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

Percentage Accurate: 99.9% → 99.9%

Time: 6.6s

Alternatives: 9

Speedup: 1.0×

• 29.4% 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, 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 2: 88.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t + y \cdot z\\ t_2 := t + x \cdot \left(y \cdot y\right)\\ t_3 := y \cdot \left(z + x \cdot y\right)\\ \mathbf{if}\;y \leq -24000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ t (* y z)))
        (t_2 (+ t (* x (* y y))))
        (t_3 (* y (+ z (* x y)))))
   (if (<= y -24000000.0)
     t_3
     (if (<= y 1.15e-114)
       t_1
       (if (<= y 8e-98)
         t_2
         (if (<= y 3.5e+15) t_1 (if (<= y 2.3e+58) t_2 t_3)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t + (y * z);
	double t_2 = t + (x * (y * y));
	double t_3 = y * (z + (x * y));
	double tmp;
	if (y <= -24000000.0) {
		tmp = t_3;
	} else if (y <= 1.15e-114) {
		tmp = t_1;
	} else if (y <= 8e-98) {
		tmp = t_2;
	} else if (y <= 3.5e+15) {
		tmp = t_1;
	} else if (y <= 2.3e+58) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_1 = t + (y * z)
    t_2 = t + (x * (y * y))
    t_3 = y * (z + (x * y))
    if (y <= (-24000000.0d0)) then
        tmp = t_3
    else if (y <= 1.15d-114) then
        tmp = t_1
    else if (y <= 8d-98) then
        tmp = t_2
    else if (y <= 3.5d+15) then
        tmp = t_1
    else if (y <= 2.3d+58) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t + (y * z);
	double t_2 = t + (x * (y * y));
	double t_3 = y * (z + (x * y));
	double tmp;
	if (y <= -24000000.0) {
		tmp = t_3;
	} else if (y <= 1.15e-114) {
		tmp = t_1;
	} else if (y <= 8e-98) {
		tmp = t_2;
	} else if (y <= 3.5e+15) {
		tmp = t_1;
	} else if (y <= 2.3e+58) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t + (y * z)
	t_2 = t + (x * (y * y))
	t_3 = y * (z + (x * y))
	tmp = 0
	if y <= -24000000.0:
		tmp = t_3
	elif y <= 1.15e-114:
		tmp = t_1
	elif y <= 8e-98:
		tmp = t_2
	elif y <= 3.5e+15:
		tmp = t_1
	elif y <= 2.3e+58:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t + Float64(y * z))
	t_2 = Float64(t + Float64(x * Float64(y * y)))
	t_3 = Float64(y * Float64(z + Float64(x * y)))
	tmp = 0.0
	if (y <= -24000000.0)
		tmp = t_3;
	elseif (y <= 1.15e-114)
		tmp = t_1;
	elseif (y <= 8e-98)
		tmp = t_2;
	elseif (y <= 3.5e+15)
		tmp = t_1;
	elseif (y <= 2.3e+58)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t + (y * z);
	t_2 = t + (x * (y * y));
	t_3 = y * (z + (x * y));
	tmp = 0.0;
	if (y <= -24000000.0)
		tmp = t_3;
	elseif (y <= 1.15e-114)
		tmp = t_1;
	elseif (y <= 8e-98)
		tmp = t_2;
	elseif (y <= 3.5e+15)
		tmp = t_1;
	elseif (y <= 2.3e+58)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -24000000.0], t$95$3, If[LessEqual[y, 1.15e-114], t$95$1, If[LessEqual[y, 8e-98], t$95$2, If[LessEqual[y, 3.5e+15], t$95$1, If[LessEqual[y, 2.3e+58], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4e7 or 2.30000000000000002e58 < y

   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. Taylor expanded in t around 0 96.0%

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

   if -2.4e7 < y < 1.15e-114 or 7.99999999999999951e-98 < y < 3.5e15

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 92.1%

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

   if 1.15e-114 < y < 7.99999999999999951e-98 or 3.5e15 < y < 2.30000000000000002e58

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. distribute-rgt-in 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in x around inf 93.0%

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

      1. unpow2 93.0%

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

      2. *-commutative 93.0%

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

   6. Simplified 93.0%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -24000000:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-114}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-98}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+15}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+58}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \]

Alternative 3: 79.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ t_2 := t + y \cdot z\\ \mathbf{if}\;y \leq -2.05 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))) (t_2 (+ t (* y z))))
   (if (<= y -2.05e+157)
     t_1
     (if (<= y -5.4e+47)
       t_2
       (if (<= y -7.8e+28) (* x (* y y)) (if (<= y 1.1e+56) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double t_2 = t + (y * z);
	double tmp;
	if (y <= -2.05e+157) {
		tmp = t_1;
	} else if (y <= -5.4e+47) {
		tmp = t_2;
	} else if (y <= -7.8e+28) {
		tmp = x * (y * y);
	} else if (y <= 1.1e+56) {
		tmp = t_2;
	} 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 = y * (x * y)
    t_2 = t + (y * z)
    if (y <= (-2.05d+157)) then
        tmp = t_1
    else if (y <= (-5.4d+47)) then
        tmp = t_2
    else if (y <= (-7.8d+28)) then
        tmp = x * (y * y)
    else if (y <= 1.1d+56) then
        tmp = t_2
    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 = y * (x * y);
	double t_2 = t + (y * z);
	double tmp;
	if (y <= -2.05e+157) {
		tmp = t_1;
	} else if (y <= -5.4e+47) {
		tmp = t_2;
	} else if (y <= -7.8e+28) {
		tmp = x * (y * y);
	} else if (y <= 1.1e+56) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * y)
	t_2 = t + (y * z)
	tmp = 0
	if y <= -2.05e+157:
		tmp = t_1
	elif y <= -5.4e+47:
		tmp = t_2
	elif y <= -7.8e+28:
		tmp = x * (y * y)
	elif y <= 1.1e+56:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x * y))
	t_2 = Float64(t + Float64(y * z))
	tmp = 0.0
	if (y <= -2.05e+157)
		tmp = t_1;
	elseif (y <= -5.4e+47)
		tmp = t_2;
	elseif (y <= -7.8e+28)
		tmp = Float64(x * Float64(y * y));
	elseif (y <= 1.1e+56)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x * y);
	t_2 = t + (y * z);
	tmp = 0.0;
	if (y <= -2.05e+157)
		tmp = t_1;
	elseif (y <= -5.4e+47)
		tmp = t_2;
	elseif (y <= -7.8e+28)
		tmp = x * (y * y);
	elseif (y <= 1.1e+56)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.05e+157], t$95$1, If[LessEqual[y, -5.4e+47], t$95$2, If[LessEqual[y, -7.8e+28], N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+56], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.05000000000000008e157 or 1.10000000000000008e56 < y

   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. Taylor expanded in t around 0 98.0%

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

   5. Taylor expanded in y around inf 79.6%

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

   if -2.05000000000000008e157 < y < -5.39999999999999991e47 or -7.7999999999999997e28 < y < 1.10000000000000008e56

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 82.8%

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

   if -5.39999999999999991e47 < y < -7.7999999999999997e28

   1. Initial program 99.4%

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

      1. fma-def 99.4%

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

      2. fma-def 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in t around 0 99.4%

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

   5. Taylor expanded in y around inf 99.4%

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

   6. Taylor expanded in y around 0 100.0%

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

      1. unpow2 100.0%

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

      2. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+47}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+56}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 4: 63.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot y\right)\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-98}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-7}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* y y))))
   (if (<= y -1.55e+26)
     t_1
     (if (<= y -4e-98) (* y z) (if (<= y 1.05e-7) t t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y * y);
	double tmp;
	if (y <= -1.55e+26) {
		tmp = t_1;
	} else if (y <= -4e-98) {
		tmp = y * z;
	} else if (y <= 1.05e-7) {
		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 <= (-1.55d+26)) then
        tmp = t_1
    else if (y <= (-4d-98)) then
        tmp = y * z
    else if (y <= 1.05d-7) 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 <= -1.55e+26) {
		tmp = t_1;
	} else if (y <= -4e-98) {
		tmp = y * z;
	} else if (y <= 1.05e-7) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y * y)
	tmp = 0
	if y <= -1.55e+26:
		tmp = t_1
	elif y <= -4e-98:
		tmp = y * z
	elif y <= 1.05e-7:
		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 <= -1.55e+26)
		tmp = t_1;
	elseif (y <= -4e-98)
		tmp = Float64(y * z);
	elseif (y <= 1.05e-7)
		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 <= -1.55e+26)
		tmp = t_1;
	elseif (y <= -4e-98)
		tmp = y * z;
	elseif (y <= 1.05e-7)
		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, -1.55e+26], t$95$1, If[LessEqual[y, -4e-98], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.05e-7], t, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55e26 or 1.05e-7 < y

   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. Taylor expanded in t around 0 90.7%

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

   5. Taylor expanded in y around inf 66.8%

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

   6. Taylor expanded in y around 0 62.9%

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

      1. unpow2 62.9%

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

      2. *-commutative 62.9%

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

   8. Simplified 62.9%

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

   if -1.55e26 < y < -3.99999999999999976e-98

   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. Taylor expanded in t around 0 69.3%

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

   5. Taylor expanded in y around 0 55.8%

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

   if -3.99999999999999976e-98 < y < 1.05e-7

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 68.3%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-98}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-7}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 5: 64.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-98}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-6}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))))
   (if (<= y -1.85e+28)
     t_1
     (if (<= y -5.5e-98) (* y z) (if (<= y 1.6e-6) t t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (y <= -1.85e+28) {
		tmp = t_1;
	} else if (y <= -5.5e-98) {
		tmp = y * z;
	} else if (y <= 1.6e-6) {
		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 = y * (x * y)
    if (y <= (-1.85d+28)) then
        tmp = t_1
    else if (y <= (-5.5d-98)) then
        tmp = y * z
    else if (y <= 1.6d-6) 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 = y * (x * y);
	double tmp;
	if (y <= -1.85e+28) {
		tmp = t_1;
	} else if (y <= -5.5e-98) {
		tmp = y * z;
	} else if (y <= 1.6e-6) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * y)
	tmp = 0
	if y <= -1.85e+28:
		tmp = t_1
	elif y <= -5.5e-98:
		tmp = y * z
	elif y <= 1.6e-6:
		tmp = t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x * y))
	tmp = 0.0
	if (y <= -1.85e+28)
		tmp = t_1;
	elseif (y <= -5.5e-98)
		tmp = Float64(y * z);
	elseif (y <= 1.6e-6)
		tmp = t;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x * y);
	tmp = 0.0;
	if (y <= -1.85e+28)
		tmp = t_1;
	elseif (y <= -5.5e-98)
		tmp = y * z;
	elseif (y <= 1.6e-6)
		tmp = t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e+28], t$95$1, If[LessEqual[y, -5.5e-98], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.6e-6], t, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.85e28 or 1.5999999999999999e-6 < y

   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. Taylor expanded in t around 0 90.7%

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

   5. Taylor expanded in y around inf 66.8%

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

   if -1.85e28 < y < -5.4999999999999997e-98

   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. Taylor expanded in t around 0 69.3%

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

   5. Taylor expanded in y around 0 55.8%

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

   if -5.4999999999999997e-98 < y < 1.5999999999999999e-6

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 68.3%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-98}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-6}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 6: 89.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1750000000 \lor \neg \left(y \leq 3.2 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1750000000.0) (not (<= y 3.2e-7)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1750000000.0) || !(y <= 3.2e-7)) {
		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 <= (-1750000000.0d0)) .or. (.not. (y <= 3.2d-7))) 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 <= -1750000000.0) || !(y <= 3.2e-7)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1750000000.0) or not (y <= 3.2e-7):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1750000000.0) || !(y <= 3.2e-7))
		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 <= -1750000000.0) || ~((y <= 3.2e-7)))
		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, -1750000000.0], N[Not[LessEqual[y, 3.2e-7]], $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 < -1.75e9 or 3.2000000000000001e-7 < y

   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. Taylor expanded in t around 0 91.0%

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

   if -1.75e9 < y < 3.2000000000000001e-7

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 89.5%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1750000000 \lor \neg \left(y \leq 3.2 \cdot 10^{-7}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 7: 88.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+25} \lor \neg \left(z \leq 1.12 \cdot 10^{+92}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.2e+25) (not (<= z 1.12e+92)))
   (+ t (* y z))
   (+ t (* y (* x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.2e+25) || !(z <= 1.12e+92)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (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 ((z <= (-5.2d+25)) .or. (.not. (z <= 1.12d+92))) then
        tmp = t + (y * z)
    else
        tmp = t + (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 ((z <= -5.2e+25) || !(z <= 1.12e+92)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.2e+25) or not (z <= 1.12e+92):
		tmp = t + (y * z)
	else:
		tmp = t + (y * (x * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.2e+25) || !(z <= 1.12e+92))
		tmp = Float64(t + Float64(y * z));
	else
		tmp = Float64(t + Float64(y * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.2e+25) || ~((z <= 1.12e+92)))
		tmp = t + (y * z);
	else
		tmp = t + (y * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.2e+25], N[Not[LessEqual[z, 1.12e+92]], $MachinePrecision]], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.1999999999999997e25 or 1.1199999999999999e92 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 84.4%

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

   if -5.1999999999999997e25 < z < 1.1199999999999999e92

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 94.2%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+25} \lor \neg \left(z \leq 1.12 \cdot 10^{+92}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 8: 51.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+95}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+27}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.7e+95) (* y z) (if (<= z 8e+27) t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.7e+95) {
		tmp = y * z;
	} else if (z <= 8e+27) {
		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 <= (-1.7d+95)) then
        tmp = y * z
    else if (z <= 8d+27) 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 <= -1.7e+95) {
		tmp = y * z;
	} else if (z <= 8e+27) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.7e+95:
		tmp = y * z
	elif z <= 8e+27:
		tmp = t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.7e+95)
		tmp = Float64(y * z);
	elseif (z <= 8e+27)
		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 <= -1.7e+95)
		tmp = y * z;
	elseif (z <= 8e+27)
		tmp = t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.7e+95], N[(y * z), $MachinePrecision], If[LessEqual[z, 8e+27], t, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.70000000000000011e95 or 8.0000000000000001e27 < z

   1. Initial program 100.0%

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

      1. fma-def 100.0%

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

      2. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 79.7%

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

   5. Taylor expanded in y around 0 61.1%

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

   if -1.70000000000000011e95 < z < 8.0000000000000001e27

   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. Taylor expanded in y around 0 46.4%

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

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+95}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+27}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 9: 38.4% 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. 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. Taylor expanded in y around 0 35.6%

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

5. Final simplification 35.6%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023268 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))