Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 7.7s

Alternatives: 14

Speedup: 1.0×

• 32.9% 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-def 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. Final simplification 100.0%

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

Alternative 2: 68.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot x\\ t_2 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -2 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-166}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-238}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 6.1:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (* y x))) (t_2 (* z (- x t))))
   (if (<= z -2e+77)
     t_2
     (if (<= z -4.8e-166)
       (* (- y z) t)
       (if (<= z -1.05e-194)
         t_1
         (if (<= z 6.5e-238) (+ x (* y t)) (if (<= z 6.1) t_1 t_2)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y * x);
	double t_2 = z * (x - t);
	double tmp;
	if (z <= -2e+77) {
		tmp = t_2;
	} else if (z <= -4.8e-166) {
		tmp = (y - z) * t;
	} else if (z <= -1.05e-194) {
		tmp = t_1;
	} else if (z <= 6.5e-238) {
		tmp = x + (y * t);
	} else if (z <= 6.1) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (y * x)
    t_2 = z * (x - t)
    if (z <= (-2d+77)) then
        tmp = t_2
    else if (z <= (-4.8d-166)) then
        tmp = (y - z) * t
    else if (z <= (-1.05d-194)) then
        tmp = t_1
    else if (z <= 6.5d-238) then
        tmp = x + (y * t)
    else if (z <= 6.1d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (y * x);
	double t_2 = z * (x - t);
	double tmp;
	if (z <= -2e+77) {
		tmp = t_2;
	} else if (z <= -4.8e-166) {
		tmp = (y - z) * t;
	} else if (z <= -1.05e-194) {
		tmp = t_1;
	} else if (z <= 6.5e-238) {
		tmp = x + (y * t);
	} else if (z <= 6.1) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y * x)
	t_2 = z * (x - t)
	tmp = 0
	if z <= -2e+77:
		tmp = t_2
	elif z <= -4.8e-166:
		tmp = (y - z) * t
	elif z <= -1.05e-194:
		tmp = t_1
	elif z <= 6.5e-238:
		tmp = x + (y * t)
	elif z <= 6.1:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y * x))
	t_2 = Float64(z * Float64(x - t))
	tmp = 0.0
	if (z <= -2e+77)
		tmp = t_2;
	elseif (z <= -4.8e-166)
		tmp = Float64(Float64(y - z) * t);
	elseif (z <= -1.05e-194)
		tmp = t_1;
	elseif (z <= 6.5e-238)
		tmp = Float64(x + Float64(y * t));
	elseif (z <= 6.1)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y * x);
	t_2 = z * (x - t);
	tmp = 0.0;
	if (z <= -2e+77)
		tmp = t_2;
	elseif (z <= -4.8e-166)
		tmp = (y - z) * t;
	elseif (z <= -1.05e-194)
		tmp = t_1;
	elseif (z <= 6.5e-238)
		tmp = x + (y * t);
	elseif (z <= 6.1)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e+77], t$95$2, If[LessEqual[z, -4.8e-166], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, -1.05e-194], t$95$1, If[LessEqual[z, 6.5e-238], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.1], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.99999999999999997e77 or 6.0999999999999996 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 84.4%

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

      1. +-commutative 84.4%

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

      2. mul-1-neg 84.4%

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

      3. unsub-neg 84.4%

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

      4. *-commutative 84.4%

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

   4. Simplified 84.4%

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

   5. Taylor expanded in z around inf 84.4%

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

   if -1.99999999999999997e77 < z < -4.7999999999999997e-166

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 81.8%

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

   3. Taylor expanded in x around 0 81.8%

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

      1. *-commutative 81.8%

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

      2. fma-def 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in t around inf 72.7%

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

   if -4.7999999999999997e-166 < z < -1.05e-194 or 6.5000000000000006e-238 < z < 6.0999999999999996

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 71.7%

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

      1. *-commutative 71.7%

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

      2. mul-1-neg 71.7%

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

      3. unsub-neg 71.7%

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

      4. distribute-lft-out-- 71.7%

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

      5. *-rgt-identity 71.7%

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

   4. Simplified 71.7%

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

   5. Taylor expanded in y around inf 69.4%

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

   if -1.05e-194 < z < 6.5000000000000006e-238

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 91.8%

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

   3. Taylor expanded in z around 0 91.8%

      \[\leadsto \color{blue}{y \cdot t + x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+77}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-166}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-194}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-238}:\\ \;\;\;\;x + y \cdot t\\ \mathbf{elif}\;z \leq 6.1:\\ \;\;\;\;x - y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 3: 75.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := x + \left(y - z\right) \cdot t\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-225}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-169}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (+ x (* (- y z) t))))
   (if (<= z -8.5e+75)
     t_1
     (if (<= z 9.5e-225)
       t_2
       (if (<= z 3e-169) (- x (* y x)) (if (<= z 5.6e+48) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = x + ((y - z) * t);
	double tmp;
	if (z <= -8.5e+75) {
		tmp = t_1;
	} else if (z <= 9.5e-225) {
		tmp = t_2;
	} else if (z <= 3e-169) {
		tmp = x - (y * x);
	} else if (z <= 5.6e+48) {
		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 = z * (x - t)
    t_2 = x + ((y - z) * t)
    if (z <= (-8.5d+75)) then
        tmp = t_1
    else if (z <= 9.5d-225) then
        tmp = t_2
    else if (z <= 3d-169) then
        tmp = x - (y * x)
    else if (z <= 5.6d+48) 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 = z * (x - t);
	double t_2 = x + ((y - z) * t);
	double tmp;
	if (z <= -8.5e+75) {
		tmp = t_1;
	} else if (z <= 9.5e-225) {
		tmp = t_2;
	} else if (z <= 3e-169) {
		tmp = x - (y * x);
	} else if (z <= 5.6e+48) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = x + ((y - z) * t)
	tmp = 0
	if z <= -8.5e+75:
		tmp = t_1
	elif z <= 9.5e-225:
		tmp = t_2
	elif z <= 3e-169:
		tmp = x - (y * x)
	elif z <= 5.6e+48:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(x + Float64(Float64(y - z) * t))
	tmp = 0.0
	if (z <= -8.5e+75)
		tmp = t_1;
	elseif (z <= 9.5e-225)
		tmp = t_2;
	elseif (z <= 3e-169)
		tmp = Float64(x - Float64(y * x));
	elseif (z <= 5.6e+48)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = x + ((y - z) * t);
	tmp = 0.0;
	if (z <= -8.5e+75)
		tmp = t_1;
	elseif (z <= 9.5e-225)
		tmp = t_2;
	elseif (z <= 3e-169)
		tmp = x - (y * x);
	elseif (z <= 5.6e+48)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+75], t$95$1, If[LessEqual[z, 9.5e-225], t$95$2, If[LessEqual[z, 3e-169], N[(x - N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e+48], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.4999999999999993e75 or 5.60000000000000025e48 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 86.7%

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

      1. +-commutative 86.7%

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

      2. mul-1-neg 86.7%

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

      3. unsub-neg 86.7%

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

      4. *-commutative 86.7%

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

   4. Simplified 86.7%

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

   5. Taylor expanded in z around inf 86.7%

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

   if -8.4999999999999993e75 < z < 9.50000000000000006e-225 or 2.9999999999999999e-169 < z < 5.60000000000000025e48

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 77.5%

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

   if 9.50000000000000006e-225 < z < 2.9999999999999999e-169

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-lft-out-- 100.0%

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

      5. *-rgt-identity 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+75}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-225}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-169}:\\ \;\;\;\;x - y \cdot x\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+48}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 4: 38.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-x\right)\\ t_2 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-188}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-133}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+239}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- x))) (t_2 (* z (- t))))
   (if (<= y -1.05e+37)
     t_1
     (if (<= y 1.22e-188)
       t_2
       (if (<= y 1.3e-133)
         (* z x)
         (if (<= y 1.6e+74) t_2 (if (<= y 2.3e+239) (* y t) t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * -x;
	double t_2 = z * -t;
	double tmp;
	if (y <= -1.05e+37) {
		tmp = t_1;
	} else if (y <= 1.22e-188) {
		tmp = t_2;
	} else if (y <= 1.3e-133) {
		tmp = z * x;
	} else if (y <= 1.6e+74) {
		tmp = t_2;
	} else if (y <= 2.3e+239) {
		tmp = y * 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) :: t_2
    real(8) :: tmp
    t_1 = y * -x
    t_2 = z * -t
    if (y <= (-1.05d+37)) then
        tmp = t_1
    else if (y <= 1.22d-188) then
        tmp = t_2
    else if (y <= 1.3d-133) then
        tmp = z * x
    else if (y <= 1.6d+74) then
        tmp = t_2
    else if (y <= 2.3d+239) then
        tmp = y * 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;
	double t_2 = z * -t;
	double tmp;
	if (y <= -1.05e+37) {
		tmp = t_1;
	} else if (y <= 1.22e-188) {
		tmp = t_2;
	} else if (y <= 1.3e-133) {
		tmp = z * x;
	} else if (y <= 1.6e+74) {
		tmp = t_2;
	} else if (y <= 2.3e+239) {
		tmp = y * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * -x
	t_2 = z * -t
	tmp = 0
	if y <= -1.05e+37:
		tmp = t_1
	elif y <= 1.22e-188:
		tmp = t_2
	elif y <= 1.3e-133:
		tmp = z * x
	elif y <= 1.6e+74:
		tmp = t_2
	elif y <= 2.3e+239:
		tmp = y * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-x))
	t_2 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -1.05e+37)
		tmp = t_1;
	elseif (y <= 1.22e-188)
		tmp = t_2;
	elseif (y <= 1.3e-133)
		tmp = Float64(z * x);
	elseif (y <= 1.6e+74)
		tmp = t_2;
	elseif (y <= 2.3e+239)
		tmp = Float64(y * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * -x;
	t_2 = z * -t;
	tmp = 0.0;
	if (y <= -1.05e+37)
		tmp = t_1;
	elseif (y <= 1.22e-188)
		tmp = t_2;
	elseif (y <= 1.3e-133)
		tmp = z * x;
	elseif (y <= 1.6e+74)
		tmp = t_2;
	elseif (y <= 2.3e+239)
		tmp = y * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * (-x)), $MachinePrecision]}, Block[{t$95$2 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -1.05e+37], t$95$1, If[LessEqual[y, 1.22e-188], t$95$2, If[LessEqual[y, 1.3e-133], N[(z * x), $MachinePrecision], If[LessEqual[y, 1.6e+74], t$95$2, If[LessEqual[y, 2.3e+239], N[(y * t), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.0500000000000001e37 or 2.3000000000000002e239 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 66.0%

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

      1. *-commutative 66.0%

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

      2. mul-1-neg 66.0%

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

      3. unsub-neg 66.0%

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

      4. distribute-lft-out-- 66.0%

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

      5. *-rgt-identity 66.0%

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

   4. Simplified 66.0%

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

   5. Taylor expanded in y around inf 54.1%

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

      1. associate-*r* 54.1%

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

      2. neg-mul-1 54.1%

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

   7. Simplified 54.1%

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

   if -1.0500000000000001e37 < y < 1.22e-188 or 1.3e-133 < y < 1.59999999999999997e74

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 75.3%

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

   3. Taylor expanded in x around 0 75.3%

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

      1. *-commutative 75.3%

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

      2. fma-def 75.3%

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

   5. Simplified 75.3%

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

   6. Taylor expanded in z around inf 47.9%

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

      1. mul-1-neg 47.9%

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

      2. distribute-rgt-neg-out 47.9%

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

   8. Simplified 47.9%

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

   if 1.22e-188 < y < 1.3e-133

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 78.0%

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

      1. *-commutative 78.0%

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

      2. mul-1-neg 78.0%

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

      3. unsub-neg 78.0%

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

      4. distribute-lft-out-- 78.0%

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

      5. *-rgt-identity 78.0%

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

   4. Simplified 78.0%

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

   5. Taylor expanded in z around inf 52.6%

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

   if 1.59999999999999997e74 < y < 2.3000000000000002e239

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 68.3%

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

   3. Taylor expanded in x around 0 68.3%

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

      1. *-commutative 68.3%

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

      2. fma-def 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in y around inf 60.4%

      \[\leadsto \color{blue}{y \cdot t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-188}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-133}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+239}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 5: 60.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ t_2 := \left(y - z\right) \cdot t\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-221}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-155}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))) (t_2 (* (- y z) t)))
   (if (<= z -3.8e+75)
     t_1
     (if (<= z 8e-221)
       t_2
       (if (<= z 1.45e-155) x (if (<= z 4.5e+51) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (x - t);
	double t_2 = (y - z) * t;
	double tmp;
	if (z <= -3.8e+75) {
		tmp = t_1;
	} else if (z <= 8e-221) {
		tmp = t_2;
	} else if (z <= 1.45e-155) {
		tmp = x;
	} else if (z <= 4.5e+51) {
		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 = z * (x - t)
    t_2 = (y - z) * t
    if (z <= (-3.8d+75)) then
        tmp = t_1
    else if (z <= 8d-221) then
        tmp = t_2
    else if (z <= 1.45d-155) then
        tmp = x
    else if (z <= 4.5d+51) 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 = z * (x - t);
	double t_2 = (y - z) * t;
	double tmp;
	if (z <= -3.8e+75) {
		tmp = t_1;
	} else if (z <= 8e-221) {
		tmp = t_2;
	} else if (z <= 1.45e-155) {
		tmp = x;
	} else if (z <= 4.5e+51) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (x - t)
	t_2 = (y - z) * t
	tmp = 0
	if z <= -3.8e+75:
		tmp = t_1
	elif z <= 8e-221:
		tmp = t_2
	elif z <= 1.45e-155:
		tmp = x
	elif z <= 4.5e+51:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(x - t))
	t_2 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (z <= -3.8e+75)
		tmp = t_1;
	elseif (z <= 8e-221)
		tmp = t_2;
	elseif (z <= 1.45e-155)
		tmp = x;
	elseif (z <= 4.5e+51)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (x - t);
	t_2 = (y - z) * t;
	tmp = 0.0;
	if (z <= -3.8e+75)
		tmp = t_1;
	elseif (z <= 8e-221)
		tmp = t_2;
	elseif (z <= 1.45e-155)
		tmp = x;
	elseif (z <= 4.5e+51)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[z, -3.8e+75], t$95$1, If[LessEqual[z, 8e-221], t$95$2, If[LessEqual[z, 1.45e-155], x, If[LessEqual[z, 4.5e+51], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8000000000000002e75 or 4.5e51 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 86.7%

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

      1. +-commutative 86.7%

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

      2. mul-1-neg 86.7%

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

      3. unsub-neg 86.7%

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

      4. *-commutative 86.7%

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

   4. Simplified 86.7%

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

   5. Taylor expanded in z around inf 86.7%

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

   if -3.8000000000000002e75 < z < 8.00000000000000014e-221 or 1.45000000000000005e-155 < z < 4.5e51

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 77.1%

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

   3. Taylor expanded in x around 0 77.1%

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

      1. *-commutative 77.1%

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

      2. fma-def 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in t around inf 60.2%

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

   if 8.00000000000000014e-221 < z < 1.45000000000000005e-155

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 62.7%

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

   3. Taylor expanded in x around inf 54.7%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+75}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-221}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-155}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+51}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 6: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x - t\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-86}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 6.5:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- x t))))
   (if (<= z -3e+76)
     t_1
     (if (<= z -8e-86)
       (+ x (* (- y z) t))
       (if (<= z 6.5) (+ x (* 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 <= -3e+76) {
		tmp = t_1;
	} else if (z <= -8e-86) {
		tmp = x + ((y - z) * t);
	} else if (z <= 6.5) {
		tmp = x + (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 <= (-3d+76)) then
        tmp = t_1
    else if (z <= (-8d-86)) then
        tmp = x + ((y - z) * t)
    else if (z <= 6.5d0) then
        tmp = x + (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 <= -3e+76) {
		tmp = t_1;
	} else if (z <= -8e-86) {
		tmp = x + ((y - z) * t);
	} else if (z <= 6.5) {
		tmp = x + (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 <= -3e+76:
		tmp = t_1
	elif z <= -8e-86:
		tmp = x + ((y - z) * t)
	elif z <= 6.5:
		tmp = x + (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 <= -3e+76)
		tmp = t_1;
	elseif (z <= -8e-86)
		tmp = Float64(x + Float64(Float64(y - z) * t));
	elseif (z <= 6.5)
		tmp = Float64(x + 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 <= -3e+76)
		tmp = t_1;
	elseif (z <= -8e-86)
		tmp = x + ((y - z) * t);
	elseif (z <= 6.5)
		tmp = x + (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, -3e+76], t$95$1, If[LessEqual[z, -8e-86], N[(x + N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9999999999999998e76 or 6.5 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 84.4%

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

      1. +-commutative 84.4%

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

      2. mul-1-neg 84.4%

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

      3. unsub-neg 84.4%

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

      4. *-commutative 84.4%

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

   4. Simplified 84.4%

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

   5. Taylor expanded in z around inf 84.4%

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

   if -2.9999999999999998e76 < z < -8.00000000000000068e-86

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 81.6%

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

   if -8.00000000000000068e-86 < z < 6.5

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 90.1%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+76}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-86}:\\ \;\;\;\;x + \left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 6.5:\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 7: 38.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{-23}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-134}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= y -9.5e-23)
     (* y t)
     (if (<= y 1.3e-188)
       t_1
       (if (<= y 9e-134) (* z x) (if (<= y 6.8e+74) t_1 (* y t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -9.5e-23) {
		tmp = y * t;
	} else if (y <= 1.3e-188) {
		tmp = t_1;
	} else if (y <= 9e-134) {
		tmp = z * x;
	} else if (y <= 6.8e+74) {
		tmp = t_1;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * -t
    if (y <= (-9.5d-23)) then
        tmp = y * t
    else if (y <= 1.3d-188) then
        tmp = t_1
    else if (y <= 9d-134) then
        tmp = z * x
    else if (y <= 6.8d+74) then
        tmp = t_1
    else
        tmp = y * t
    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 <= -9.5e-23) {
		tmp = y * t;
	} else if (y <= 1.3e-188) {
		tmp = t_1;
	} else if (y <= 9e-134) {
		tmp = z * x;
	} else if (y <= 6.8e+74) {
		tmp = t_1;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if y <= -9.5e-23:
		tmp = y * t
	elif y <= 1.3e-188:
		tmp = t_1
	elif y <= 9e-134:
		tmp = z * x
	elif y <= 6.8e+74:
		tmp = t_1
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -9.5e-23)
		tmp = Float64(y * t);
	elseif (y <= 1.3e-188)
		tmp = t_1;
	elseif (y <= 9e-134)
		tmp = Float64(z * x);
	elseif (y <= 6.8e+74)
		tmp = t_1;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * -t;
	tmp = 0.0;
	if (y <= -9.5e-23)
		tmp = y * t;
	elseif (y <= 1.3e-188)
		tmp = t_1;
	elseif (y <= 9e-134)
		tmp = z * x;
	elseif (y <= 6.8e+74)
		tmp = t_1;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * (-t)), $MachinePrecision]}, If[LessEqual[y, -9.5e-23], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.3e-188], t$95$1, If[LessEqual[y, 9e-134], N[(z * x), $MachinePrecision], If[LessEqual[y, 6.8e+74], t$95$1, N[(y * t), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.50000000000000058e-23 or 6.7999999999999998e74 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 55.6%

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

   3. Taylor expanded in x around 0 55.6%

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

      1. *-commutative 55.6%

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

      2. fma-def 55.6%

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

   5. Simplified 55.6%

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

   6. Taylor expanded in y around inf 45.2%

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

   if -9.50000000000000058e-23 < y < 1.3e-188 or 9.000000000000001e-134 < y < 6.7999999999999998e74

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 76.0%

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

   3. Taylor expanded in x around 0 76.0%

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

      1. *-commutative 76.0%

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

      2. fma-def 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in z around inf 50.6%

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

      1. mul-1-neg 50.6%

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

      2. distribute-rgt-neg-out 50.6%

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

   8. Simplified 50.6%

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

   if 1.3e-188 < y < 9.000000000000001e-134

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 78.0%

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

      1. *-commutative 78.0%

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

      2. mul-1-neg 78.0%

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

      3. unsub-neg 78.0%

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

      4. distribute-lft-out-- 78.0%

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

      5. *-rgt-identity 78.0%

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

   4. Simplified 78.0%

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

   5. Taylor expanded in z around inf 52.6%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-23}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-188}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-134}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+74}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 8: 38.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+76}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-229}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-159}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{+51}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -9e+76)
   (* z x)
   (if (<= z 7.5e-229)
     (* y t)
     (if (<= z 3e-159) x (if (<= z 1e+51) (* y t) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9e+76) {
		tmp = z * x;
	} else if (z <= 7.5e-229) {
		tmp = y * t;
	} else if (z <= 3e-159) {
		tmp = x;
	} else if (z <= 1e+51) {
		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 <= (-9d+76)) then
        tmp = z * x
    else if (z <= 7.5d-229) then
        tmp = y * t
    else if (z <= 3d-159) then
        tmp = x
    else if (z <= 1d+51) 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 <= -9e+76) {
		tmp = z * x;
	} else if (z <= 7.5e-229) {
		tmp = y * t;
	} else if (z <= 3e-159) {
		tmp = x;
	} else if (z <= 1e+51) {
		tmp = y * t;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -9e+76:
		tmp = z * x
	elif z <= 7.5e-229:
		tmp = y * t
	elif z <= 3e-159:
		tmp = x
	elif z <= 1e+51:
		tmp = y * t
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9e+76)
		tmp = Float64(z * x);
	elseif (z <= 7.5e-229)
		tmp = Float64(y * t);
	elseif (z <= 3e-159)
		tmp = x;
	elseif (z <= 1e+51)
		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 <= -9e+76)
		tmp = z * x;
	elseif (z <= 7.5e-229)
		tmp = y * t;
	elseif (z <= 3e-159)
		tmp = x;
	elseif (z <= 1e+51)
		tmp = y * t;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -9e+76], N[(z * x), $MachinePrecision], If[LessEqual[z, 7.5e-229], N[(y * t), $MachinePrecision], If[LessEqual[z, 3e-159], x, If[LessEqual[z, 1e+51], N[(y * t), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999995e76 or 1e51 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 55.1%

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

      1. *-commutative 55.1%

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

      2. mul-1-neg 55.1%

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

      3. unsub-neg 55.1%

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

      4. distribute-lft-out-- 55.1%

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

      5. *-rgt-identity 55.1%

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

   4. Simplified 55.1%

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

   5. Taylor expanded in z around inf 45.2%

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

   if -8.9999999999999995e76 < z < 7.4999999999999999e-229 or 3.00000000000000009e-159 < z < 1e51

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 76.9%

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

   3. Taylor expanded in x around 0 76.9%

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

      1. *-commutative 76.9%

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

      2. fma-def 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in y around inf 41.8%

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

   if 7.4999999999999999e-229 < z < 3.00000000000000009e-159

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 65.5%

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

   3. Taylor expanded in x around inf 51.0%

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

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+76}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-229}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-159}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 10^{+51}:\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]

Alternative 9: 53.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-249}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-111}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -2.25e-156)
     t_1
     (if (<= t -7.8e-249) (* y (- x)) (if (<= t 1.02e-111) (* z x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -2.25e-156) {
		tmp = t_1;
	} else if (t <= -7.8e-249) {
		tmp = y * -x;
	} else if (t <= 1.02e-111) {
		tmp = z * 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 = (y - z) * t
    if (t <= (-2.25d-156)) then
        tmp = t_1
    else if (t <= (-7.8d-249)) then
        tmp = y * -x
    else if (t <= 1.02d-111) then
        tmp = z * 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 = (y - z) * t;
	double tmp;
	if (t <= -2.25e-156) {
		tmp = t_1;
	} else if (t <= -7.8e-249) {
		tmp = y * -x;
	} else if (t <= 1.02e-111) {
		tmp = z * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -2.25e-156:
		tmp = t_1
	elif t <= -7.8e-249:
		tmp = y * -x
	elif t <= 1.02e-111:
		tmp = z * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -2.25e-156)
		tmp = t_1;
	elseif (t <= -7.8e-249)
		tmp = Float64(y * Float64(-x));
	elseif (t <= 1.02e-111)
		tmp = Float64(z * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -2.25e-156)
		tmp = t_1;
	elseif (t <= -7.8e-249)
		tmp = y * -x;
	elseif (t <= 1.02e-111)
		tmp = z * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -2.25e-156], t$95$1, If[LessEqual[t, -7.8e-249], N[(y * (-x)), $MachinePrecision], If[LessEqual[t, 1.02e-111], N[(z * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.24999999999999993e-156 or 1.02000000000000003e-111 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 79.9%

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

   3. Taylor expanded in x around 0 79.9%

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

      1. *-commutative 79.9%

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

      2. fma-def 80.0%

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

   5. Simplified 80.0%

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

   6. Taylor expanded in t around inf 69.9%

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

   if -2.24999999999999993e-156 < t < -7.7999999999999998e-249

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 94.3%

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

      1. *-commutative 94.3%

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

      2. mul-1-neg 94.3%

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

      3. unsub-neg 94.3%

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

      4. distribute-lft-out-- 94.4%

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

      5. *-rgt-identity 94.4%

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

   4. Simplified 94.4%

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

   5. Taylor expanded in y around inf 66.2%

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

      1. associate-*r* 66.2%

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

      2. neg-mul-1 66.2%

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

   7. Simplified 66.2%

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

   if -7.7999999999999998e-249 < t < 1.02000000000000003e-111

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 93.6%

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

      1. *-commutative 93.6%

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

      2. mul-1-neg 93.6%

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

      3. unsub-neg 93.6%

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

      4. distribute-lft-out-- 93.7%

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

      5. *-rgt-identity 93.7%

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

   4. Simplified 93.7%

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

   5. Taylor expanded in z around inf 48.7%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{-156}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-249}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-111}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \end{array} \]

Alternative 10: 82.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+65} \lor \neg \left(y \leq 5.5 \cdot 10^{+76}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.2e+65) (not (<= y 5.5e+76)))
   (+ x (* y (- t x)))
   (+ x (* z (- x t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.2e+65) || !(y <= 5.5e+76)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (x - 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 ((y <= (-3.2d+65)) .or. (.not. (y <= 5.5d+76))) then
        tmp = x + (y * (t - x))
    else
        tmp = x + (z * (x - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.2e+65) || !(y <= 5.5e+76)) {
		tmp = x + (y * (t - x));
	} else {
		tmp = x + (z * (x - t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.2e+65) or not (y <= 5.5e+76):
		tmp = x + (y * (t - x))
	else:
		tmp = x + (z * (x - t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.2e+65) || !(y <= 5.5e+76))
		tmp = Float64(x + Float64(y * Float64(t - x)));
	else
		tmp = Float64(x + Float64(z * Float64(x - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.2e+65) || ~((y <= 5.5e+76)))
		tmp = x + (y * (t - x));
	else
		tmp = x + (z * (x - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.2e+65], N[Not[LessEqual[y, 5.5e+76]], $MachinePrecision]], N[(x + N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.20000000000000007e65 or 5.5000000000000001e76 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 85.5%

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

   if -3.20000000000000007e65 < y < 5.5000000000000001e76

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 87.9%

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

      1. +-commutative 87.9%

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

      2. mul-1-neg 87.9%

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

      3. unsub-neg 87.9%

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

      4. *-commutative 87.9%

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

   4. Simplified 87.9%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+65} \lor \neg \left(y \leq 5.5 \cdot 10^{+76}\right):\\ \;\;\;\;x + y \cdot \left(t - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x - t\right)\\ \end{array} \]

Alternative 11: 71.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-16} \lor \neg \left(z \leq 0.455\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.45e-16) (not (<= z 0.455))) (* z (- x t)) (+ x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.45e-16) || !(z <= 0.455)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.45d-16)) .or. (.not. (z <= 0.455d0))) then
        tmp = z * (x - t)
    else
        tmp = x + (y * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.45e-16) || !(z <= 0.455)) {
		tmp = z * (x - t);
	} else {
		tmp = x + (y * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.45e-16) or not (z <= 0.455):
		tmp = z * (x - t)
	else:
		tmp = x + (y * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.45e-16) || !(z <= 0.455))
		tmp = Float64(z * Float64(x - t));
	else
		tmp = Float64(x + Float64(y * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.45e-16) || ~((z <= 0.455)))
		tmp = z * (x - t);
	else
		tmp = x + (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.45e-16], N[Not[LessEqual[z, 0.455]], $MachinePrecision]], N[(z * N[(x - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4499999999999999e-16 or 0.455000000000000016 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 83.3%

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

      1. +-commutative 83.3%

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

      2. mul-1-neg 83.3%

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

      3. unsub-neg 83.3%

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

      4. *-commutative 83.3%

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

   4. Simplified 83.3%

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

   5. Taylor expanded in z around inf 82.0%

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

   if -1.4499999999999999e-16 < z < 0.455000000000000016

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 76.9%

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

   3. Taylor expanded in z around 0 66.3%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-16} \lor \neg \left(z \leq 0.455\right):\\ \;\;\;\;z \cdot \left(x - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot t\\ \end{array} \]

Alternative 12: 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. Final simplification 100.0%

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

Alternative 13: 37.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-16}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.4e-16) (* y t) (if (<= y 1.45e-5) x (* y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e-16) {
		tmp = y * t;
	} else if (y <= 1.45e-5) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.4d-16)) then
        tmp = y * t
    else if (y <= 1.45d-5) then
        tmp = x
    else
        tmp = y * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e-16) {
		tmp = y * t;
	} else if (y <= 1.45e-5) {
		tmp = x;
	} else {
		tmp = y * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.4e-16:
		tmp = y * t
	elif y <= 1.45e-5:
		tmp = x
	else:
		tmp = y * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.4e-16)
		tmp = Float64(y * t);
	elseif (y <= 1.45e-5)
		tmp = x;
	else
		tmp = Float64(y * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.4e-16)
		tmp = y * t;
	elseif (y <= 1.45e-5)
		tmp = x;
	else
		tmp = y * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.4e-16], N[(y * t), $MachinePrecision], If[LessEqual[y, 1.45e-5], x, N[(y * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.4e-16 or 1.45e-5 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 55.9%

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

   3. Taylor expanded in x around 0 55.9%

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

      1. *-commutative 55.9%

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

      2. fma-def 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in y around inf 42.7%

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

   if -3.4e-16 < y < 1.45e-5

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 75.8%

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

   3. Taylor expanded in x around inf 25.1%

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

4. Final simplification 34.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-16}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot t\\ \end{array} \]

Alternative 14: 18.3% 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. Taylor expanded in t around inf 65.4%

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

3. Taylor expanded in x around inf 13.2%

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

4. Final simplification 13.2%

   \[\leadsto x \]

Developer target: 96.2% 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 2023221 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

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