(log (- (exp (/ (- z0) z1)) -1))

Percentage Accurate: 99.3% → 99.3%

Time: 3.9s

Alternatives: 5

Speedup: 1.0×

• could not determine a ground truth

  1. z0 = 5.567200723259838e+62
  2. z1 = -3.8109717685804577e+36

Specification

Math

\[\log \left(e^{\frac{-z0}{z1}} - -1\right) \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (log (- (exp (/ (- z0) z1)) -1.0)))

C

double code(double z0, double z1) {
	return log((exp((-z0 / z1)) - -1.0));
}

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(z0, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    code = log((exp((-z0 / z1)) - (-1.0d0)))
end function

Java

public static double code(double z0, double z1) {
	return Math.log((Math.exp((-z0 / z1)) - -1.0));
}

Python

def code(z0, z1):
	return math.log((math.exp((-z0 / z1)) - -1.0))

Julia

function code(z0, z1)
	return log(Float64(exp(Float64(Float64(-z0) / z1)) - -1.0))
end

MATLAB

function tmp = code(z0, z1)
	tmp = log((exp((-z0 / z1)) - -1.0));
end

Wolfram

code[z0_, z1_] := N[Log[N[(N[Exp[N[((-z0) / z1), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]], $MachinePrecision]

Initial Program: 99.3% accurate, 1.0× speedup

Math

\[\log \left(e^{\frac{-z0}{z1}} - -1\right) \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (log (- (exp (/ (- z0) z1)) -1.0)))

C

double code(double z0, double z1) {
	return log((exp((-z0 / z1)) - -1.0));
}

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(z0, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    code = log((exp((-z0 / z1)) - (-1.0d0)))
end function

Java

public static double code(double z0, double z1) {
	return Math.log((Math.exp((-z0 / z1)) - -1.0));
}

Python

def code(z0, z1):
	return math.log((math.exp((-z0 / z1)) - -1.0))

Julia

function code(z0, z1)
	return log(Float64(exp(Float64(Float64(-z0) / z1)) - -1.0))
end

MATLAB

function tmp = code(z0, z1)
	tmp = log((exp((-z0 / z1)) - -1.0));
end

Wolfram

code[z0_, z1_] := N[Log[N[(N[Exp[N[((-z0) / z1), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]], $MachinePrecision]

Alternative 1: 69.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} t_0 := \frac{-z0}{z1}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+57}:\\ \;\;\;\;z0 \cdot \frac{0.6931471805599453 \cdot z1 - 0.5 \cdot z0}{z0 \cdot z1}\\ \mathbf{elif}\;t\_0 \leq -1000000000000:\\ \;\;\;\;\frac{\frac{\left(\log 2 \cdot z1\right) \cdot z1 - \left(0.5 \cdot z0\right) \cdot z1}{z1}}{z1}\\ \mathbf{else}:\\ \;\;\;\;0.6931471805599453 + -0.5 \cdot \frac{z0}{z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (let* ((t_0 (/ (- z0) z1)))
  (if (<= t_0 -1e+57)
    (* z0 (/ (- (* 0.6931471805599453 z1) (* 0.5 z0)) (* z0 z1)))
    (if (<= t_0 -1000000000000.0)
      (/ (/ (- (* (* (log 2.0) z1) z1) (* (* 0.5 z0) z1)) z1) z1)
      (+ 0.6931471805599453 (* -0.5 (/ z0 z1)))))))

C

double code(double z0, double z1) {
	double t_0 = -z0 / z1;
	double tmp;
	if (t_0 <= -1e+57) {
		tmp = z0 * (((0.6931471805599453 * z1) - (0.5 * z0)) / (z0 * z1));
	} else if (t_0 <= -1000000000000.0) {
		tmp = ((((log(2.0) * z1) * z1) - ((0.5 * z0) * z1)) / z1) / z1;
	} else {
		tmp = 0.6931471805599453 + (-0.5 * (z0 / z1));
	}
	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(z0, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -z0 / z1
    if (t_0 <= (-1d+57)) then
        tmp = z0 * (((0.6931471805599453d0 * z1) - (0.5d0 * z0)) / (z0 * z1))
    else if (t_0 <= (-1000000000000.0d0)) then
        tmp = ((((log(2.0d0) * z1) * z1) - ((0.5d0 * z0) * z1)) / z1) / z1
    else
        tmp = 0.6931471805599453d0 + ((-0.5d0) * (z0 / z1))
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1) {
	double t_0 = -z0 / z1;
	double tmp;
	if (t_0 <= -1e+57) {
		tmp = z0 * (((0.6931471805599453 * z1) - (0.5 * z0)) / (z0 * z1));
	} else if (t_0 <= -1000000000000.0) {
		tmp = ((((Math.log(2.0) * z1) * z1) - ((0.5 * z0) * z1)) / z1) / z1;
	} else {
		tmp = 0.6931471805599453 + (-0.5 * (z0 / z1));
	}
	return tmp;
}

Python

def code(z0, z1):
	t_0 = -z0 / z1
	tmp = 0
	if t_0 <= -1e+57:
		tmp = z0 * (((0.6931471805599453 * z1) - (0.5 * z0)) / (z0 * z1))
	elif t_0 <= -1000000000000.0:
		tmp = ((((math.log(2.0) * z1) * z1) - ((0.5 * z0) * z1)) / z1) / z1
	else:
		tmp = 0.6931471805599453 + (-0.5 * (z0 / z1))
	return tmp

Julia

function code(z0, z1)
	t_0 = Float64(Float64(-z0) / z1)
	tmp = 0.0
	if (t_0 <= -1e+57)
		tmp = Float64(z0 * Float64(Float64(Float64(0.6931471805599453 * z1) - Float64(0.5 * z0)) / Float64(z0 * z1)));
	elseif (t_0 <= -1000000000000.0)
		tmp = Float64(Float64(Float64(Float64(Float64(log(2.0) * z1) * z1) - Float64(Float64(0.5 * z0) * z1)) / z1) / z1);
	else
		tmp = Float64(0.6931471805599453 + Float64(-0.5 * Float64(z0 / z1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	t_0 = -z0 / z1;
	tmp = 0.0;
	if (t_0 <= -1e+57)
		tmp = z0 * (((0.6931471805599453 * z1) - (0.5 * z0)) / (z0 * z1));
	elseif (t_0 <= -1000000000000.0)
		tmp = ((((log(2.0) * z1) * z1) - ((0.5 * z0) * z1)) / z1) / z1;
	else
		tmp = 0.6931471805599453 + (-0.5 * (z0 / z1));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := Block[{t$95$0 = N[((-z0) / z1), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+57], N[(z0 * N[(N[(N[(0.6931471805599453 * z1), $MachinePrecision] - N[(0.5 * z0), $MachinePrecision]), $MachinePrecision] / N[(z0 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, -1000000000000.0], N[(N[(N[(N[(N[(N[Log[2.0], $MachinePrecision] * z1), $MachinePrecision] * z1), $MachinePrecision] - N[(N[(0.5 * z0), $MachinePrecision] * z1), $MachinePrecision]), $MachinePrecision] / z1), $MachinePrecision] / z1), $MachinePrecision], N[(0.6931471805599453 + N[(-0.5 * N[(z0 / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (neg.f64 z0) z1) < -1e57

   1. Initial program 99.3%

      \[\log \left(e^{\frac{-z0}{z1}} - -1\right) \]

   2. Taylor expanded in z0 around 0

      \[\leadsto \color{blue}{\log 2 + \frac{-1}{2} \cdot \frac{z0}{z1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \log 2 + \color{blue}{\frac{-1}{2} \cdot \frac{z0}{z1}} \]

      2. lower-log.f64 N/A

         \[\leadsto \log 2 + \color{blue}{\frac{-1}{2}} \cdot \frac{z0}{z1} \]

      3. lower-*.f64 N/A

         \[\leadsto \log 2 + \frac{-1}{2} \cdot \color{blue}{\frac{z0}{z1}} \]

      4. lower-/.f64 66.4%

         \[\leadsto \log 2 + -0.5 \cdot \frac{z0}{\color{blue}{z1}} \]

   4. Applied rewrites 66.4%

      \[\leadsto \color{blue}{\log 2 + -0.5 \cdot \frac{z0}{z1}} \]

   5. Taylor expanded in z0 around inf

      \[\leadsto z0 \cdot \color{blue}{\left(\frac{\log 2}{z0} - \frac{1}{2} \cdot \frac{1}{z1}\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{\log 2}{z0} - \color{blue}{\frac{1}{2} \cdot \frac{1}{z1}}\right) \]

      2. lower--.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{\log 2}{z0} - \frac{1}{2} \cdot \color{blue}{\frac{1}{z1}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{\log 2}{z0} - \frac{1}{2} \cdot \frac{\color{blue}{1}}{z1}\right) \]

      4. lower-log.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{\log 2}{z0} - \frac{1}{2} \cdot \frac{1}{z1}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{\log 2}{z0} - \frac{1}{2} \cdot \frac{1}{\color{blue}{z1}}\right) \]

      6. lower-/.f64 66.3%

         \[\leadsto z0 \cdot \left(\frac{\log 2}{z0} - 0.5 \cdot \frac{1}{z1}\right) \]

   7. Applied rewrites 66.3%

      \[\leadsto z0 \cdot \color{blue}{\left(\frac{\log 2}{z0} - 0.5 \cdot \frac{1}{z1}\right)} \]

   8. Evaluated real constant 66.3%

      \[\leadsto z0 \cdot \left(\frac{0.6931471805599453}{z0} - 0.5 \cdot \frac{1}{z1}\right) \]
   9. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{\frac{6243314768165359}{9007199254740992}}{z0} - \frac{1}{2} \cdot \color{blue}{\frac{1}{z1}}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{\frac{6243314768165359}{9007199254740992}}{z0} - \frac{1}{2} \cdot \frac{1}{\color{blue}{z1}}\right) \]

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

         \[\leadsto z0 \cdot \left(\frac{\frac{6243314768165359}{9007199254740992}}{z0} + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right) \cdot \color{blue}{\frac{1}{z1}}\right) \]

      4. lift-/.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{\frac{6243314768165359}{9007199254740992}}{z0} + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right) \cdot \frac{\color{blue}{1}}{z1}\right) \]

      5. metadata-eval N/A

         \[\leadsto z0 \cdot \left(\frac{\frac{6243314768165359}{9007199254740992}}{z0} + \frac{-1}{2} \cdot \frac{1}{z1}\right) \]

      6. lift-/.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{\frac{6243314768165359}{9007199254740992}}{z0} + \frac{-1}{2} \cdot \frac{1}{z1}\right) \]

      7. mult-flip N/A

         \[\leadsto z0 \cdot \left(\frac{\frac{6243314768165359}{9007199254740992}}{z0} + \frac{\frac{-1}{2}}{z1}\right) \]

      8. common-denominator N/A

         \[\leadsto z0 \cdot \frac{\frac{6243314768165359}{9007199254740992} \cdot z1 + \frac{-1}{2} \cdot z0}{z0 \cdot \color{blue}{z1}} \]

      9. lower-/.f64 N/A

         \[\leadsto z0 \cdot \frac{\frac{6243314768165359}{9007199254740992} \cdot z1 + \frac{-1}{2} \cdot z0}{z0 \cdot \color{blue}{z1}} \]

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

          \[\leadsto z0 \cdot \frac{\frac{6243314768165359}{9007199254740992} \cdot z1 - \left(\mathsf{neg}\left(\frac{-1}{2}\right)\right) \cdot z0}{z0 \cdot z1} \]

      11. metadata-eval N/A

          \[\leadsto z0 \cdot \frac{\frac{6243314768165359}{9007199254740992} \cdot z1 - \frac{1}{2} \cdot z0}{z0 \cdot z1} \]

      12. lower--.f64 N/A

          \[\leadsto z0 \cdot \frac{\frac{6243314768165359}{9007199254740992} \cdot z1 - \frac{1}{2} \cdot z0}{z0 \cdot z1} \]

      13. lower-*.f64 N/A

          \[\leadsto z0 \cdot \frac{\frac{6243314768165359}{9007199254740992} \cdot z1 - \frac{1}{2} \cdot z0}{z0 \cdot z1} \]

      14. lower-*.f64 N/A

          \[\leadsto z0 \cdot \frac{\frac{6243314768165359}{9007199254740992} \cdot z1 - \frac{1}{2} \cdot z0}{z0 \cdot z1} \]

      15. lower-*.f64 55.3%

          \[\leadsto z0 \cdot \frac{0.6931471805599453 \cdot z1 - 0.5 \cdot z0}{z0 \cdot z1} \]

   10. Applied rewrites 55.3%

       \[\leadsto z0 \cdot \frac{0.6931471805599453 \cdot z1 - 0.5 \cdot z0}{z0 \cdot \color{blue}{z1}} \]

   if -1e57 < (/.f64 (neg.f64 z0) z1) < -1e12

   1. Initial program 99.3%

      \[\log \left(e^{\frac{-z0}{z1}} - -1\right) \]

   2. Taylor expanded in z0 around 0

      \[\leadsto \color{blue}{\log 2 + \frac{-1}{2} \cdot \frac{z0}{z1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \log 2 + \color{blue}{\frac{-1}{2} \cdot \frac{z0}{z1}} \]

      2. lower-log.f64 N/A

         \[\leadsto \log 2 + \color{blue}{\frac{-1}{2}} \cdot \frac{z0}{z1} \]

      3. lower-*.f64 N/A

         \[\leadsto \log 2 + \frac{-1}{2} \cdot \color{blue}{\frac{z0}{z1}} \]

      4. lower-/.f64 66.4%

         \[\leadsto \log 2 + -0.5 \cdot \frac{z0}{\color{blue}{z1}} \]

   4. Applied rewrites 66.4%

      \[\leadsto \color{blue}{\log 2 + -0.5 \cdot \frac{z0}{z1}} \]
   5. Step-by-step derivation

      1. lift-+.f64 N/A

         \[\leadsto \log 2 + \color{blue}{\frac{-1}{2} \cdot \frac{z0}{z1}} \]

      2. lift-*.f64 N/A

         \[\leadsto \log 2 + \frac{-1}{2} \cdot \color{blue}{\frac{z0}{z1}} \]

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

         \[\leadsto \log 2 - \color{blue}{\left(\mathsf{neg}\left(\frac{-1}{2}\right)\right) \cdot \frac{z0}{z1}} \]

      4. lift-/.f64 N/A

         \[\leadsto \log 2 - \left(\mathsf{neg}\left(\frac{-1}{2}\right)\right) \cdot \frac{z0}{\color{blue}{z1}} \]

      5. associate-*r/ N/A

         \[\leadsto \log 2 - \frac{\left(\mathsf{neg}\left(\frac{-1}{2}\right)\right) \cdot z0}{\color{blue}{z1}} \]

      6. sub-to-fraction N/A

         \[\leadsto \frac{\log 2 \cdot z1 - \left(\mathsf{neg}\left(\frac{-1}{2}\right)\right) \cdot z0}{\color{blue}{z1}} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\log 2 \cdot z1 - \left(\mathsf{neg}\left(\frac{-1}{2}\right)\right) \cdot z0}{\color{blue}{z1}} \]

      8. lower--.f64 N/A

         \[\leadsto \frac{\log 2 \cdot z1 - \left(\mathsf{neg}\left(\frac{-1}{2}\right)\right) \cdot z0}{z1} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{\log 2 \cdot z1 - \left(\mathsf{neg}\left(\frac{-1}{2}\right)\right) \cdot z0}{z1} \]

      10. lower-*.f64 N/A

          \[\leadsto \frac{\log 2 \cdot z1 - \left(\mathsf{neg}\left(\frac{-1}{2}\right)\right) \cdot z0}{z1} \]

      11. metadata-eval 66.3%

          \[\leadsto \frac{\log 2 \cdot z1 - 0.5 \cdot z0}{z1} \]

   6. Applied rewrites 66.3%

      \[\leadsto \frac{\log 2 \cdot z1 - 0.5 \cdot z0}{\color{blue}{z1}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{\log 2 \cdot z1 - \frac{1}{2} \cdot z0}{\color{blue}{z1}} \]

      2. lift--.f64 N/A

         \[\leadsto \frac{\log 2 \cdot z1 - \frac{1}{2} \cdot z0}{z1} \]

      3. div-sub N/A

         \[\leadsto \frac{\log 2 \cdot z1}{z1} - \color{blue}{\frac{\frac{1}{2} \cdot z0}{z1}} \]

      4. frac-sub N/A

         \[\leadsto \frac{\left(\log 2 \cdot z1\right) \cdot z1 - z1 \cdot \left(\frac{1}{2} \cdot z0\right)}{\color{blue}{z1 \cdot z1}} \]

      5. associate-/r* N/A

         \[\leadsto \frac{\frac{\left(\log 2 \cdot z1\right) \cdot z1 - z1 \cdot \left(\frac{1}{2} \cdot z0\right)}{z1}}{\color{blue}{z1}} \]

      6. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\left(\log 2 \cdot z1\right) \cdot z1 - z1 \cdot \left(\frac{1}{2} \cdot z0\right)}{z1}}{\color{blue}{z1}} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\frac{\left(\log 2 \cdot z1\right) \cdot z1 - z1 \cdot \left(\frac{1}{2} \cdot z0\right)}{z1}}{z1} \]

      8. lower--.f64 N/A

         \[\leadsto \frac{\frac{\left(\log 2 \cdot z1\right) \cdot z1 - z1 \cdot \left(\frac{1}{2} \cdot z0\right)}{z1}}{z1} \]

      9. lower-*.f64 N/A

         \[\leadsto \frac{\frac{\left(\log 2 \cdot z1\right) \cdot z1 - z1 \cdot \left(\frac{1}{2} \cdot z0\right)}{z1}}{z1} \]

      10. *-commutative N/A

          \[\leadsto \frac{\frac{\left(\log 2 \cdot z1\right) \cdot z1 - \left(\frac{1}{2} \cdot z0\right) \cdot z1}{z1}}{z1} \]

      11. lower-*.f64 38.1%

          \[\leadsto \frac{\frac{\left(\log 2 \cdot z1\right) \cdot z1 - \left(0.5 \cdot z0\right) \cdot z1}{z1}}{z1} \]

   8. Applied rewrites 38.1%

      \[\leadsto \frac{\frac{\left(\log 2 \cdot z1\right) \cdot z1 - \left(0.5 \cdot z0\right) \cdot z1}{z1}}{\color{blue}{z1}} \]

   if -1e12 < (/.f64 (neg.f64 z0) z1)

   1. Initial program 99.3%

      \[\log \left(e^{\frac{-z0}{z1}} - -1\right) \]

   2. Taylor expanded in z0 around 0

      \[\leadsto \color{blue}{\log 2 + \frac{-1}{2} \cdot \frac{z0}{z1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \log 2 + \color{blue}{\frac{-1}{2} \cdot \frac{z0}{z1}} \]

      2. lower-log.f64 N/A

         \[\leadsto \log 2 + \color{blue}{\frac{-1}{2}} \cdot \frac{z0}{z1} \]

      3. lower-*.f64 N/A

         \[\leadsto \log 2 + \frac{-1}{2} \cdot \color{blue}{\frac{z0}{z1}} \]

      4. lower-/.f64 66.4%

         \[\leadsto \log 2 + -0.5 \cdot \frac{z0}{\color{blue}{z1}} \]

   4. Applied rewrites 66.4%

      \[\leadsto \color{blue}{\log 2 + -0.5 \cdot \frac{z0}{z1}} \]

   5. Evaluated real constant 66.4%

      \[\leadsto 0.6931471805599453 + \color{blue}{-0.5} \cdot \frac{z0}{z1} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 2: 69.1% accurate, 4.0× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{-z0}{z1} \leq -1 \cdot 10^{+57}:\\ \;\;\;\;z0 \cdot \frac{0.6931471805599453 \cdot z1 - 0.5 \cdot z0}{z0 \cdot z1}\\ \mathbf{else}:\\ \;\;\;\;0.6931471805599453 + -0.5 \cdot \frac{z0}{z1}\\ \end{array} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (if (<= (/ (- z0) z1) -1e+57)
  (* z0 (/ (- (* 0.6931471805599453 z1) (* 0.5 z0)) (* z0 z1)))
  (+ 0.6931471805599453 (* -0.5 (/ z0 z1)))))

C

double code(double z0, double z1) {
	double tmp;
	if ((-z0 / z1) <= -1e+57) {
		tmp = z0 * (((0.6931471805599453 * z1) - (0.5 * z0)) / (z0 * z1));
	} else {
		tmp = 0.6931471805599453 + (-0.5 * (z0 / z1));
	}
	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(z0, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    real(8) :: tmp
    if ((-z0 / z1) <= (-1d+57)) then
        tmp = z0 * (((0.6931471805599453d0 * z1) - (0.5d0 * z0)) / (z0 * z1))
    else
        tmp = 0.6931471805599453d0 + ((-0.5d0) * (z0 / z1))
    end if
    code = tmp
end function

Java

public static double code(double z0, double z1) {
	double tmp;
	if ((-z0 / z1) <= -1e+57) {
		tmp = z0 * (((0.6931471805599453 * z1) - (0.5 * z0)) / (z0 * z1));
	} else {
		tmp = 0.6931471805599453 + (-0.5 * (z0 / z1));
	}
	return tmp;
}

Python

def code(z0, z1):
	tmp = 0
	if (-z0 / z1) <= -1e+57:
		tmp = z0 * (((0.6931471805599453 * z1) - (0.5 * z0)) / (z0 * z1))
	else:
		tmp = 0.6931471805599453 + (-0.5 * (z0 / z1))
	return tmp

Julia

function code(z0, z1)
	tmp = 0.0
	if (Float64(Float64(-z0) / z1) <= -1e+57)
		tmp = Float64(z0 * Float64(Float64(Float64(0.6931471805599453 * z1) - Float64(0.5 * z0)) / Float64(z0 * z1)));
	else
		tmp = Float64(0.6931471805599453 + Float64(-0.5 * Float64(z0 / z1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(z0, z1)
	tmp = 0.0;
	if ((-z0 / z1) <= -1e+57)
		tmp = z0 * (((0.6931471805599453 * z1) - (0.5 * z0)) / (z0 * z1));
	else
		tmp = 0.6931471805599453 + (-0.5 * (z0 / z1));
	end
	tmp_2 = tmp;
end

Wolfram

code[z0_, z1_] := If[LessEqual[N[((-z0) / z1), $MachinePrecision], -1e+57], N[(z0 * N[(N[(N[(0.6931471805599453 * z1), $MachinePrecision] - N[(0.5 * z0), $MachinePrecision]), $MachinePrecision] / N[(z0 * z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.6931471805599453 + N[(-0.5 * N[(z0 / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (neg.f64 z0) z1) < -1e57

   1. Initial program 99.3%

      \[\log \left(e^{\frac{-z0}{z1}} - -1\right) \]

   2. Taylor expanded in z0 around 0

      \[\leadsto \color{blue}{\log 2 + \frac{-1}{2} \cdot \frac{z0}{z1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \log 2 + \color{blue}{\frac{-1}{2} \cdot \frac{z0}{z1}} \]

      2. lower-log.f64 N/A

         \[\leadsto \log 2 + \color{blue}{\frac{-1}{2}} \cdot \frac{z0}{z1} \]

      3. lower-*.f64 N/A

         \[\leadsto \log 2 + \frac{-1}{2} \cdot \color{blue}{\frac{z0}{z1}} \]

      4. lower-/.f64 66.4%

         \[\leadsto \log 2 + -0.5 \cdot \frac{z0}{\color{blue}{z1}} \]

   4. Applied rewrites 66.4%

      \[\leadsto \color{blue}{\log 2 + -0.5 \cdot \frac{z0}{z1}} \]

   5. Taylor expanded in z0 around inf

      \[\leadsto z0 \cdot \color{blue}{\left(\frac{\log 2}{z0} - \frac{1}{2} \cdot \frac{1}{z1}\right)} \]
   6. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{\log 2}{z0} - \color{blue}{\frac{1}{2} \cdot \frac{1}{z1}}\right) \]

      2. lower--.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{\log 2}{z0} - \frac{1}{2} \cdot \color{blue}{\frac{1}{z1}}\right) \]

      3. lower-/.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{\log 2}{z0} - \frac{1}{2} \cdot \frac{\color{blue}{1}}{z1}\right) \]

      4. lower-log.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{\log 2}{z0} - \frac{1}{2} \cdot \frac{1}{z1}\right) \]

      5. lower-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{\log 2}{z0} - \frac{1}{2} \cdot \frac{1}{\color{blue}{z1}}\right) \]

      6. lower-/.f64 66.3%

         \[\leadsto z0 \cdot \left(\frac{\log 2}{z0} - 0.5 \cdot \frac{1}{z1}\right) \]

   7. Applied rewrites 66.3%

      \[\leadsto z0 \cdot \color{blue}{\left(\frac{\log 2}{z0} - 0.5 \cdot \frac{1}{z1}\right)} \]

   8. Evaluated real constant 66.3%

      \[\leadsto z0 \cdot \left(\frac{0.6931471805599453}{z0} - 0.5 \cdot \frac{1}{z1}\right) \]
   9. Step-by-step derivation

      1. lift--.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{\frac{6243314768165359}{9007199254740992}}{z0} - \frac{1}{2} \cdot \color{blue}{\frac{1}{z1}}\right) \]

      2. lift-*.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{\frac{6243314768165359}{9007199254740992}}{z0} - \frac{1}{2} \cdot \frac{1}{\color{blue}{z1}}\right) \]

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

         \[\leadsto z0 \cdot \left(\frac{\frac{6243314768165359}{9007199254740992}}{z0} + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right) \cdot \color{blue}{\frac{1}{z1}}\right) \]

      4. lift-/.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{\frac{6243314768165359}{9007199254740992}}{z0} + \left(\mathsf{neg}\left(\frac{1}{2}\right)\right) \cdot \frac{\color{blue}{1}}{z1}\right) \]

      5. metadata-eval N/A

         \[\leadsto z0 \cdot \left(\frac{\frac{6243314768165359}{9007199254740992}}{z0} + \frac{-1}{2} \cdot \frac{1}{z1}\right) \]

      6. lift-/.f64 N/A

         \[\leadsto z0 \cdot \left(\frac{\frac{6243314768165359}{9007199254740992}}{z0} + \frac{-1}{2} \cdot \frac{1}{z1}\right) \]

      7. mult-flip N/A

         \[\leadsto z0 \cdot \left(\frac{\frac{6243314768165359}{9007199254740992}}{z0} + \frac{\frac{-1}{2}}{z1}\right) \]

      8. common-denominator N/A

         \[\leadsto z0 \cdot \frac{\frac{6243314768165359}{9007199254740992} \cdot z1 + \frac{-1}{2} \cdot z0}{z0 \cdot \color{blue}{z1}} \]

      9. lower-/.f64 N/A

         \[\leadsto z0 \cdot \frac{\frac{6243314768165359}{9007199254740992} \cdot z1 + \frac{-1}{2} \cdot z0}{z0 \cdot \color{blue}{z1}} \]

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

          \[\leadsto z0 \cdot \frac{\frac{6243314768165359}{9007199254740992} \cdot z1 - \left(\mathsf{neg}\left(\frac{-1}{2}\right)\right) \cdot z0}{z0 \cdot z1} \]

      11. metadata-eval N/A

          \[\leadsto z0 \cdot \frac{\frac{6243314768165359}{9007199254740992} \cdot z1 - \frac{1}{2} \cdot z0}{z0 \cdot z1} \]

      12. lower--.f64 N/A

          \[\leadsto z0 \cdot \frac{\frac{6243314768165359}{9007199254740992} \cdot z1 - \frac{1}{2} \cdot z0}{z0 \cdot z1} \]

      13. lower-*.f64 N/A

          \[\leadsto z0 \cdot \frac{\frac{6243314768165359}{9007199254740992} \cdot z1 - \frac{1}{2} \cdot z0}{z0 \cdot z1} \]

      14. lower-*.f64 N/A

          \[\leadsto z0 \cdot \frac{\frac{6243314768165359}{9007199254740992} \cdot z1 - \frac{1}{2} \cdot z0}{z0 \cdot z1} \]

      15. lower-*.f64 55.3%

          \[\leadsto z0 \cdot \frac{0.6931471805599453 \cdot z1 - 0.5 \cdot z0}{z0 \cdot z1} \]

   10. Applied rewrites 55.3%

       \[\leadsto z0 \cdot \frac{0.6931471805599453 \cdot z1 - 0.5 \cdot z0}{z0 \cdot \color{blue}{z1}} \]

   if -1e57 < (/.f64 (neg.f64 z0) z1)

   1. Initial program 99.3%

      \[\log \left(e^{\frac{-z0}{z1}} - -1\right) \]

   2. Taylor expanded in z0 around 0

      \[\leadsto \color{blue}{\log 2 + \frac{-1}{2} \cdot \frac{z0}{z1}} \]
   3. Step-by-step derivation

      1. lower-+.f64 N/A

         \[\leadsto \log 2 + \color{blue}{\frac{-1}{2} \cdot \frac{z0}{z1}} \]

      2. lower-log.f64 N/A

         \[\leadsto \log 2 + \color{blue}{\frac{-1}{2}} \cdot \frac{z0}{z1} \]

      3. lower-*.f64 N/A

         \[\leadsto \log 2 + \frac{-1}{2} \cdot \color{blue}{\frac{z0}{z1}} \]

      4. lower-/.f64 66.4%

         \[\leadsto \log 2 + -0.5 \cdot \frac{z0}{\color{blue}{z1}} \]

   4. Applied rewrites 66.4%

      \[\leadsto \color{blue}{\log 2 + -0.5 \cdot \frac{z0}{z1}} \]

   5. Evaluated real constant 66.4%

      \[\leadsto 0.6931471805599453 + \color{blue}{-0.5} \cdot \frac{z0}{z1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 66.4% accurate, 10.9× speedup

Math

\[0.6931471805599453 + -0.5 \cdot \frac{z0}{z1} \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  (+ 0.6931471805599453 (* -0.5 (/ z0 z1))))

C

double code(double z0, double z1) {
	return 0.6931471805599453 + (-0.5 * (z0 / z1));
}

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(z0, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    code = 0.6931471805599453d0 + ((-0.5d0) * (z0 / z1))
end function

Java

public static double code(double z0, double z1) {
	return 0.6931471805599453 + (-0.5 * (z0 / z1));
}

Python

def code(z0, z1):
	return 0.6931471805599453 + (-0.5 * (z0 / z1))

Julia

function code(z0, z1)
	return Float64(0.6931471805599453 + Float64(-0.5 * Float64(z0 / z1)))
end

MATLAB

function tmp = code(z0, z1)
	tmp = 0.6931471805599453 + (-0.5 * (z0 / z1));
end

Wolfram

code[z0_, z1_] := N[(0.6931471805599453 + N[(-0.5 * N[(z0 / z1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.3%

   \[\log \left(e^{\frac{-z0}{z1}} - -1\right) \]

2. Taylor expanded in z0 around 0

   \[\leadsto \color{blue}{\log 2 + \frac{-1}{2} \cdot \frac{z0}{z1}} \]
3. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto \log 2 + \color{blue}{\frac{-1}{2} \cdot \frac{z0}{z1}} \]

   2. lower-log.f64 N/A

      \[\leadsto \log 2 + \color{blue}{\frac{-1}{2}} \cdot \frac{z0}{z1} \]

   3. lower-*.f64 N/A

      \[\leadsto \log 2 + \frac{-1}{2} \cdot \color{blue}{\frac{z0}{z1}} \]

   4. lower-/.f64 66.4%

      \[\leadsto \log 2 + -0.5 \cdot \frac{z0}{\color{blue}{z1}} \]

4. Applied rewrites 66.4%

   \[\leadsto \color{blue}{\log 2 + -0.5 \cdot \frac{z0}{z1}} \]

5. Evaluated real constant 66.4%

   \[\leadsto 0.6931471805599453 + \color{blue}{-0.5} \cdot \frac{z0}{z1} \]
6. Add Preprocessing

Alternative 4: 65.9% accurate, 217.0× speedup

Math

\[0.6931471805599453 \]

FPCore

(FPCore (z0 z1)
  :precision binary64
  0.6931471805599453)

C

double code(double z0, double z1) {
	return 0.6931471805599453;
}

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(z0, z1)
use fmin_fmax_functions
    real(8), intent (in) :: z0
    real(8), intent (in) :: z1
    code = 0.6931471805599453d0
end function

Java

public static double code(double z0, double z1) {
	return 0.6931471805599453;
}

Python

def code(z0, z1):
	return 0.6931471805599453

Julia

function code(z0, z1)
	return 0.6931471805599453
end

MATLAB

function tmp = code(z0, z1)
	tmp = 0.6931471805599453;
end

Wolfram

code[z0_, z1_] := 0.6931471805599453

Derivation

1. Initial program 99.3%

   \[\log \left(e^{\frac{-z0}{z1}} - -1\right) \]

2. Taylor expanded in z0 around 0

   \[\leadsto \color{blue}{\log 2 + \frac{-1}{2} \cdot \frac{z0}{z1}} \]
3. Step-by-step derivation

   1. lower-+.f64 N/A

      \[\leadsto \log 2 + \color{blue}{\frac{-1}{2} \cdot \frac{z0}{z1}} \]

   2. lower-log.f64 N/A

      \[\leadsto \log 2 + \color{blue}{\frac{-1}{2}} \cdot \frac{z0}{z1} \]

   3. lower-*.f64 N/A

      \[\leadsto \log 2 + \frac{-1}{2} \cdot \color{blue}{\frac{z0}{z1}} \]

   4. lower-/.f64 66.4%

      \[\leadsto \log 2 + -0.5 \cdot \frac{z0}{\color{blue}{z1}} \]

4. Applied rewrites 66.4%

   \[\leadsto \color{blue}{\log 2 + -0.5 \cdot \frac{z0}{z1}} \]

5. Evaluated real constant 66.4%

   \[\leadsto 0.6931471805599453 + \color{blue}{-0.5} \cdot \frac{z0}{z1} \]

6. Taylor expanded in z0 around 0

   \[\leadsto \frac{6243314768165359}{9007199254740992} \]
7. Step-by-step derivation

8. Applied rewrites 65.9%

   \[\leadsto 0.6931471805599453 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2025250 
(FPCore (z0 z1)
  :name "(log (- (exp (/ (- z0) z1)) -1))"
  :precision binary64
  (log (- (exp (/ (- z0) z1)) -1.0)))