System.Random.MWC.Distributions:truncatedExp from mwc-random-0.13.3.2

Percentage Accurate: 61.7% → 98.3%

Time: 17.4s

Alternatives: 8

Speedup: 211.0×

• could not determine a ground truth

  1. x = 9.656351081615472e-6
  2. y = 1.2416626545790604e-265
  3. z = 6.0382192803895884e+119
  4. t = -1.3535136851179894e+59

Specification

Math

\[\begin{array}{l} \\ x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- x (/ (log (+ (- 1.0 y) (* y (exp z)))) t)))

C

double code(double x, double y, double z, double t) {
	return x - (log(((1.0 - y) + (y * exp(z)))) / t);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x - (log(((1.0d0 - y) + (y * exp(z)))) / t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return x - (Math.log(((1.0 - y) + (y * Math.exp(z)))) / t);
}

Python

def code(x, y, z, t):
	return x - (math.log(((1.0 - y) + (y * math.exp(z)))) / t)

Julia

function code(x, y, z, t)
	return Float64(x - Float64(log(Float64(Float64(1.0 - y) + Float64(y * exp(z)))) / t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x - (log(((1.0 - y) + (y * exp(z)))) / t);
end

Wolfram

code[x_, y_, z_, t_] := N[(x - N[(N[Log[N[(N[(1.0 - y), $MachinePrecision] + N[(y * N[Exp[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

Initial Program: 61.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- x (/ (log (+ (- 1.0 y) (* y (exp z)))) t)))

C

double code(double x, double y, double z, double t) {
	return x - (log(((1.0 - y) + (y * exp(z)))) / t);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x - (log(((1.0d0 - y) + (y * exp(z)))) / t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return x - (Math.log(((1.0 - y) + (y * Math.exp(z)))) / t);
}

Python

def code(x, y, z, t):
	return x - (math.log(((1.0 - y) + (y * math.exp(z)))) / t)

Julia

function code(x, y, z, t)
	return Float64(x - Float64(log(Float64(Float64(1.0 - y) + Float64(y * exp(z)))) / t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x - (log(((1.0 - y) + (y * exp(z)))) / t);
end

Wolfram

code[x_, y_, z_, t_] := N[(x - N[(N[Log[N[(N[(1.0 - y), $MachinePrecision] + N[(y * N[Exp[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (- x (/ (log1p (* y (expm1 z))) t)))

C

double code(double x, double y, double z, double t) {
	return x - (log1p((y * expm1(z))) / t);
}

Java

public static double code(double x, double y, double z, double t) {
	return x - (Math.log1p((y * Math.expm1(z))) / t);
}

Python

def code(x, y, z, t):
	return x - (math.log1p((y * math.expm1(z))) / t)

Julia

function code(x, y, z, t)
	return Float64(x - Float64(log1p(Float64(y * expm1(z))) / t))
end

Wolfram

code[x_, y_, z_, t_] := N[(x - N[(N[Log[1 + N[(y * N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 58.6%

   \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
2. Step-by-step derivation

   1. remove-double-neg 58.6%

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

   2. neg-mul-1 58.6%

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

   3. *-commutative 58.6%

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

   4. *-commutative 58.6%

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

   5. neg-mul-1 58.6%

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

   6. remove-double-neg 58.6%

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

   7. sub-neg 58.6%

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

   8. associate-+l+ 76.4%

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

   9. cancel-sign-sub 76.4%

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

   10. log1p-def 81.9%

       \[\leadsto x - \frac{\color{blue}{\mathsf{log1p}\left(\left(-y\right) - \left(-y\right) \cdot e^{z}\right)}}{t} \]

   11. cancel-sign-sub 81.9%

       \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(-y\right) + y \cdot e^{z}}\right)}{t} \]

   12. +-commutative 81.9%

       \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} + \left(-y\right)}\right)}{t} \]

   13. unsub-neg 81.9%

       \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} - y}\right)}{t} \]

   14. *-rgt-identity 81.9%

       \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot e^{z} - \color{blue}{y \cdot 1}\right)}{t} \]

   15. distribute-lft-out-- 81.9%

       \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot \left(e^{z} - 1\right)}\right)}{t} \]

   16. expm1-def 97.7%

       \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \color{blue}{\mathsf{expm1}\left(z\right)}\right)}{t} \]

3. Simplified 97.7%

   \[\leadsto \color{blue}{x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}} \]
4. Add Preprocessing

5. Final simplification 97.7%

   \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t} \]
6. Add Preprocessing

Alternative 2: 89.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ x + \frac{-1}{t \cdot \left(0.5 + \frac{1}{y \cdot \mathsf{expm1}\left(z\right)}\right)} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ x (/ -1.0 (* t (+ 0.5 (/ 1.0 (* y (expm1 z))))))))

C

double code(double x, double y, double z, double t) {
	return x + (-1.0 / (t * (0.5 + (1.0 / (y * expm1(z))))));
}

Java

public static double code(double x, double y, double z, double t) {
	return x + (-1.0 / (t * (0.5 + (1.0 / (y * Math.expm1(z))))));
}

Python

def code(x, y, z, t):
	return x + (-1.0 / (t * (0.5 + (1.0 / (y * math.expm1(z))))))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(-1.0 / Float64(t * Float64(0.5 + Float64(1.0 / Float64(y * expm1(z)))))))
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(-1.0 / N[(t * N[(0.5 + N[(1.0 / N[(y * N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 58.6%

   \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
2. Step-by-step derivation

   1. remove-double-neg 58.6%

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

   2. neg-mul-1 58.6%

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

   3. *-commutative 58.6%

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

   4. *-commutative 58.6%

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

   5. neg-mul-1 58.6%

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

   6. remove-double-neg 58.6%

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

   7. sub-neg 58.6%

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

   8. associate-+l+ 76.4%

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

   9. cancel-sign-sub 76.4%

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

   10. log1p-def 81.9%

       \[\leadsto x - \frac{\color{blue}{\mathsf{log1p}\left(\left(-y\right) - \left(-y\right) \cdot e^{z}\right)}}{t} \]

   11. cancel-sign-sub 81.9%

       \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(-y\right) + y \cdot e^{z}}\right)}{t} \]

   12. +-commutative 81.9%

       \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} + \left(-y\right)}\right)}{t} \]

   13. unsub-neg 81.9%

       \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} - y}\right)}{t} \]

   14. *-rgt-identity 81.9%

       \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot e^{z} - \color{blue}{y \cdot 1}\right)}{t} \]

   15. distribute-lft-out-- 81.9%

       \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot \left(e^{z} - 1\right)}\right)}{t} \]

   16. expm1-def 97.7%

       \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \color{blue}{\mathsf{expm1}\left(z\right)}\right)}{t} \]

3. Simplified 97.7%

   \[\leadsto \color{blue}{x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. clear-num 97.7%

      \[\leadsto x - \color{blue}{\frac{1}{\frac{t}{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}}} \]

   2. inv-pow 97.7%

      \[\leadsto x - \color{blue}{{\left(\frac{t}{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}\right)}^{-1}} \]

6. Applied egg-rr 97.7%

   \[\leadsto x - \color{blue}{{\left(\frac{t}{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}\right)}^{-1}} \]
7. Step-by-step derivation

   1. unpow-1 97.7%

      \[\leadsto x - \color{blue}{\frac{1}{\frac{t}{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}}} \]

8. Applied egg-rr 97.7%

   \[\leadsto x - \color{blue}{\frac{1}{\frac{t}{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}}} \]
9. Step-by-step derivation

   1. div-inv 97.3%

      \[\leadsto x - \frac{1}{\color{blue}{t \cdot \frac{1}{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}}} \]

10. Applied egg-rr 97.3%

    \[\leadsto x - \frac{1}{\color{blue}{t \cdot \frac{1}{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}}} \]

11. Taylor expanded in y around 0 77.9%

    \[\leadsto x - \frac{1}{t \cdot \color{blue}{\left(0.5 + \frac{1}{y \cdot \left(e^{z} - 1\right)}\right)}} \]
12. Step-by-step derivation

    1. expm1-def 88.0%

       \[\leadsto x - \frac{1}{t \cdot \left(0.5 + \frac{1}{y \cdot \color{blue}{\mathsf{expm1}\left(z\right)}}\right)} \]

13. Simplified 88.0%

    \[\leadsto x - \frac{1}{t \cdot \color{blue}{\left(0.5 + \frac{1}{y \cdot \mathsf{expm1}\left(z\right)}\right)}} \]

14. Final simplification 88.0%

    \[\leadsto x + \frac{-1}{t \cdot \left(0.5 + \frac{1}{y \cdot \mathsf{expm1}\left(z\right)}\right)} \]
15. Add Preprocessing

Alternative 3: 86.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{\mathsf{expm1}\left(z\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.3e+73) x (- x (/ y (/ t (expm1 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.3e+73) {
		tmp = x;
	} else {
		tmp = x - (y / (t / expm1(z)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.3e+73) {
		tmp = x;
	} else {
		tmp = x - (y / (t / Math.expm1(z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.3e+73:
		tmp = x
	else:
		tmp = x - (y / (t / math.expm1(z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.3e+73)
		tmp = x;
	else
		tmp = Float64(x - Float64(y / Float64(t / expm1(z))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.3e+73], x, N[(x - N[(y / N[(t / N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e73

   1. Initial program 46.2%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Step-by-step derivation

      1. remove-double-neg 46.2%

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

      2. neg-mul-1 46.2%

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

      3. *-commutative 46.2%

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

      4. *-commutative 46.2%

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

      5. neg-mul-1 46.2%

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

      6. remove-double-neg 46.2%

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

      7. sub-neg 46.2%

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

      8. associate-+l+ 84.0%

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

      9. cancel-sign-sub 84.0%

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

      10. log1p-def 84.0%

          \[\leadsto x - \frac{\color{blue}{\mathsf{log1p}\left(\left(-y\right) - \left(-y\right) \cdot e^{z}\right)}}{t} \]

      11. cancel-sign-sub 84.0%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(-y\right) + y \cdot e^{z}}\right)}{t} \]

      12. +-commutative 84.0%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} + \left(-y\right)}\right)}{t} \]

      13. unsub-neg 84.0%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} - y}\right)}{t} \]

      14. *-rgt-identity 84.0%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot e^{z} - \color{blue}{y \cdot 1}\right)}{t} \]

      15. distribute-lft-out-- 84.0%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot \left(e^{z} - 1\right)}\right)}{t} \]

      16. expm1-def 99.9%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \color{blue}{\mathsf{expm1}\left(z\right)}\right)}{t} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 61.2%

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

   if -2.3e73 < y

   1. Initial program 61.0%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Step-by-step derivation

      1. remove-double-neg 61.0%

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

      2. neg-mul-1 61.0%

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

      3. *-commutative 61.0%

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

      4. *-commutative 61.0%

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

      5. neg-mul-1 61.0%

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

      6. remove-double-neg 61.0%

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

      7. sub-neg 61.0%

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

      8. associate-+l+ 74.9%

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

      9. cancel-sign-sub 74.9%

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

      10. log1p-def 81.5%

          \[\leadsto x - \frac{\color{blue}{\mathsf{log1p}\left(\left(-y\right) - \left(-y\right) \cdot e^{z}\right)}}{t} \]

      11. cancel-sign-sub 81.5%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(-y\right) + y \cdot e^{z}}\right)}{t} \]

      12. +-commutative 81.5%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} + \left(-y\right)}\right)}{t} \]

      13. unsub-neg 81.5%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} - y}\right)}{t} \]

      14. *-rgt-identity 81.5%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot e^{z} - \color{blue}{y \cdot 1}\right)}{t} \]

      15. distribute-lft-out-- 81.5%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot \left(e^{z} - 1\right)}\right)}{t} \]

      16. expm1-def 97.3%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \color{blue}{\mathsf{expm1}\left(z\right)}\right)}{t} \]

   3. Simplified 97.3%

      \[\leadsto \color{blue}{x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.0%

      \[\leadsto x - \color{blue}{\frac{y \cdot \left(e^{z} - 1\right)}{t}} \]
   6. Step-by-step derivation

      1. associate-/l* 80.0%

         \[\leadsto x - \color{blue}{\frac{y}{\frac{t}{e^{z} - 1}}} \]

      2. expm1-def 92.5%

         \[\leadsto x - \frac{y}{\frac{t}{\color{blue}{\mathsf{expm1}\left(z\right)}}} \]

   7. Simplified 92.5%

      \[\leadsto x - \color{blue}{\frac{y}{\frac{t}{\mathsf{expm1}\left(z\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{\mathsf{expm1}\left(z\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.8% accurate, 13.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{t \cdot \left(\frac{1}{z} - 0.5\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.8e+72) x (- x (/ y (* t (- (/ 1.0 z) 0.5))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e+72) {
		tmp = x;
	} else {
		tmp = x - (y / (t * ((1.0 / z) - 0.5)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.8d+72)) then
        tmp = x
    else
        tmp = x - (y / (t * ((1.0d0 / z) - 0.5d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e+72) {
		tmp = x;
	} else {
		tmp = x - (y / (t * ((1.0 / z) - 0.5)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.8e+72:
		tmp = x
	else:
		tmp = x - (y / (t * ((1.0 / z) - 0.5)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.8e+72)
		tmp = x;
	else
		tmp = Float64(x - Float64(y / Float64(t * Float64(Float64(1.0 / z) - 0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.8e+72)
		tmp = x;
	else
		tmp = x - (y / (t * ((1.0 / z) - 0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.8e+72], x, N[(x - N[(y / N[(t * N[(N[(1.0 / z), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8000000000000002e72

   1. Initial program 46.2%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Step-by-step derivation

      1. remove-double-neg 46.2%

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

      2. neg-mul-1 46.2%

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

      3. *-commutative 46.2%

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

      4. *-commutative 46.2%

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

      5. neg-mul-1 46.2%

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

      6. remove-double-neg 46.2%

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

      7. sub-neg 46.2%

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

      8. associate-+l+ 84.0%

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

      9. cancel-sign-sub 84.0%

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

      10. log1p-def 84.0%

          \[\leadsto x - \frac{\color{blue}{\mathsf{log1p}\left(\left(-y\right) - \left(-y\right) \cdot e^{z}\right)}}{t} \]

      11. cancel-sign-sub 84.0%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(-y\right) + y \cdot e^{z}}\right)}{t} \]

      12. +-commutative 84.0%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} + \left(-y\right)}\right)}{t} \]

      13. unsub-neg 84.0%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} - y}\right)}{t} \]

      14. *-rgt-identity 84.0%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot e^{z} - \color{blue}{y \cdot 1}\right)}{t} \]

      15. distribute-lft-out-- 84.0%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot \left(e^{z} - 1\right)}\right)}{t} \]

      16. expm1-def 99.9%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \color{blue}{\mathsf{expm1}\left(z\right)}\right)}{t} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 61.2%

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

   if -4.8000000000000002e72 < y

   1. Initial program 61.0%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Step-by-step derivation

      1. remove-double-neg 61.0%

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

      2. neg-mul-1 61.0%

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

      3. *-commutative 61.0%

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

      4. *-commutative 61.0%

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

      5. neg-mul-1 61.0%

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

      6. remove-double-neg 61.0%

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

      7. sub-neg 61.0%

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

      8. associate-+l+ 74.9%

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

      9. cancel-sign-sub 74.9%

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

      10. log1p-def 81.5%

          \[\leadsto x - \frac{\color{blue}{\mathsf{log1p}\left(\left(-y\right) - \left(-y\right) \cdot e^{z}\right)}}{t} \]

      11. cancel-sign-sub 81.5%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(-y\right) + y \cdot e^{z}}\right)}{t} \]

      12. +-commutative 81.5%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} + \left(-y\right)}\right)}{t} \]

      13. unsub-neg 81.5%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} - y}\right)}{t} \]

      14. *-rgt-identity 81.5%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot e^{z} - \color{blue}{y \cdot 1}\right)}{t} \]

      15. distribute-lft-out-- 81.5%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot \left(e^{z} - 1\right)}\right)}{t} \]

      16. expm1-def 97.3%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \color{blue}{\mathsf{expm1}\left(z\right)}\right)}{t} \]

   3. Simplified 97.3%

      \[\leadsto \color{blue}{x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.0%

      \[\leadsto x - \color{blue}{\frac{y \cdot \left(e^{z} - 1\right)}{t}} \]
   6. Step-by-step derivation

      1. associate-/l* 80.0%

         \[\leadsto x - \color{blue}{\frac{y}{\frac{t}{e^{z} - 1}}} \]

      2. expm1-def 92.5%

         \[\leadsto x - \frac{y}{\frac{t}{\color{blue}{\mathsf{expm1}\left(z\right)}}} \]

   7. Simplified 92.5%

      \[\leadsto x - \color{blue}{\frac{y}{\frac{t}{\mathsf{expm1}\left(z\right)}}} \]
   8. Step-by-step derivation

      1. div-inv 92.5%

         \[\leadsto x - \frac{y}{\color{blue}{t \cdot \frac{1}{\mathsf{expm1}\left(z\right)}}} \]

   9. Applied egg-rr 92.5%

      \[\leadsto x - \frac{y}{\color{blue}{t \cdot \frac{1}{\mathsf{expm1}\left(z\right)}}} \]

   10. Taylor expanded in z around 0 87.4%

       \[\leadsto x - \frac{y}{t \cdot \color{blue}{\left(\frac{1}{z} - 0.5\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{t \cdot \left(\frac{1}{z} - 0.5\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.8% accurate, 13.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{t \cdot -0.5 + \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.1e+73) x (- x (/ y (+ (* t -0.5) (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.1e+73) {
		tmp = x;
	} else {
		tmp = x - (y / ((t * -0.5) + (t / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.1d+73)) then
        tmp = x
    else
        tmp = x - (y / ((t * (-0.5d0)) + (t / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.1e+73) {
		tmp = x;
	} else {
		tmp = x - (y / ((t * -0.5) + (t / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.1e+73:
		tmp = x
	else:
		tmp = x - (y / ((t * -0.5) + (t / z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.1e+73)
		tmp = x;
	else
		tmp = Float64(x - Float64(y / Float64(Float64(t * -0.5) + Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.1e+73)
		tmp = x;
	else
		tmp = x - (y / ((t * -0.5) + (t / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.1e+73], x, N[(x - N[(y / N[(N[(t * -0.5), $MachinePrecision] + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1000000000000001e73

   1. Initial program 46.2%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Step-by-step derivation

      1. remove-double-neg 46.2%

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

      2. neg-mul-1 46.2%

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

      3. *-commutative 46.2%

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

      4. *-commutative 46.2%

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

      5. neg-mul-1 46.2%

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

      6. remove-double-neg 46.2%

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

      7. sub-neg 46.2%

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

      8. associate-+l+ 84.0%

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

      9. cancel-sign-sub 84.0%

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

      10. log1p-def 84.0%

          \[\leadsto x - \frac{\color{blue}{\mathsf{log1p}\left(\left(-y\right) - \left(-y\right) \cdot e^{z}\right)}}{t} \]

      11. cancel-sign-sub 84.0%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(-y\right) + y \cdot e^{z}}\right)}{t} \]

      12. +-commutative 84.0%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} + \left(-y\right)}\right)}{t} \]

      13. unsub-neg 84.0%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} - y}\right)}{t} \]

      14. *-rgt-identity 84.0%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot e^{z} - \color{blue}{y \cdot 1}\right)}{t} \]

      15. distribute-lft-out-- 84.0%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot \left(e^{z} - 1\right)}\right)}{t} \]

      16. expm1-def 99.9%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \color{blue}{\mathsf{expm1}\left(z\right)}\right)}{t} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 61.2%

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

   if -2.1000000000000001e73 < y

   1. Initial program 61.0%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Step-by-step derivation

      1. remove-double-neg 61.0%

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

      2. neg-mul-1 61.0%

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

      3. *-commutative 61.0%

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

      4. *-commutative 61.0%

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

      5. neg-mul-1 61.0%

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

      6. remove-double-neg 61.0%

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

      7. sub-neg 61.0%

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

      8. associate-+l+ 74.9%

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

      9. cancel-sign-sub 74.9%

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

      10. log1p-def 81.5%

          \[\leadsto x - \frac{\color{blue}{\mathsf{log1p}\left(\left(-y\right) - \left(-y\right) \cdot e^{z}\right)}}{t} \]

      11. cancel-sign-sub 81.5%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(-y\right) + y \cdot e^{z}}\right)}{t} \]

      12. +-commutative 81.5%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} + \left(-y\right)}\right)}{t} \]

      13. unsub-neg 81.5%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} - y}\right)}{t} \]

      14. *-rgt-identity 81.5%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot e^{z} - \color{blue}{y \cdot 1}\right)}{t} \]

      15. distribute-lft-out-- 81.5%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot \left(e^{z} - 1\right)}\right)}{t} \]

      16. expm1-def 97.3%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \color{blue}{\mathsf{expm1}\left(z\right)}\right)}{t} \]

   3. Simplified 97.3%

      \[\leadsto \color{blue}{x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.0%

      \[\leadsto x - \color{blue}{\frac{y \cdot \left(e^{z} - 1\right)}{t}} \]
   6. Step-by-step derivation

      1. associate-/l* 80.0%

         \[\leadsto x - \color{blue}{\frac{y}{\frac{t}{e^{z} - 1}}} \]

      2. expm1-def 92.5%

         \[\leadsto x - \frac{y}{\frac{t}{\color{blue}{\mathsf{expm1}\left(z\right)}}} \]

   7. Simplified 92.5%

      \[\leadsto x - \color{blue}{\frac{y}{\frac{t}{\mathsf{expm1}\left(z\right)}}} \]

   8. Taylor expanded in z around 0 87.4%

      \[\leadsto x - \frac{y}{\color{blue}{-0.5 \cdot t + \frac{t}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{t \cdot -0.5 + \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.3% accurate, 17.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= z -3.2) x (- x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.2) {
		tmp = x;
	} else {
		tmp = x - (y * (z / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3.2d0)) then
        tmp = x
    else
        tmp = x - (y * (z / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.2) {
		tmp = x;
	} else {
		tmp = x - (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3.2:
		tmp = x
	else:
		tmp = x - (y * (z / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.2)
		tmp = x;
	else
		tmp = Float64(x - Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.2)
		tmp = x;
	else
		tmp = x - (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3.2], x, N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2000000000000002

   1. Initial program 83.5%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Step-by-step derivation

      1. remove-double-neg 83.5%

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

      2. neg-mul-1 83.5%

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

      3. *-commutative 83.5%

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

      4. *-commutative 83.5%

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

      5. neg-mul-1 83.5%

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

      6. remove-double-neg 83.5%

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

      7. sub-neg 83.5%

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

      8. associate-+l+ 83.5%

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

      9. cancel-sign-sub 83.5%

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

      10. log1p-def 99.9%

          \[\leadsto x - \frac{\color{blue}{\mathsf{log1p}\left(\left(-y\right) - \left(-y\right) \cdot e^{z}\right)}}{t} \]

      11. cancel-sign-sub 99.9%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(-y\right) + y \cdot e^{z}}\right)}{t} \]

      12. +-commutative 99.9%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} + \left(-y\right)}\right)}{t} \]

      13. unsub-neg 99.9%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} - y}\right)}{t} \]

      14. *-rgt-identity 99.9%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot e^{z} - \color{blue}{y \cdot 1}\right)}{t} \]

      15. distribute-lft-out-- 99.9%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot \left(e^{z} - 1\right)}\right)}{t} \]

      16. expm1-def 99.9%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \color{blue}{\mathsf{expm1}\left(z\right)}\right)}{t} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 66.1%

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

   if -3.2000000000000002 < z

   1. Initial program 48.5%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Step-by-step derivation

      1. remove-double-neg 48.5%

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

      2. neg-mul-1 48.5%

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

      3. *-commutative 48.5%

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

      4. *-commutative 48.5%

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

      5. neg-mul-1 48.5%

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

      6. remove-double-neg 48.5%

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

      7. sub-neg 48.5%

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

      8. associate-+l+ 73.5%

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

      9. cancel-sign-sub 73.5%

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

      10. log1p-def 74.6%

          \[\leadsto x - \frac{\color{blue}{\mathsf{log1p}\left(\left(-y\right) - \left(-y\right) \cdot e^{z}\right)}}{t} \]

      11. cancel-sign-sub 74.6%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(-y\right) + y \cdot e^{z}}\right)}{t} \]

      12. +-commutative 74.6%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} + \left(-y\right)}\right)}{t} \]

      13. unsub-neg 74.6%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} - y}\right)}{t} \]

      14. *-rgt-identity 74.6%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot e^{z} - \color{blue}{y \cdot 1}\right)}{t} \]

      15. distribute-lft-out-- 74.6%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot \left(e^{z} - 1\right)}\right)}{t} \]

      16. expm1-def 96.8%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \color{blue}{\mathsf{expm1}\left(z\right)}\right)}{t} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 96.8%

         \[\leadsto x - \color{blue}{\frac{1}{\frac{t}{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}}} \]

      2. inv-pow 96.8%

         \[\leadsto x - \color{blue}{{\left(\frac{t}{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}\right)}^{-1}} \]

   6. Applied egg-rr 96.8%

      \[\leadsto x - \color{blue}{{\left(\frac{t}{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}\right)}^{-1}} \]
   7. Step-by-step derivation

      1. unpow-1 96.8%

         \[\leadsto x - \color{blue}{\frac{1}{\frac{t}{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}}} \]

   8. Applied egg-rr 96.8%

      \[\leadsto x - \color{blue}{\frac{1}{\frac{t}{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}}} \]

   9. Taylor expanded in z around 0 85.8%

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

       1. associate-*r/ 87.7%

          \[\leadsto x - \color{blue}{y \cdot \frac{z}{t}} \]

   11. Simplified 87.7%

       \[\leadsto x - \color{blue}{y \cdot \frac{z}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.3% accurate, 17.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.028:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (if (<= z -0.028) x (- x (/ y (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.028) {
		tmp = x;
	} else {
		tmp = x - (y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-0.028d0)) then
        tmp = x
    else
        tmp = x - (y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.028) {
		tmp = x;
	} else {
		tmp = x - (y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -0.028:
		tmp = x
	else:
		tmp = x - (y / (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.028)
		tmp = x;
	else
		tmp = Float64(x - Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.028)
		tmp = x;
	else
		tmp = x - (y / (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -0.028], x, N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0280000000000000006

   1. Initial program 83.5%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Step-by-step derivation

      1. remove-double-neg 83.5%

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

      2. neg-mul-1 83.5%

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

      3. *-commutative 83.5%

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

      4. *-commutative 83.5%

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

      5. neg-mul-1 83.5%

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

      6. remove-double-neg 83.5%

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

      7. sub-neg 83.5%

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

      8. associate-+l+ 83.5%

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

      9. cancel-sign-sub 83.5%

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

      10. log1p-def 99.9%

          \[\leadsto x - \frac{\color{blue}{\mathsf{log1p}\left(\left(-y\right) - \left(-y\right) \cdot e^{z}\right)}}{t} \]

      11. cancel-sign-sub 99.9%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(-y\right) + y \cdot e^{z}}\right)}{t} \]

      12. +-commutative 99.9%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} + \left(-y\right)}\right)}{t} \]

      13. unsub-neg 99.9%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} - y}\right)}{t} \]

      14. *-rgt-identity 99.9%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot e^{z} - \color{blue}{y \cdot 1}\right)}{t} \]

      15. distribute-lft-out-- 99.9%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot \left(e^{z} - 1\right)}\right)}{t} \]

      16. expm1-def 99.9%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \color{blue}{\mathsf{expm1}\left(z\right)}\right)}{t} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 66.1%

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

   if -0.0280000000000000006 < z

   1. Initial program 48.5%

      \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
   2. Step-by-step derivation

      1. remove-double-neg 48.5%

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

      2. neg-mul-1 48.5%

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

      3. *-commutative 48.5%

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

      4. *-commutative 48.5%

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

      5. neg-mul-1 48.5%

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

      6. remove-double-neg 48.5%

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

      7. sub-neg 48.5%

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

      8. associate-+l+ 73.5%

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

      9. cancel-sign-sub 73.5%

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

      10. log1p-def 74.6%

          \[\leadsto x - \frac{\color{blue}{\mathsf{log1p}\left(\left(-y\right) - \left(-y\right) \cdot e^{z}\right)}}{t} \]

      11. cancel-sign-sub 74.6%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(-y\right) + y \cdot e^{z}}\right)}{t} \]

      12. +-commutative 74.6%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} + \left(-y\right)}\right)}{t} \]

      13. unsub-neg 74.6%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} - y}\right)}{t} \]

      14. *-rgt-identity 74.6%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot e^{z} - \color{blue}{y \cdot 1}\right)}{t} \]

      15. distribute-lft-out-- 74.6%

          \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot \left(e^{z} - 1\right)}\right)}{t} \]

      16. expm1-def 96.8%

          \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \color{blue}{\mathsf{expm1}\left(z\right)}\right)}{t} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 85.8%

      \[\leadsto x - \color{blue}{\frac{y \cdot z}{t}} \]
   6. Step-by-step derivation

      1. associate-/l* 87.7%

         \[\leadsto x - \color{blue}{\frac{y}{\frac{t}{z}}} \]

   7. Simplified 87.7%

      \[\leadsto x - \color{blue}{\frac{y}{\frac{t}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.028:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.6% accurate, 211.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

double code(double x, double y, double z, double t) {
	return x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

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

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 58.6%

   \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t} \]
2. Step-by-step derivation

   1. remove-double-neg 58.6%

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

   2. neg-mul-1 58.6%

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

   3. *-commutative 58.6%

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

   4. *-commutative 58.6%

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

   5. neg-mul-1 58.6%

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

   6. remove-double-neg 58.6%

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

   7. sub-neg 58.6%

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

   8. associate-+l+ 76.4%

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

   9. cancel-sign-sub 76.4%

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

   10. log1p-def 81.9%

       \[\leadsto x - \frac{\color{blue}{\mathsf{log1p}\left(\left(-y\right) - \left(-y\right) \cdot e^{z}\right)}}{t} \]

   11. cancel-sign-sub 81.9%

       \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{\left(-y\right) + y \cdot e^{z}}\right)}{t} \]

   12. +-commutative 81.9%

       \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} + \left(-y\right)}\right)}{t} \]

   13. unsub-neg 81.9%

       \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot e^{z} - y}\right)}{t} \]

   14. *-rgt-identity 81.9%

       \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot e^{z} - \color{blue}{y \cdot 1}\right)}{t} \]

   15. distribute-lft-out-- 81.9%

       \[\leadsto x - \frac{\mathsf{log1p}\left(\color{blue}{y \cdot \left(e^{z} - 1\right)}\right)}{t} \]

   16. expm1-def 97.7%

       \[\leadsto x - \frac{\mathsf{log1p}\left(y \cdot \color{blue}{\mathsf{expm1}\left(z\right)}\right)}{t} \]

3. Simplified 97.7%

   \[\leadsto \color{blue}{x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 71.5%

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

6. Final simplification 71.5%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 74.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-0.5}{y \cdot t}\\ \mathbf{if}\;z < -2.8874623088207947 \cdot 10^{+119}:\\ \;\;\;\;\left(x - \frac{t_1}{z \cdot z}\right) - t_1 \cdot \frac{\frac{2}{z}}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\log \left(1 + z \cdot y\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- 0.5) (* y t))))
   (if (< z -2.8874623088207947e+119)
     (- (- x (/ t_1 (* z z))) (* t_1 (/ (/ 2.0 z) (* z z))))
     (- x (/ (log (+ 1.0 (* z y))) t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -0.5 / (y * t);
	double tmp;
	if (z < -2.8874623088207947e+119) {
		tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0 / z) / (z * z)));
	} else {
		tmp = x - (log((1.0 + (z * y))) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -0.5d0 / (y * t)
    if (z < (-2.8874623088207947d+119)) then
        tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0d0 / z) / (z * z)))
    else
        tmp = x - (log((1.0d0 + (z * y))) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -0.5 / (y * t);
	double tmp;
	if (z < -2.8874623088207947e+119) {
		tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0 / z) / (z * z)));
	} else {
		tmp = x - (Math.log((1.0 + (z * y))) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -0.5 / (y * t)
	tmp = 0
	if z < -2.8874623088207947e+119:
		tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0 / z) / (z * z)))
	else:
		tmp = x - (math.log((1.0 + (z * y))) / t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-0.5) / Float64(y * t))
	tmp = 0.0
	if (z < -2.8874623088207947e+119)
		tmp = Float64(Float64(x - Float64(t_1 / Float64(z * z))) - Float64(t_1 * Float64(Float64(2.0 / z) / Float64(z * z))));
	else
		tmp = Float64(x - Float64(log(Float64(1.0 + Float64(z * y))) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -0.5 / (y * t);
	tmp = 0.0;
	if (z < -2.8874623088207947e+119)
		tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0 / z) / (z * z)));
	else
		tmp = x - (log((1.0 + (z * y))) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-0.5) / N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -2.8874623088207947e+119], N[(N[(x - N[(t$95$1 / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * N[(N[(2.0 / z), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024019 
(FPCore (x y z t)
  :name "System.Random.MWC.Distributions:truncatedExp from mwc-random-0.13.3.2"
  :precision binary64

  :herbie-target
  (if (< z -2.8874623088207947e+119) (- (- x (/ (/ (- 0.5) (* y t)) (* z z))) (* (/ (- 0.5) (* y t)) (/ (/ 2.0 z) (* z z)))) (- x (/ (log (+ 1.0 (* z y))) t)))

  (- x (/ (log (+ (- 1.0 y) (* y (exp z)))) t)))