 d2 around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 37.1

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

   5. Applied rewrites 37.1%

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

   if 1.09999999999999999e-57 < d4

   1. Initial program 77.4%

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

   3. Taylor expanded in d4 around inf

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

      1. *-commutative N/A

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

      2. lift-*.f64 42.2

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

   5. Applied rewrites 42.2%

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

Alternative 11: 31.5% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ d2 \cdot d1 \end{array} \]

FPCore

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

C

double code(double d1, double d2, double d3, double d4) {
	return d2 * 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 = d2 * d1
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.9%

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

3. Taylor expanded in d2 around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 34.6

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

5. Applied rewrites 34.6%

   \[\leadsto \color{blue}{d2 \cdot d1} \]
6. 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 2025080 
(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)))