Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23

Percentage Accurate: 99.9% → 99.9%

Time: 7.1s

Alternatives: 9

Speedup: 1.0×

• 30.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x \cdot y + z\right) \cdot y + t \]
2. Step-by-step derivation

   1. fma-def 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot y + z, y, t\right)} \]

   2. fma-def 99.9%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{fma}\left(x, y, z\right)}, y, t\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)} \]

4. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right) \]

Alternative 2: 64.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot y\right)\\ \mathbf{if}\;y \leq -0.0138:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-64}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-18}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* y y))))
   (if (<= y -0.0138)
     t_1
     (if (<= y 1.22e-64)
       t
       (if (<= y 5.2e-18) (* y z) (if (<= y 1.95e+42) t t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y * y);
	double tmp;
	if (y <= -0.0138) {
		tmp = t_1;
	} else if (y <= 1.22e-64) {
		tmp = t;
	} else if (y <= 5.2e-18) {
		tmp = y * z;
	} else if (y <= 1.95e+42) {
		tmp = t;
	} 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) :: tmp
    t_1 = x * (y * y)
    if (y <= (-0.0138d0)) then
        tmp = t_1
    else if (y <= 1.22d-64) then
        tmp = t
    else if (y <= 5.2d-18) then
        tmp = y * z
    else if (y <= 1.95d+42) then
        tmp = t
    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 * y);
	double tmp;
	if (y <= -0.0138) {
		tmp = t_1;
	} else if (y <= 1.22e-64) {
		tmp = t;
	} else if (y <= 5.2e-18) {
		tmp = y * z;
	} else if (y <= 1.95e+42) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y * y)
	tmp = 0
	if y <= -0.0138:
		tmp = t_1
	elif y <= 1.22e-64:
		tmp = t
	elif y <= 5.2e-18:
		tmp = y * z
	elif y <= 1.95e+42:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y * y))
	tmp = 0.0
	if (y <= -0.0138)
		tmp = t_1;
	elseif (y <= 1.22e-64)
		tmp = t;
	elseif (y <= 5.2e-18)
		tmp = Float64(y * z);
	elseif (y <= 1.95e+42)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (y * y);
	tmp = 0.0;
	if (y <= -0.0138)
		tmp = t_1;
	elseif (y <= 1.22e-64)
		tmp = t;
	elseif (y <= 5.2e-18)
		tmp = y * z;
	elseif (y <= 1.95e+42)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.0138], t$95$1, If[LessEqual[y, 1.22e-64], t, If[LessEqual[y, 5.2e-18], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.95e+42], t, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0138 or 1.94999999999999985e42 < y

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in t around 0 87.6%

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

   3. Taylor expanded in z around 0 65.4%

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

   4. Taylor expanded in y around 0 66.3%

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

      1. unpow2 66.3%

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

   6. Simplified 66.3%

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

   if -0.0138 < y < 1.22000000000000003e-64 or 5.2000000000000001e-18 < y < 1.94999999999999985e42

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in y around 0 64.7%

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

   if 1.22000000000000003e-64 < y < 5.2000000000000001e-18

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in t around 0 87.6%

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

   3. Taylor expanded in z around inf 77.0%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0138:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-64}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-18}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 3: 65.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-64}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-16}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.1)
   (* x (* y y))
   (if (<= y 3.8e-64)
     t
     (if (<= y 2e-16) (* y z) (if (<= y 7.5e+42) t (* y (* x y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.1) {
		tmp = x * (y * y);
	} else if (y <= 3.8e-64) {
		tmp = t;
	} else if (y <= 2e-16) {
		tmp = y * z;
	} else if (y <= 7.5e+42) {
		tmp = t;
	} else {
		tmp = y * (x * 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) :: tmp
    if (y <= (-2.1d0)) then
        tmp = x * (y * y)
    else if (y <= 3.8d-64) then
        tmp = t
    else if (y <= 2d-16) then
        tmp = y * z
    else if (y <= 7.5d+42) then
        tmp = t
    else
        tmp = y * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.1) {
		tmp = x * (y * y);
	} else if (y <= 3.8e-64) {
		tmp = t;
	} else if (y <= 2e-16) {
		tmp = y * z;
	} else if (y <= 7.5e+42) {
		tmp = t;
	} else {
		tmp = y * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.1:
		tmp = x * (y * y)
	elif y <= 3.8e-64:
		tmp = t
	elif y <= 2e-16:
		tmp = y * z
	elif y <= 7.5e+42:
		tmp = t
	else:
		tmp = y * (x * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.1)
		tmp = Float64(x * Float64(y * y));
	elseif (y <= 3.8e-64)
		tmp = t;
	elseif (y <= 2e-16)
		tmp = Float64(y * z);
	elseif (y <= 7.5e+42)
		tmp = t;
	else
		tmp = Float64(y * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.1)
		tmp = x * (y * y);
	elseif (y <= 3.8e-64)
		tmp = t;
	elseif (y <= 2e-16)
		tmp = y * z;
	elseif (y <= 7.5e+42)
		tmp = t;
	else
		tmp = y * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.1], N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e-64], t, If[LessEqual[y, 2e-16], N[(y * z), $MachinePrecision], If[LessEqual[y, 7.5e+42], t, N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.10000000000000009

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in t around 0 91.2%

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

   3. Taylor expanded in z around 0 72.4%

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

   4. Taylor expanded in y around 0 74.1%

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

      1. unpow2 74.1%

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

   6. Simplified 74.1%

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

   if -2.10000000000000009 < y < 3.8000000000000002e-64 or 2e-16 < y < 7.50000000000000041e42

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in y around 0 64.7%

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

   if 3.8000000000000002e-64 < y < 2e-16

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in t around 0 87.6%

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

   3. Taylor expanded in z around inf 77.0%

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

   if 7.50000000000000041e42 < y

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in t around 0 83.3%

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

   3. Taylor expanded in z around 0 57.1%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-64}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-16}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+42}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 4: 89.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -550 \lor \neg \left(y \leq 3 \cdot 10^{+43}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -550.0) (not (<= y 3e+43))) (* y (+ z (* x y))) (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -550.0) || !(y <= 3e+43)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (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) :: tmp
    if ((y <= (-550.0d0)) .or. (.not. (y <= 3d+43))) then
        tmp = y * (z + (x * y))
    else
        tmp = t + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -550.0) || !(y <= 3e+43)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -550.0) or not (y <= 3e+43):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -550.0) || !(y <= 3e+43))
		tmp = Float64(y * Float64(z + Float64(x * y)));
	else
		tmp = Float64(t + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -550.0) || ~((y <= 3e+43)))
		tmp = y * (z + (x * y));
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -550.0], N[Not[LessEqual[y, 3e+43]], $MachinePrecision]], N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -550 or 3.00000000000000017e43 < y

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in t around 0 87.5%

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

   if -550 < y < 3.00000000000000017e43

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in x around 0 93.0%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -550 \lor \neg \left(y \leq 3 \cdot 10^{+43}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 5: 87.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+60}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.2e+29)
   (* y (+ z (* x y)))
   (if (<= z 3.7e+60) (+ t (* y (* x y))) (+ t (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.2e+29) {
		tmp = y * (z + (x * y));
	} else if (z <= 3.7e+60) {
		tmp = t + (y * (x * y));
	} else {
		tmp = t + (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) :: tmp
    if (z <= (-9.2d+29)) then
        tmp = y * (z + (x * y))
    else if (z <= 3.7d+60) then
        tmp = t + (y * (x * y))
    else
        tmp = t + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.2e+29) {
		tmp = y * (z + (x * y));
	} else if (z <= 3.7e+60) {
		tmp = t + (y * (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.2e+29:
		tmp = y * (z + (x * y))
	elif z <= 3.7e+60:
		tmp = t + (y * (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.2e+29)
		tmp = Float64(y * Float64(z + Float64(x * y)));
	elseif (z <= 3.7e+60)
		tmp = Float64(t + Float64(y * Float64(x * y)));
	else
		tmp = Float64(t + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.2e+29)
		tmp = y * (z + (x * y));
	elseif (z <= 3.7e+60)
		tmp = t + (y * (x * y));
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.2e+29], N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+60], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.2000000000000004e29

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in t around 0 84.8%

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

   if -9.2000000000000004e29 < z < 3.69999999999999988e60

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in x around inf 96.3%

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

      1. *-commutative 96.3%

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

   4. Simplified 96.3%

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

   if 3.69999999999999988e60 < z

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in x around 0 90.2%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+60}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 6: 77.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+197}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.8e+52)
   (* x (* y y))
   (if (<= y 1.5e+197) (+ t (* y z)) (* y (* x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.8e+52) {
		tmp = x * (y * y);
	} else if (y <= 1.5e+197) {
		tmp = t + (y * z);
	} else {
		tmp = y * (x * 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) :: tmp
    if (y <= (-3.8d+52)) then
        tmp = x * (y * y)
    else if (y <= 1.5d+197) then
        tmp = t + (y * z)
    else
        tmp = y * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.8e+52) {
		tmp = x * (y * y);
	} else if (y <= 1.5e+197) {
		tmp = t + (y * z);
	} else {
		tmp = y * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.8e+52:
		tmp = x * (y * y)
	elif y <= 1.5e+197:
		tmp = t + (y * z)
	else:
		tmp = y * (x * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.8e+52)
		tmp = Float64(x * Float64(y * y));
	elseif (y <= 1.5e+197)
		tmp = Float64(t + Float64(y * z));
	else
		tmp = Float64(y * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.8e+52)
		tmp = x * (y * y);
	elseif (y <= 1.5e+197)
		tmp = t + (y * z);
	else
		tmp = y * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.8e+52], N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+197], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8e52

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in t around 0 94.2%

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

   3. Taylor expanded in z around 0 79.0%

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

   4. Taylor expanded in y around 0 80.9%

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

      1. unpow2 80.9%

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

   6. Simplified 80.9%

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

   if -3.8e52 < y < 1.5000000000000001e197

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in x around 0 84.3%

      \[\leadsto \color{blue}{z} \cdot y + t \]

   if 1.5000000000000001e197 < y

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in t around 0 94.6%

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

   3. Taylor expanded in z around 0 83.5%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+52}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+197}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 7: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x \cdot y + z\right) \cdot y + t \]

2. Final simplification 99.9%

   \[\leadsto t + y \cdot \left(z + x \cdot y\right) \]

Alternative 8: 51.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+29}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+65}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.2e+29) (* y z) (if (<= z 1.15e+65) t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.2e+29) {
		tmp = y * z;
	} else if (z <= 1.15e+65) {
		tmp = t;
	} else {
		tmp = 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) :: tmp
    if (z <= (-9.2d+29)) then
        tmp = y * z
    else if (z <= 1.15d+65) then
        tmp = t
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.2e+29) {
		tmp = y * z;
	} else if (z <= 1.15e+65) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9.2e+29:
		tmp = y * z
	elif z <= 1.15e+65:
		tmp = t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.2e+29)
		tmp = Float64(y * z);
	elseif (z <= 1.15e+65)
		tmp = t;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.2e+29)
		tmp = y * z;
	elseif (z <= 1.15e+65)
		tmp = t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9.2e+29], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.15e+65], t, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -9.2000000000000004e29 or 1.15e65 < z

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in t around 0 79.7%

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

   3. Taylor expanded in z around inf 66.3%

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

   if -9.2000000000000004e29 < z < 1.15e65

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in y around 0 57.3%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+29}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+65}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 9: 37.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 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 = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\left(x \cdot y + z\right) \cdot y + t \]

2. Taylor expanded in y around 0 40.1%

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

3. Final simplification 40.1%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))