Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A

Percentage Accurate: 99.1% → 98.7%

Time: 10.1s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 1.0 - (x / ((y - z) * (y - 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 = 1.0d0 - (x / ((y - z) * (y - t)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0 - (x / ((y - z) * (y - t)));
}

Python

def code(x, y, z, t):
	return 1.0 - (x / ((y - z) * (y - t)))

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 1.0 - (x / ((y - z) * (y - 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 = 1.0d0 - (x / ((y - z) * (y - t)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0 - (x / ((y - z) * (y - t)));
}

Python

def code(x, y, z, t):
	return 1.0 - (x / ((y - z) * (y - t)))

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.7% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 1.0 + (x / ((y - z) * (t - (t * (y / 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 = 1.0d0 + (x / ((y - z) * (t - (t * (y / t)))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

   \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
2. Add Preprocessing

3. Taylor expanded in t around inf

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

   1. sub-neg N/A

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

   2. metadata-eval N/A

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

   3. distribute-rgt-in N/A

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

   4. mul-1-neg N/A

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

   5. unsub-neg N/A

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

   6. --lowering--.f64 N/A

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

   7. remove-double-neg N/A

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

   8. distribute-lft-neg-out N/A

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

   9. mul-1-neg N/A

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

   10. *-commutative N/A

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

   11. mul-1-neg N/A

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

   12. distribute-rgt-neg-out N/A

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

   13. remove-double-neg N/A

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

   14. *-lowering-*.f64 N/A

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

   15. /-lowering-/.f64 99.2

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

5. Simplified 99.2%

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

6. Final simplification 99.2%

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

Alternative 2: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ t_2 := \frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_1 \leq -1000000000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))) (t_2 (/ x (* (- y z) (- t y)))))
   (if (<= t_1 -1000000000000.0) t_2 (if (<= t_1 5e-19) 1.0 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double t_2 = x / ((y - z) * (t - y));
	double tmp;
	if (t_1 <= -1000000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 5e-19) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x / ((y - z) * (y - t))
    t_2 = x / ((y - z) * (t - y))
    if (t_1 <= (-1000000000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 5d-19) then
        tmp = 1.0d0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double t_2 = x / ((y - z) * (t - y));
	double tmp;
	if (t_1 <= -1000000000000.0) {
		tmp = t_2;
	} else if (t_1 <= 5e-19) {
		tmp = 1.0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	t_2 = x / ((y - z) * (t - y))
	tmp = 0
	if t_1 <= -1000000000000.0:
		tmp = t_2
	elif t_1 <= 5e-19:
		tmp = 1.0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	t_2 = Float64(x / Float64(Float64(y - z) * Float64(t - y)))
	tmp = 0.0
	if (t_1 <= -1000000000000.0)
		tmp = t_2;
	elseif (t_1 <= 5e-19)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	t_2 = x / ((y - z) * (t - y));
	tmp = 0.0;
	if (t_1 <= -1000000000000.0)
		tmp = t_2;
	elseif (t_1 <= 5e-19)
		tmp = 1.0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1000000000000.0], t$95$2, If[LessEqual[t$95$1, 5e-19], 1.0, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -1e12 or 5.0000000000000004e-19 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 96.2%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. /-lowering-/.f64 N/A

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

      4. distribute-rgt-neg-in N/A

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

      5. mul-1-neg N/A

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

      6. *-lowering-*.f64 N/A

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

      7. --lowering--.f64 N/A

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

      8. mul-1-neg N/A

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

      9. sub-neg N/A

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

      10. mul-1-neg N/A

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

      11. +-commutative N/A

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

      12. distribute-neg-in N/A

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

      13. unsub-neg N/A

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

      14. mul-1-neg N/A

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

      15. remove-double-neg N/A

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

      16. --lowering--.f64 95.1

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

   5. Simplified 95.1%

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

   if -1e12 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 5.0000000000000004e-19

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 99.8%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -1000000000000:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 5 \cdot 10^{-19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -6 \cdot 10^{-14}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (<= t_1 -6e-14)
     (+ 1.0 (/ x (* y (- t y))))
     (if (<= t_1 5e-19) 1.0 (+ 1.0 (/ x (* y (- z y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -6e-14) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else if (t_1 <= 5e-19) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + (x / (y * (z - y)));
	}
	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 = x / ((y - z) * (y - t))
    if (t_1 <= (-6d-14)) then
        tmp = 1.0d0 + (x / (y * (t - y)))
    else if (t_1 <= 5d-19) then
        tmp = 1.0d0
    else
        tmp = 1.0d0 + (x / (y * (z - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -6e-14) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else if (t_1 <= 5e-19) {
		tmp = 1.0;
	} else {
		tmp = 1.0 + (x / (y * (z - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if t_1 <= -6e-14:
		tmp = 1.0 + (x / (y * (t - y)))
	elif t_1 <= 5e-19:
		tmp = 1.0
	else:
		tmp = 1.0 + (x / (y * (z - y)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if (t_1 <= -6e-14)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	elseif (t_1 <= 5e-19)
		tmp = 1.0;
	else
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(z - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if (t_1 <= -6e-14)
		tmp = 1.0 + (x / (y * (t - y)));
	elseif (t_1 <= 5e-19)
		tmp = 1.0;
	else
		tmp = 1.0 + (x / (y * (z - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -6e-14], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-19], 1.0, N[(1.0 + N[(x / N[(y * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -5.9999999999999997e-14

   1. Initial program 96.8%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. --lowering--.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 48.8

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

   5. Simplified 48.8%

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

   if -5.9999999999999997e-14 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 5.0000000000000004e-19

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 99.9%

      \[\leadsto \color{blue}{1} \]

   if 5.0000000000000004e-19 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 95.6%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Simplified 57.3%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -6 \cdot 10^{-14}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 5 \cdot 10^{-19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(z - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot z}\\ t_2 := 1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* y z))) (t_2 (+ 1.0 (/ x (* (- y z) (- t y))))))
   (if (<= t_2 -2e+17) t_1 (if (<= t_2 2.0) 1.0 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (y * z);
	double t_2 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_2 <= -2e+17) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x / (y * z)
    t_2 = 1.0d0 + (x / ((y - z) * (t - y)))
    if (t_2 <= (-2d+17)) then
        tmp = t_1
    else if (t_2 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (y * z);
	double t_2 = 1.0 + (x / ((y - z) * (t - y)));
	double tmp;
	if (t_2 <= -2e+17) {
		tmp = t_1;
	} else if (t_2 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (y * z)
	t_2 = 1.0 + (x / ((y - z) * (t - y)))
	tmp = 0
	if t_2 <= -2e+17:
		tmp = t_1
	elif t_2 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(y * z))
	t_2 = Float64(1.0 + Float64(x / Float64(Float64(y - z) * Float64(t - y))))
	tmp = 0.0
	if (t_2 <= -2e+17)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (y * z);
	t_2 = 1.0 + (x / ((y - z) * (t - y)));
	tmp = 0.0;
	if (t_2 <= -2e+17)
		tmp = t_1;
	elseif (t_2 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+17], t$95$1, If[LessEqual[t$95$2, 2.0], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < -2e17 or 2 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))))

   1. Initial program 96.1%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Simplified 59.3%

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

   6. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 31.0

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

   8. Simplified 31.0%

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

   if -2e17 < (-.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))) < 2

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 99.3%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq -2 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{elif}\;1 + \frac{x}{\left(y - z\right) \cdot \left(t - y\right)} \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -6 \cdot 10^{-14}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (<= t_1 -6e-14)
     (+ 1.0 (/ x (* y (- t y))))
     (if (<= t_1 5e-19) 1.0 (- 1.0 (/ x (* y y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -6e-14) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else if (t_1 <= 5e-19) {
		tmp = 1.0;
	} else {
		tmp = 1.0 - (x / (y * y));
	}
	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 = x / ((y - z) * (y - t))
    if (t_1 <= (-6d-14)) then
        tmp = 1.0d0 + (x / (y * (t - y)))
    else if (t_1 <= 5d-19) then
        tmp = 1.0d0
    else
        tmp = 1.0d0 - (x / (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -6e-14) {
		tmp = 1.0 + (x / (y * (t - y)));
	} else if (t_1 <= 5e-19) {
		tmp = 1.0;
	} else {
		tmp = 1.0 - (x / (y * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if t_1 <= -6e-14:
		tmp = 1.0 + (x / (y * (t - y)))
	elif t_1 <= 5e-19:
		tmp = 1.0
	else:
		tmp = 1.0 - (x / (y * y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if (t_1 <= -6e-14)
		tmp = Float64(1.0 + Float64(x / Float64(y * Float64(t - y))));
	elseif (t_1 <= 5e-19)
		tmp = 1.0;
	else
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if (t_1 <= -6e-14)
		tmp = 1.0 + (x / (y * (t - y)));
	elseif (t_1 <= 5e-19)
		tmp = 1.0;
	else
		tmp = 1.0 - (x / (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -6e-14], N[(1.0 + N[(x / N[(y * N[(t - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-19], 1.0, N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -5.9999999999999997e-14

   1. Initial program 96.8%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. --lowering--.f64 N/A

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

      2. /-lowering-/.f64 N/A

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

      3. *-lowering-*.f64 N/A

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

      4. --lowering--.f64 48.8

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

   5. Simplified 48.8%

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

   if -5.9999999999999997e-14 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 5.0000000000000004e-19

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 99.9%

      \[\leadsto \color{blue}{1} \]

   if 5.0000000000000004e-19 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 95.6%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{x}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto 1 + \color{blue}{\left(\mathsf{neg}\left(\frac{x}{{y}^{2}}\right)\right)} \]

      2. unsub-neg N/A

         \[\leadsto \color{blue}{1 - \frac{x}{{y}^{2}}} \]

      3. --lowering--.f64 N/A

         \[\leadsto \color{blue}{1 - \frac{x}{{y}^{2}}} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto 1 - \color{blue}{\frac{x}{{y}^{2}}} \]

      5. unpow2 N/A

         \[\leadsto 1 - \frac{x}{\color{blue}{y \cdot y}} \]

      6. *-lowering-*.f64 53.3

         \[\leadsto 1 - \frac{x}{\color{blue}{y \cdot y}} \]

   5. Simplified 53.3%

      \[\leadsto \color{blue}{1 - \frac{x}{y \cdot y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -6 \cdot 10^{-14}:\\ \;\;\;\;1 + \frac{x}{y \cdot \left(t - y\right)}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 5 \cdot 10^{-19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (<= t_1 -1e+23)
     (/ x (* (- y z) t))
     (if (<= t_1 5e-19) 1.0 (- 1.0 (/ x (* y y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -1e+23) {
		tmp = x / ((y - z) * t);
	} else if (t_1 <= 5e-19) {
		tmp = 1.0;
	} else {
		tmp = 1.0 - (x / (y * y));
	}
	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 = x / ((y - z) * (y - t))
    if (t_1 <= (-1d+23)) then
        tmp = x / ((y - z) * t)
    else if (t_1 <= 5d-19) then
        tmp = 1.0d0
    else
        tmp = 1.0d0 - (x / (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -1e+23) {
		tmp = x / ((y - z) * t);
	} else if (t_1 <= 5e-19) {
		tmp = 1.0;
	} else {
		tmp = 1.0 - (x / (y * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if t_1 <= -1e+23:
		tmp = x / ((y - z) * t)
	elif t_1 <= 5e-19:
		tmp = 1.0
	else:
		tmp = 1.0 - (x / (y * y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if (t_1 <= -1e+23)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	elseif (t_1 <= 5e-19)
		tmp = 1.0;
	else
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if (t_1 <= -1e+23)
		tmp = x / ((y - z) * t);
	elseif (t_1 <= 5e-19)
		tmp = 1.0;
	else
		tmp = 1.0 - (x / (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+23], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-19], 1.0, N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -9.9999999999999992e22

   1. Initial program 96.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

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

      4. /-lowering-/.f64 N/A

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

      5. --lowering--.f64 N/A

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

      6. --lowering--.f64 93.3

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

   4. Applied egg-rr 93.3%

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

   5. Taylor expanded in y around 0

      \[\leadsto 1 - \frac{\color{blue}{-1 \cdot \frac{x}{t}}}{y - z} \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-lowering-neg.f64 47.9

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

   7. Simplified 47.9%

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

   8. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 N/A

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

      3. --lowering--.f64 51.0

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

   10. Simplified 51.0%

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

   if -9.9999999999999992e22 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 5.0000000000000004e-19

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 98.9%

      \[\leadsto \color{blue}{1} \]

   if 5.0000000000000004e-19 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 95.6%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{x}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto 1 + \color{blue}{\left(\mathsf{neg}\left(\frac{x}{{y}^{2}}\right)\right)} \]

      2. unsub-neg N/A

         \[\leadsto \color{blue}{1 - \frac{x}{{y}^{2}}} \]

      3. --lowering--.f64 N/A

         \[\leadsto \color{blue}{1 - \frac{x}{{y}^{2}}} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto 1 - \color{blue}{\frac{x}{{y}^{2}}} \]

      5. unpow2 N/A

         \[\leadsto 1 - \frac{x}{\color{blue}{y \cdot y}} \]

      6. *-lowering-*.f64 53.3

         \[\leadsto 1 - \frac{x}{\color{blue}{y \cdot y}} \]

   5. Simplified 53.3%

      \[\leadsto \color{blue}{1 - \frac{x}{y \cdot y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -1 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 5 \cdot 10^{-19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (<= t_1 -1e+23)
     (/ x (* z (- t)))
     (if (<= t_1 5e-19) 1.0 (- 1.0 (/ x (* y y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -1e+23) {
		tmp = x / (z * -t);
	} else if (t_1 <= 5e-19) {
		tmp = 1.0;
	} else {
		tmp = 1.0 - (x / (y * y));
	}
	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 = x / ((y - z) * (y - t))
    if (t_1 <= (-1d+23)) then
        tmp = x / (z * -t)
    else if (t_1 <= 5d-19) then
        tmp = 1.0d0
    else
        tmp = 1.0d0 - (x / (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -1e+23) {
		tmp = x / (z * -t);
	} else if (t_1 <= 5e-19) {
		tmp = 1.0;
	} else {
		tmp = 1.0 - (x / (y * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if t_1 <= -1e+23:
		tmp = x / (z * -t)
	elif t_1 <= 5e-19:
		tmp = 1.0
	else:
		tmp = 1.0 - (x / (y * y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if (t_1 <= -1e+23)
		tmp = Float64(x / Float64(z * Float64(-t)));
	elseif (t_1 <= 5e-19)
		tmp = 1.0;
	else
		tmp = Float64(1.0 - Float64(x / Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if (t_1 <= -1e+23)
		tmp = x / (z * -t);
	elseif (t_1 <= 5e-19)
		tmp = 1.0;
	else
		tmp = 1.0 - (x / (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+23], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-19], 1.0, N[(1.0 - N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -9.9999999999999992e22

   1. Initial program 96.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 - \frac{x}{t \cdot z}} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \color{blue}{1 - \frac{x}{t \cdot z}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto 1 - \color{blue}{\frac{x}{t \cdot z}} \]

      3. *-lowering-*.f64 48.1

         \[\leadsto 1 - \frac{x}{\color{blue}{t \cdot z}} \]

   5. Simplified 48.1%

      \[\leadsto \color{blue}{1 - \frac{x}{t \cdot z}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. neg-lowering-neg.f64 48.1

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

   8. Simplified 48.1%

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

   if -9.9999999999999992e22 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 5.0000000000000004e-19

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 98.9%

      \[\leadsto \color{blue}{1} \]

   if 5.0000000000000004e-19 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 95.6%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{x}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto 1 + \color{blue}{\left(\mathsf{neg}\left(\frac{x}{{y}^{2}}\right)\right)} \]

      2. unsub-neg N/A

         \[\leadsto \color{blue}{1 - \frac{x}{{y}^{2}}} \]

      3. --lowering--.f64 N/A

         \[\leadsto \color{blue}{1 - \frac{x}{{y}^{2}}} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto 1 - \color{blue}{\frac{x}{{y}^{2}}} \]

      5. unpow2 N/A

         \[\leadsto 1 - \frac{x}{\color{blue}{y \cdot y}} \]

      6. *-lowering-*.f64 53.3

         \[\leadsto 1 - \frac{x}{\color{blue}{y \cdot y}} \]

   5. Simplified 53.3%

      \[\leadsto \color{blue}{1 - \frac{x}{y \cdot y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -1 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 5 \cdot 10^{-19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{y \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (<= t_1 -1e+23)
     (/ x (* z (- t)))
     (if (<= t_1 5e-19) 1.0 (/ (- x) (* y y))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -1e+23) {
		tmp = x / (z * -t);
	} else if (t_1 <= 5e-19) {
		tmp = 1.0;
	} else {
		tmp = -x / (y * y);
	}
	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 = x / ((y - z) * (y - t))
    if (t_1 <= (-1d+23)) then
        tmp = x / (z * -t)
    else if (t_1 <= 5d-19) then
        tmp = 1.0d0
    else
        tmp = -x / (y * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -1e+23) {
		tmp = x / (z * -t);
	} else if (t_1 <= 5e-19) {
		tmp = 1.0;
	} else {
		tmp = -x / (y * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if t_1 <= -1e+23:
		tmp = x / (z * -t)
	elif t_1 <= 5e-19:
		tmp = 1.0
	else:
		tmp = -x / (y * y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if (t_1 <= -1e+23)
		tmp = Float64(x / Float64(z * Float64(-t)));
	elseif (t_1 <= 5e-19)
		tmp = 1.0;
	else
		tmp = Float64(Float64(-x) / Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if (t_1 <= -1e+23)
		tmp = x / (z * -t);
	elseif (t_1 <= 5e-19)
		tmp = 1.0;
	else
		tmp = -x / (y * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+23], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-19], 1.0, N[((-x) / N[(y * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -9.9999999999999992e22

   1. Initial program 96.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 - \frac{x}{t \cdot z}} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \color{blue}{1 - \frac{x}{t \cdot z}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto 1 - \color{blue}{\frac{x}{t \cdot z}} \]

      3. *-lowering-*.f64 48.1

         \[\leadsto 1 - \frac{x}{\color{blue}{t \cdot z}} \]

   5. Simplified 48.1%

      \[\leadsto \color{blue}{1 - \frac{x}{t \cdot z}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. neg-lowering-neg.f64 48.1

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

   8. Simplified 48.1%

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

   if -9.9999999999999992e22 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 5.0000000000000004e-19

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 98.9%

      \[\leadsto \color{blue}{1} \]

   if 5.0000000000000004e-19 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 95.6%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{1 + -1 \cdot \frac{x}{{y}^{2}}} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto 1 + \color{blue}{\left(\mathsf{neg}\left(\frac{x}{{y}^{2}}\right)\right)} \]

      2. unsub-neg N/A

         \[\leadsto \color{blue}{1 - \frac{x}{{y}^{2}}} \]

      3. --lowering--.f64 N/A

         \[\leadsto \color{blue}{1 - \frac{x}{{y}^{2}}} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto 1 - \color{blue}{\frac{x}{{y}^{2}}} \]

      5. unpow2 N/A

         \[\leadsto 1 - \frac{x}{\color{blue}{y \cdot y}} \]

      6. *-lowering-*.f64 53.3

         \[\leadsto 1 - \frac{x}{\color{blue}{y \cdot y}} \]

   5. Simplified 53.3%

      \[\leadsto \color{blue}{1 - \frac{x}{y \cdot y}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{{y}^{2}}} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{x}{{y}^{2}}\right)} \]

      2. distribute-neg-frac2 N/A

         \[\leadsto \color{blue}{\frac{x}{\mathsf{neg}\left({y}^{2}\right)}} \]

      3. mul-1-neg N/A

         \[\leadsto \frac{x}{\color{blue}{-1 \cdot {y}^{2}}} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{-1 \cdot {y}^{2}}} \]

      5. unpow2 N/A

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

      6. associate-*r* N/A

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

      7. *-lowering-*.f64 N/A

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

      8. mul-1-neg N/A

         \[\leadsto \frac{x}{\color{blue}{\left(\mathsf{neg}\left(y\right)\right)} \cdot y} \]

      9. neg-lowering-neg.f64 51.6

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

   8. Simplified 51.6%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -1 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 5 \cdot 10^{-19}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{y \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(y - t\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;t\_1 \leq 500000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- y t)))))
   (if (<= t_1 -1e+23)
     (/ x (* z (- t)))
     (if (<= t_1 500000000.0) 1.0 (/ x (* y z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -1e+23) {
		tmp = x / (z * -t);
	} else if (t_1 <= 500000000.0) {
		tmp = 1.0;
	} else {
		tmp = x / (y * 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) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (y - t))
    if (t_1 <= (-1d+23)) then
        tmp = x / (z * -t)
    else if (t_1 <= 500000000.0d0) then
        tmp = 1.0d0
    else
        tmp = x / (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (y - t));
	double tmp;
	if (t_1 <= -1e+23) {
		tmp = x / (z * -t);
	} else if (t_1 <= 500000000.0) {
		tmp = 1.0;
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / ((y - z) * (y - t))
	tmp = 0
	if t_1 <= -1e+23:
		tmp = x / (z * -t)
	elif t_1 <= 500000000.0:
		tmp = 1.0
	else:
		tmp = x / (y * z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(y - t)))
	tmp = 0.0
	if (t_1 <= -1e+23)
		tmp = Float64(x / Float64(z * Float64(-t)));
	elseif (t_1 <= 500000000.0)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (y - t));
	tmp = 0.0;
	if (t_1 <= -1e+23)
		tmp = x / (z * -t);
	elseif (t_1 <= 500000000.0)
		tmp = 1.0;
	else
		tmp = x / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(y - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+23], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 500000000.0], 1.0, N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < -9.9999999999999992e22

   1. Initial program 96.4%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{1 - \frac{x}{t \cdot z}} \]
   4. Step-by-step derivation

      1. --lowering--.f64 N/A

         \[\leadsto \color{blue}{1 - \frac{x}{t \cdot z}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto 1 - \color{blue}{\frac{x}{t \cdot z}} \]

      3. *-lowering-*.f64 48.1

         \[\leadsto 1 - \frac{x}{\color{blue}{t \cdot z}} \]

   5. Simplified 48.1%

      \[\leadsto \color{blue}{1 - \frac{x}{t \cdot z}} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{t \cdot z}} \]
   7. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

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

      5. mul-1-neg N/A

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

      6. distribute-rgt-neg-in N/A

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

      7. mul-1-neg N/A

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

      8. *-lowering-*.f64 N/A

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

      9. mul-1-neg N/A

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

      10. neg-lowering-neg.f64 48.1

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

   8. Simplified 48.1%

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

   if -9.9999999999999992e22 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t))) < 5e8

   1. Initial program 100.0%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Simplified 98.4%

      \[\leadsto \color{blue}{1} \]

   if 5e8 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 y t)))

   1. Initial program 95.3%

      \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Simplified 55.4%

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

   6. Taylor expanded in y around 0

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

      1. /-lowering-/.f64 N/A

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

      2. *-lowering-*.f64 24.8

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

   8. Simplified 24.8%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq -1 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;\frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \leq 500000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 = 1.0d0 + (x / ((y - z) * (t - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

   \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
2. Add Preprocessing

3. Final simplification 99.2%

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

Alternative 11: 74.5% accurate, 26.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 1.0)

C

double code(double x, double y, double z, double t) {
	return 1.0;
}

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 = 1.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0;
}

Python

def code(x, y, z, t):
	return 1.0

Julia

function code(x, y, z, t)
	return 1.0
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 99.2%

   \[1 - \frac{x}{\left(y - z\right) \cdot \left(y - t\right)} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Simplified 79.1%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024204 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, A"
  :precision binary64
  (- 1.0 (/ x (* (- y z) (- y t)))))