Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 9.1s

Alternatives: 16

Speedup: 1.0×

• 34.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

function code(x, y, z, t)
	return fma(Float64(y - z), Float64(t - x), x)
end

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, t - x, x\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 67.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-122}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1.45e+78)
     t_1
     (if (<= z -2.1e-122)
       (* (- y z) t)
       (if (<= z 3.9e-63)
         (* x (- 1.0 y))
         (if (<= z 5e+51) (* y (- t x)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.45e+78) {
		tmp = t_1;
	} else if (z <= -2.1e-122) {
		tmp = (y - z) * t;
	} else if (z <= 3.9e-63) {
		tmp = x * (1.0 - y);
	} else if (z <= 5e+51) {
		tmp = y * (t - x);
	} 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 = z * (x - t)
    if (z <= (-1.45d+78)) then
        tmp = t_1
    else if (z <= (-2.1d-122)) then
        tmp = (y - z) * t
    else if (z <= 3.9d-63) then
        tmp = x * (1.0d0 - y)
    else if (z <= 5d+51) then
        tmp = y * (t - x)
    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 = z * (x - t);
	double tmp;
	if (z <= -1.45e+78) {
		tmp = t_1;
	} else if (z <= -2.1e-122) {
		tmp = (y - z) * t;
	} else if (z <= 3.9e-63) {
		tmp = x * (1.0 - y);
	} else if (z <= 5e+51) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -1.45e+78:
		tmp = t_1
	elif z <= -2.1e-122:
		tmp = (y - z) * t
	elif z <= 3.9e-63:
		tmp = x * (1.0 - y)
	elif z <= 5e+51:
		tmp = y * (t - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -1.45e+78)
		tmp = t_1;
	elseif (z <= -2.1e-122)
		tmp = Float64(Float64(y - z) * t);
	elseif (z <= 3.9e-63)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (z <= 5e+51)
		tmp = Float64(y * Float64(t - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -1.45e+78)
		tmp = t_1;
	elseif (z <= -2.1e-122)
		tmp = (y - z) * t;
	elseif (z <= 3.9e-63)
		tmp = x * (1.0 - y);
	elseif (z <= 5e+51)
		tmp = y * (t - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e+78], t$95$1, If[LessEqual[z, -2.1e-122], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 3.9e-63], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+51], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.45000000000000008e78 or 5e51 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 94.8%

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

      1. fma-define 94.8%

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

      2. +-commutative 94.8%

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

      3. mul-1-neg 94.8%

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

   5. Simplified 94.8%

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

   6. Taylor expanded in z around inf 86.1%

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

      1. neg-mul-1 86.1%

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

      2. unsub-neg 86.1%

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

   8. Simplified 86.1%

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

   if -1.45000000000000008e78 < z < -2.09999999999999992e-122

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 97.9%

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

      1. fma-define 97.9%

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

      2. +-commutative 97.9%

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

      3. mul-1-neg 97.9%

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

   5. Simplified 97.9%

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

   6. Taylor expanded in t around inf 67.4%

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

   if -2.09999999999999992e-122 < z < 3.90000000000000022e-63

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 70.1%

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

      1. mul-1-neg 70.1%

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

      2. unsub-neg 70.1%

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

   5. Simplified 70.1%

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

   6. Taylor expanded in z around 0 70.1%

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

   if 3.90000000000000022e-63 < z < 5e51

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.9%

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

      1. fma-define 100.0%

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

      2. +-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 79.0%

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

      1. mul-1-neg 79.0%

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

      2. unsub-neg 79.0%

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

   8. Simplified 79.0%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{+78}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-122}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-63}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y \leq -1 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-111}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+15}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))) (t_2 (* (- y z) t)))
   (if (<= y -1e+99)
     t_1
     (if (<= y -1.7e-111)
       t_2
       (if (<= y 4.8e-52) (* x (+ z 1.0)) (if (<= y 1.85e+15) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double t_2 = (y - z) * t;
	double tmp;
	if (y <= -1e+99) {
		tmp = t_1;
	} else if (y <= -1.7e-111) {
		tmp = t_2;
	} else if (y <= 4.8e-52) {
		tmp = x * (z + 1.0);
	} else if (y <= 1.85e+15) {
		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 * (t - x)
    t_2 = (y - z) * t
    if (y <= (-1d+99)) then
        tmp = t_1
    else if (y <= (-1.7d-111)) then
        tmp = t_2
    else if (y <= 4.8d-52) then
        tmp = x * (z + 1.0d0)
    else if (y <= 1.85d+15) 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 * (t - x);
	double t_2 = (y - z) * t;
	double tmp;
	if (y <= -1e+99) {
		tmp = t_1;
	} else if (y <= -1.7e-111) {
		tmp = t_2;
	} else if (y <= 4.8e-52) {
		tmp = x * (z + 1.0);
	} else if (y <= 1.85e+15) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	t_2 = (y - z) * t
	tmp = 0
	if y <= -1e+99:
		tmp = t_1
	elif y <= -1.7e-111:
		tmp = t_2
	elif y <= 4.8e-52:
		tmp = x * (z + 1.0)
	elif y <= 1.85e+15:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	t_2 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (y <= -1e+99)
		tmp = t_1;
	elseif (y <= -1.7e-111)
		tmp = t_2;
	elseif (y <= 4.8e-52)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 1.85e+15)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	t_2 = (y - z) * t;
	tmp = 0.0;
	if (y <= -1e+99)
		tmp = t_1;
	elseif (y <= -1.7e-111)
		tmp = t_2;
	elseif (y <= 4.8e-52)
		tmp = x * (z + 1.0);
	elseif (y <= 1.85e+15)
		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[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -1e+99], t$95$1, If[LessEqual[y, -1.7e-111], t$95$2, If[LessEqual[y, 4.8e-52], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+15], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.9999999999999997e98 or 1.85e15 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 94.0%

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

      1. fma-define 94.9%

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

      2. +-commutative 94.9%

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

      3. mul-1-neg 94.9%

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

   5. Simplified 94.9%

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

   6. Taylor expanded in y around inf 79.3%

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

      1. mul-1-neg 79.3%

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

      2. unsub-neg 79.3%

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

   8. Simplified 79.3%

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

   if -9.9999999999999997e98 < y < -1.69999999999999998e-111 or 4.8000000000000003e-52 < y < 1.85e15

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.3%

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

      1. fma-define 98.3%

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

      2. +-commutative 98.3%

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

      3. mul-1-neg 98.3%

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

   5. Simplified 98.3%

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

   6. Taylor expanded in t around inf 63.5%

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

   if -1.69999999999999998e-111 < y < 4.8000000000000003e-52

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 69.0%

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

      1. mul-1-neg 69.0%

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

      2. unsub-neg 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in y around 0 69.0%

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

      1. +-commutative 69.0%

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

   8. Simplified 69.0%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-111}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+15}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 37.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+78}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= y -1.5e+78)
     (* y t)
     (if (<= y -2.05e-159)
       t_1
       (if (<= y 3.6e-59) x (if (<= y 2.85e+17) t_1 (* y (- x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -1.5e+78) {
		tmp = y * t;
	} else if (y <= -2.05e-159) {
		tmp = t_1;
	} else if (y <= 3.6e-59) {
		tmp = x;
	} else if (y <= 2.85e+17) {
		tmp = t_1;
	} else {
		tmp = y * -x;
	}
	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 = z * -t
    if (y <= (-1.5d+78)) then
        tmp = y * t
    else if (y <= (-2.05d-159)) then
        tmp = t_1
    else if (y <= 3.6d-59) then
        tmp = x
    else if (y <= 2.85d+17) then
        tmp = t_1
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -1.5e+78) {
		tmp = y * t;
	} else if (y <= -2.05e-159) {
		tmp = t_1;
	} else if (y <= 3.6e-59) {
		tmp = x;
	} else if (y <= 2.85e+17) {
		tmp = t_1;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if y <= -1.5e+78:
		tmp = y * t
	elif y <= -2.05e-159:
		tmp = t_1
	elif y <= 3.6e-59:
		tmp = x
	elif y <= 2.85e+17:
		tmp = t_1
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -1.5e+78)
		tmp = Float64(y * t);
	elseif (y <= -2.05e-159)
		tmp = t_1;
	elseif (y <= 3.6e-59)
		tmp = x;
	elseif (y <= 2.85e+17)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (y <= -1.5e+78)
		tmp = y * t;
	elseif (y <= -2.05e-159)
		tmp = t_1;
	elseif (y <= 3.6e-59)
		tmp = x;
	elseif (y <= 2.85e+17)
		tmp = t_1;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -1.5e+78], N[(y * t), $MachinePrecision], If[LessEqual[y, -2.05e-159], t$95$1, If[LessEqual[y, 3.6e-59], x, If[LessEqual[y, 2.85e+17], t$95$1, N[(y * (-x)), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.49999999999999991e78

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 93.1%

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

      1. fma-define 93.2%

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

      2. +-commutative 93.2%

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

      3. mul-1-neg 93.2%

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

   5. Simplified 93.2%

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

   6. Taylor expanded in z around inf 71.3%

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

   7. Taylor expanded in y around inf 53.4%

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

   if -1.49999999999999991e78 < y < -2.05000000000000007e-159 or 3.6e-59 < y < 2.85e17

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. unsub-neg 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in t around inf 58.2%

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

      1. *-commutative 58.2%

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

   8. Simplified 58.2%

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

   9. Taylor expanded in x around 0 41.9%

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

       1. mul-1-neg 41.9%

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

       2. *-commutative 41.9%

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

       3. distribute-rgt-neg-in 41.9%

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

   11. Simplified 41.9%

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

   if -2.05000000000000007e-159 < y < 3.6e-59

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 52.0%

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

      1. *-commutative 52.0%

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

   5. Simplified 52.0%

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

   6. Taylor expanded in y around 0 45.6%

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

   if 2.85e17 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. unsub-neg 59.9%

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

   5. Simplified 59.9%

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

   6. Taylor expanded in y around inf 47.8%

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

      1. mul-1-neg 47.8%

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

      2. distribute-lft-neg-out 47.8%

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

      3. *-commutative 47.8%

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

   8. Simplified 47.8%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+78}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-159}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 38.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+77}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-158}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+40}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.8e+77)
   (* z x)
   (if (<= z 4.6e-158)
     (* y t)
     (if (<= z 5e-63) x (if (<= z 7.8e+40) (* y t) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+77) {
		tmp = z * x;
	} else if (z <= 4.6e-158) {
		tmp = y * t;
	} else if (z <= 5e-63) {
		tmp = x;
	} else if (z <= 7.8e+40) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	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 <= (-2.8d+77)) then
        tmp = z * x
    else if (z <= 4.6d-158) then
        tmp = y * t
    else if (z <= 5d-63) then
        tmp = x
    else if (z <= 7.8d+40) then
        tmp = y * t
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+77) {
		tmp = z * x;
	} else if (z <= 4.6e-158) {
		tmp = y * t;
	} else if (z <= 5e-63) {
		tmp = x;
	} else if (z <= 7.8e+40) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.8e+77:
		tmp = z * x
	elif z <= 4.6e-158:
		tmp = y * t
	elif z <= 5e-63:
		tmp = x
	elif z <= 7.8e+40:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.8e+77)
		tmp = Float64(z * x);
	elseif (z <= 4.6e-158)
		tmp = Float64(y * t);
	elseif (z <= 5e-63)
		tmp = x;
	elseif (z <= 7.8e+40)
		tmp = Float64(y * t);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.8e+77)
		tmp = z * x;
	elseif (z <= 4.6e-158)
		tmp = y * t;
	elseif (z <= 5e-63)
		tmp = x;
	elseif (z <= 7.8e+40)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.8e+77], N[(z * x), $MachinePrecision], If[LessEqual[z, 4.6e-158], N[(y * t), $MachinePrecision], If[LessEqual[z, 5e-63], x, If[LessEqual[z, 7.8e+40], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8e77 or 7.8000000000000002e40 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 56.0%

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

      1. mul-1-neg 56.0%

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

      2. unsub-neg 56.0%

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

   5. Simplified 56.0%

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

   6. Taylor expanded in z around inf 45.6%

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

      1. *-commutative 45.6%

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

   8. Simplified 45.6%

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

   if -2.8e77 < z < 4.5999999999999998e-158 or 5.0000000000000002e-63 < z < 7.8000000000000002e40

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 97.8%

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

      1. fma-define 98.6%

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

      2. +-commutative 98.6%

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

      3. mul-1-neg 98.6%

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

   5. Simplified 98.6%

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

   6. Taylor expanded in z around inf 53.6%

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

   7. Taylor expanded in y around inf 39.0%

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

   if 4.5999999999999998e-158 < z < 5.0000000000000002e-63

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 94.7%

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

      1. *-commutative 94.7%

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

   5. Simplified 94.7%

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

   6. Taylor expanded in y around 0 66.3%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+77}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-158}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+40}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -1.3:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-59}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -1.3)
     t_1
     (if (<= z 1.2e-59) (+ x (* y t)) (if (<= z 6.5e+52) (* y (- t x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -1.3) {
		tmp = t_1;
	} else if (z <= 1.2e-59) {
		tmp = x + (y * t);
	} else if (z <= 6.5e+52) {
		tmp = y * (t - x);
	} 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 = z * (x - t)
    if (z <= (-1.3d0)) then
        tmp = t_1
    else if (z <= 1.2d-59) then
        tmp = x + (y * t)
    else if (z <= 6.5d+52) then
        tmp = y * (t - x)
    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 = z * (x - t);
	double tmp;
	if (z <= -1.3) {
		tmp = t_1;
	} else if (z <= 1.2e-59) {
		tmp = x + (y * t);
	} else if (z <= 6.5e+52) {
		tmp = y * (t - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -1.3:
		tmp = t_1
	elif z <= 1.2e-59:
		tmp = x + (y * t)
	elif z <= 6.5e+52:
		tmp = y * (t - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -1.3)
		tmp = t_1;
	elseif (z <= 1.2e-59)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 6.5e+52)
		tmp = Float64(y * Float64(t - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -1.3)
		tmp = t_1;
	elseif (z <= 1.2e-59)
		tmp = x + (y * t);
	elseif (z <= 6.5e+52)
		tmp = y * (t - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3], t$95$1, If[LessEqual[z, 1.2e-59], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+52], N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.30000000000000004 or 6.49999999999999996e52 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 94.8%

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

      1. fma-define 94.9%

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

      2. +-commutative 94.9%

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

      3. mul-1-neg 94.9%

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

   5. Simplified 94.9%

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

   6. Taylor expanded in z around inf 83.4%

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

      1. neg-mul-1 83.4%

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

      2. unsub-neg 83.4%

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

   8. Simplified 83.4%

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

   if -1.30000000000000004 < z < 1.20000000000000008e-59

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 77.9%

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

   4. Taylor expanded in y around inf 72.7%

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

   if 1.20000000000000008e-59 < z < 6.49999999999999996e52

   1. Initial program 99.9%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.9%

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

      1. fma-define 100.0%

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

      2. +-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 79.0%

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

      1. mul-1-neg 79.0%

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

      2. unsub-neg 79.0%

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

   8. Simplified 79.0%

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

Alternative 7: 55.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y - z \leq -2 \cdot 10^{-11} \lor \neg \left(y - z \leq 2 \cdot 10^{-51}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (- y z) -2e-11) (not (<= (- y z) 2e-51))) (* (- y z) t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((y - z) <= -2e-11) || !((y - z) <= 2e-51)) {
		tmp = (y - z) * t;
	} else {
		tmp = x;
	}
	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 - z) <= (-2d-11)) .or. (.not. ((y - z) <= 2d-51))) then
        tmp = (y - z) * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((y - z) <= -2e-11) || !((y - z) <= 2e-51)) {
		tmp = (y - z) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((y - z) <= -2e-11) or not ((y - z) <= 2e-51):
		tmp = (y - z) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(y - z) <= -2e-11) || !(Float64(y - z) <= 2e-51))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((y - z) <= -2e-11) || ~(((y - z) <= 2e-51)))
		tmp = (y - z) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(y - z), $MachinePrecision], -2e-11], N[Not[LessEqual[N[(y - z), $MachinePrecision], 2e-51]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (-.f64 y z) < -1.99999999999999988e-11 or 2e-51 < (-.f64 y z)

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 96.0%

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

      1. fma-define 96.5%

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

      2. +-commutative 96.5%

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

      3. mul-1-neg 96.5%

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

   5. Simplified 96.5%

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

   6. Taylor expanded in t around inf 53.1%

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

   if -1.99999999999999988e-11 < (-.f64 y z) < 2e-51

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 91.4%

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

      1. *-commutative 91.4%

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

   5. Simplified 91.4%

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

   6. Taylor expanded in y around 0 72.1%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y - z \leq -2 \cdot 10^{-11} \lor \neg \left(y - z \leq 2 \cdot 10^{-51}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 35.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+64}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+26}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.15e+64)
   (* y t)
   (if (<= y 9e-51) x (if (<= y 6.2e+26) (* y t) (* y (- x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e+64) {
		tmp = y * t;
	} else if (y <= 9e-51) {
		tmp = x;
	} else if (y <= 6.2e+26) {
		tmp = y * t;
	} else {
		tmp = y * -x;
	}
	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 <= (-1.15d+64)) then
        tmp = y * t
    else if (y <= 9d-51) then
        tmp = x
    else if (y <= 6.2d+26) then
        tmp = y * t
    else
        tmp = y * -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e+64) {
		tmp = y * t;
	} else if (y <= 9e-51) {
		tmp = x;
	} else if (y <= 6.2e+26) {
		tmp = y * t;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.15e+64:
		tmp = y * t
	elif y <= 9e-51:
		tmp = x
	elif y <= 6.2e+26:
		tmp = y * t
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.15e+64)
		tmp = Float64(y * t);
	elseif (y <= 9e-51)
		tmp = x;
	elseif (y <= 6.2e+26)
		tmp = Float64(y * t);
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.15e+64)
		tmp = y * t;
	elseif (y <= 9e-51)
		tmp = x;
	elseif (y <= 6.2e+26)
		tmp = y * t;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.15e+64], N[(y * t), $MachinePrecision], If[LessEqual[y, 9e-51], x, If[LessEqual[y, 6.2e+26], N[(y * t), $MachinePrecision], N[(y * (-x)), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15e64 or 8.99999999999999948e-51 < y < 6.1999999999999999e26

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 95.1%

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

      1. fma-define 95.2%

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

      2. +-commutative 95.2%

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

      3. mul-1-neg 95.2%

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

   5. Simplified 95.2%

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

   6. Taylor expanded in z around inf 77.1%

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

   7. Taylor expanded in y around inf 48.4%

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

   if -1.15e64 < y < 8.99999999999999948e-51

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 48.9%

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

      1. *-commutative 48.9%

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

   5. Simplified 48.9%

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

   6. Taylor expanded in y around 0 38.3%

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

   if 6.1999999999999999e26 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 60.1%

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

      1. mul-1-neg 60.1%

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

      2. unsub-neg 60.1%

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

   5. Simplified 60.1%

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

   6. Taylor expanded in y around inf 48.9%

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

      1. mul-1-neg 48.9%

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

      2. distribute-lft-neg-out 48.9%

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

      3. *-commutative 48.9%

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

   8. Simplified 48.9%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+64}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+26}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -940 \lor \neg \left(z \leq 1.1 \cdot 10^{+47}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -940.0) (not (<= z 1.1e+47)))
   (* z (- x t))
   (+ x (* y (- t x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -940.0) || !(z <= 1.1e+47)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	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 <= (-940.0d0)) .or. (.not. (z <= 1.1d+47))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * (t - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -940.0) || !(z <= 1.1e+47)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * (t - x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -940.0) or not (z <= 1.1e+47):
		tmp = z * (x - t)
	else:
		tmp = x + (y * (t - x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -940.0) || !(z <= 1.1e+47))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * Float64(t - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -940.0) || ~((z <= 1.1e+47)))
		tmp = z * (x - t);
	else
		tmp = x + (y * (t - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -940.0], N[Not[LessEqual[z, 1.1e+47]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -940 or 1.1e47 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 94.8%

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

      1. fma-define 94.9%

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

      2. +-commutative 94.9%

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

      3. mul-1-neg 94.9%

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

   5. Simplified 94.9%

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

   6. Taylor expanded in z around inf 83.4%

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

      1. neg-mul-1 83.4%

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

      2. unsub-neg 83.4%

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

   8. Simplified 83.4%

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

   if -940 < z < 1.1e47

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 92.5%

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

      1. *-commutative 92.5%

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

   5. Simplified 92.5%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -940 \lor \neg \left(z \leq 1.1 \cdot 10^{+47}\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-18} \lor \neg \left(x \leq 1.7 \cdot 10^{+22}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.15e-18) (not (<= x 1.7e+22)))
   (* x (+ (- z y) 1.0))
   (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.15e-18) || !(x <= 1.7e+22)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.15d-18)) .or. (.not. (x <= 1.7d+22))) then
        tmp = x * ((z - y) + 1.0d0)
    else
        tmp = (y - z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.15e-18) || !(x <= 1.7e+22)) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.15e-18) or not (x <= 1.7e+22):
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.15e-18) || !(x <= 1.7e+22))
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.15e-18) || ~((x <= 1.7e+22)))
		tmp = x * ((z - y) + 1.0);
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.15e-18], N[Not[LessEqual[x, 1.7e+22]], $MachinePrecision]], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15e-18 or 1.7e22 < x

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 86.0%

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

      1. mul-1-neg 86.0%

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

      2. unsub-neg 86.0%

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

   5. Simplified 86.0%

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

   if -1.15e-18 < x < 1.7e22

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 100.0%

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

      1. fma-define 100.0%

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

      2. +-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 76.0%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-18} \lor \neg \left(x \leq 1.7 \cdot 10^{+22}\right):\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -22.5:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+48}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -22.5) t_1 (if (<= z 1.38e+48) (+ x (* y (- t x))) (+ x t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -22.5) {
		tmp = t_1;
	} else if (z <= 1.38e+48) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + 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 = z * (x - t)
    if (z <= (-22.5d0)) then
        tmp = t_1
    else if (z <= 1.38d+48) then
        tmp = x + (y * (t - x))
    else
        tmp = x + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double tmp;
	if (z <= -22.5) {
		tmp = t_1;
	} else if (z <= 1.38e+48) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	tmp = 0
	if z <= -22.5:
		tmp = t_1
	elif z <= 1.38e+48:
		tmp = x + (y * (t - x))
	else:
		tmp = x + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -22.5)
		tmp = t_1;
	elseif (z <= 1.38e+48)
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	tmp = 0.0;
	if (z <= -22.5)
		tmp = t_1;
	elseif (z <= 1.38e+48)
		tmp = x + (y * (t - x));
	else
		tmp = x + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -22.5], t$95$1, If[LessEqual[z, 1.38e+48], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -22.5

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 93.5%

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

      1. fma-define 93.5%

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

      2. +-commutative 93.5%

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

      3. mul-1-neg 93.5%

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

   5. Simplified 93.5%

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

   6. Taylor expanded in z around inf 79.6%

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

      1. neg-mul-1 79.6%

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

      2. unsub-neg 79.6%

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

   8. Simplified 79.6%

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

   if -22.5 < z < 1.3800000000000001e48

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 92.5%

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

      1. *-commutative 92.5%

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

   5. Simplified 92.5%

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

   if 1.3800000000000001e48 < z

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 87.7%

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

      1. mul-1-neg 87.7%

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

      2. unsub-neg 87.7%

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

   5. Simplified 87.7%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -22.5:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+48}:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.15 \cdot 10^{-18} \lor \neg \left(x \leq 1.2 \cdot 10^{+22}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -3.15e-18) (not (<= x 1.2e+22))) (* x (- 1.0 y)) (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.15e-18) || !(x <= 1.2e+22)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-3.15d-18)) .or. (.not. (x <= 1.2d+22))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = (y - z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -3.15e-18) || !(x <= 1.2e+22)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -3.15e-18) or not (x <= 1.2e+22):
		tmp = x * (1.0 - y)
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -3.15e-18) || !(x <= 1.2e+22))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -3.15e-18) || ~((x <= 1.2e+22)))
		tmp = x * (1.0 - y);
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -3.15e-18], N[Not[LessEqual[x, 1.2e+22]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.1500000000000002e-18 or 1.2e22 < x

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 86.0%

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

      1. mul-1-neg 86.0%

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

      2. unsub-neg 86.0%

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

   5. Simplified 86.0%

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

   6. Taylor expanded in z around 0 60.0%

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

   if -3.1500000000000002e-18 < x < 1.2e22

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 100.0%

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

      1. fma-define 100.0%

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

      2. +-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 76.0%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.15 \cdot 10^{-18} \lor \neg \left(x \leq 1.2 \cdot 10^{+22}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.98 \lor \neg \left(x \leq 4.2 \cdot 10^{+21}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.98) (not (<= x 4.2e+21))) (* x (+ z 1.0)) (* (- y z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.98) || !(x <= 4.2e+21)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-1.98d0)) .or. (.not. (x <= 4.2d+21))) then
        tmp = x * (z + 1.0d0)
    else
        tmp = (y - z) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.98) || !(x <= 4.2e+21)) {
		tmp = x * (z + 1.0);
	} else {
		tmp = (y - z) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.98) or not (x <= 4.2e+21):
		tmp = x * (z + 1.0)
	else:
		tmp = (y - z) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.98) || !(x <= 4.2e+21))
		tmp = Float64(x * Float64(z + 1.0));
	else
		tmp = Float64(Float64(y - z) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -1.98) || ~((x <= 4.2e+21)))
		tmp = x * (z + 1.0);
	else
		tmp = (y - z) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.98], N[Not[LessEqual[x, 4.2e+21]], $MachinePrecision]], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.98 or 4.2e21 < x

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 86.5%

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

      1. mul-1-neg 86.5%

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

      2. unsub-neg 86.5%

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

   5. Simplified 86.5%

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

   6. Taylor expanded in y around 0 55.5%

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

      1. +-commutative 55.5%

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

   8. Simplified 55.5%

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

   if -1.98 < x < 4.2e21

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 100.0%

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

      1. fma-define 100.0%

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

      2. +-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in t around inf 75.1%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.98 \lor \neg \left(x \leq 4.2 \cdot 10^{+21}\right):\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 35.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+64} \lor \neg \left(y \leq 10^{-50}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.15e+64) (not (<= y 1e-50))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.15e+64) || !(y <= 1e-50)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	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 <= (-1.15d+64)) .or. (.not. (y <= 1d-50))) then
        tmp = y * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.15e+64) || !(y <= 1e-50)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.15e+64) or not (y <= 1e-50):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.15e+64) || !(y <= 1e-50))
		tmp = Float64(y * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.15e+64) || ~((y <= 1e-50)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.15e+64], N[Not[LessEqual[y, 1e-50]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e64 or 1.00000000000000001e-50 < y

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 94.9%

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

      1. fma-define 95.7%

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

      2. +-commutative 95.7%

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

      3. mul-1-neg 95.7%

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

   5. Simplified 95.7%

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

   6. Taylor expanded in z around inf 67.1%

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

   7. Taylor expanded in y around inf 41.6%

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

   if -1.15e64 < y < 1.00000000000000001e-50

   1. Initial program 100.0%

      \[x + \left(y - z\right) \cdot \left(t - x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 48.9%

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

      1. *-commutative 48.9%

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

   5. Simplified 48.9%

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

   6. Taylor expanded in y around 0 38.3%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+64} \lor \neg \left(y \leq 10^{-50}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 16: 17.5% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \left(y - z\right) \cdot \left(t - x\right) \]
2. Add Preprocessing

3. Taylor expanded in y around inf 62.9%

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

   1. *-commutative 62.9%

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

5. Simplified 62.9%

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

6. Taylor expanded in y around 0 18.8%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Developer Target 1: 96.1% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

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 + ((t * (y - z)) + (-x * (y - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024144 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (+ (* t (- y z)) (* (- x) (- y z)))))

  (+ x (* (- y z) (- t x))))