Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 8.5s

Alternatives: 13

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-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: 65.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z + 1\right)\\ t_2 := y \cdot \left(t - x\right)\\ t_3 := \left(y - z\right) \cdot t\\ \mathbf{if}\;y \leq -19500:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-40}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-134}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-81}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (+ z 1.0))) (t_2 (* y (- t x))) (t_3 (* (- y z) t)))
   (if (<= y -19500.0)
     t_2
     (if (<= y -5e-40)
       t_3
       (if (<= y -1.55e-125)
         t_1
         (if (<= y -1.4e-134)
           t_3
           (if (<= y 3.15e-198)
             t_1
             (if (<= y 3.6e-81) t_3 (if (<= y 4.9e-54) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (z + 1.0);
	double t_2 = y * (t - x);
	double t_3 = (y - z) * t;
	double tmp;
	if (y <= -19500.0) {
		tmp = t_2;
	} else if (y <= -5e-40) {
		tmp = t_3;
	} else if (y <= -1.55e-125) {
		tmp = t_1;
	} else if (y <= -1.4e-134) {
		tmp = t_3;
	} else if (y <= 3.15e-198) {
		tmp = t_1;
	} else if (y <= 3.6e-81) {
		tmp = t_3;
	} else if (y <= 4.9e-54) {
		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) :: t_3
    real(8) :: tmp
    t_1 = x * (z + 1.0d0)
    t_2 = y * (t - x)
    t_3 = (y - z) * t
    if (y <= (-19500.0d0)) then
        tmp = t_2
    else if (y <= (-5d-40)) then
        tmp = t_3
    else if (y <= (-1.55d-125)) then
        tmp = t_1
    else if (y <= (-1.4d-134)) then
        tmp = t_3
    else if (y <= 3.15d-198) then
        tmp = t_1
    else if (y <= 3.6d-81) then
        tmp = t_3
    else if (y <= 4.9d-54) 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 * (z + 1.0);
	double t_2 = y * (t - x);
	double t_3 = (y - z) * t;
	double tmp;
	if (y <= -19500.0) {
		tmp = t_2;
	} else if (y <= -5e-40) {
		tmp = t_3;
	} else if (y <= -1.55e-125) {
		tmp = t_1;
	} else if (y <= -1.4e-134) {
		tmp = t_3;
	} else if (y <= 3.15e-198) {
		tmp = t_1;
	} else if (y <= 3.6e-81) {
		tmp = t_3;
	} else if (y <= 4.9e-54) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (z + 1.0)
	t_2 = y * (t - x)
	t_3 = (y - z) * t
	tmp = 0
	if y <= -19500.0:
		tmp = t_2
	elif y <= -5e-40:
		tmp = t_3
	elif y <= -1.55e-125:
		tmp = t_1
	elif y <= -1.4e-134:
		tmp = t_3
	elif y <= 3.15e-198:
		tmp = t_1
	elif y <= 3.6e-81:
		tmp = t_3
	elif y <= 4.9e-54:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(z + 1.0))
	t_2 = Float64(y * Float64(t - x))
	t_3 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (y <= -19500.0)
		tmp = t_2;
	elseif (y <= -5e-40)
		tmp = t_3;
	elseif (y <= -1.55e-125)
		tmp = t_1;
	elseif (y <= -1.4e-134)
		tmp = t_3;
	elseif (y <= 3.15e-198)
		tmp = t_1;
	elseif (y <= 3.6e-81)
		tmp = t_3;
	elseif (y <= 4.9e-54)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x * (z + 1.0);
	t_2 = y * (t - x);
	t_3 = (y - z) * t;
	tmp = 0.0;
	if (y <= -19500.0)
		tmp = t_2;
	elseif (y <= -5e-40)
		tmp = t_3;
	elseif (y <= -1.55e-125)
		tmp = t_1;
	elseif (y <= -1.4e-134)
		tmp = t_3;
	elseif (y <= 3.15e-198)
		tmp = t_1;
	elseif (y <= 3.6e-81)
		tmp = t_3;
	elseif (y <= 4.9e-54)
		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[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(t - x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -19500.0], t$95$2, If[LessEqual[y, -5e-40], t$95$3, If[LessEqual[y, -1.55e-125], t$95$1, If[LessEqual[y, -1.4e-134], t$95$3, If[LessEqual[y, 3.15e-198], t$95$1, If[LessEqual[y, 3.6e-81], t$95$3, If[LessEqual[y, 4.9e-54], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -19500 or 4.90000000000000021e-54 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 81.0%

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

      1. *-commutative 81.0%

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

   4. Simplified 81.0%

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

   5. Taylor expanded in x around -inf 75.1%

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

      1. +-commutative 75.1%

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

      2. mul-1-neg 75.1%

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

      3. unsub-neg 75.1%

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

      4. *-commutative 75.1%

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

      5. sub-neg 75.1%

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

      6. metadata-eval 75.1%

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

      7. +-commutative 75.1%

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

   7. Simplified 75.1%

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

   8. Taylor expanded in y around inf 79.2%

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

   if -19500 < y < -4.99999999999999965e-40 or -1.55000000000000006e-125 < y < -1.3999999999999999e-134 or 3.15000000000000008e-198 < y < 3.5999999999999999e-81

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 100.0%

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

      4. fma-def 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 83.5%

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

      1. associate-+r+ 83.5%

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

      2. mul-1-neg 83.5%

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

      3. *-commutative 83.5%

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

      4. sub-neg 83.5%

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

      5. associate-+l- 83.5%

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

      6. *-commutative 83.5%

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

   6. Applied egg-rr 83.5%

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

   7. Taylor expanded in x around 0 74.8%

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

      1. distribute-lft-out-- 74.8%

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

   9. Simplified 74.8%

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

   if -4.99999999999999965e-40 < y < -1.55000000000000006e-125 or -1.3999999999999999e-134 < y < 3.15000000000000008e-198 or 3.5999999999999999e-81 < y < 4.90000000000000021e-54

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. unsub-neg 73.4%

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

   4. Simplified 73.4%

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

   5. Taylor expanded in y around 0 73.4%

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

      1. +-commutative 73.4%

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

   7. Simplified 73.4%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -19500:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-40}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-134}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 3.15 \cdot 10^{-198}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-81}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 3: 38.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{-12}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-53}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 0.0018:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (- t))))
   (if (<= y -1.7e-12)
     (* y t)
     (if (<= y -1.4e-39)
       t_1
       (if (<= y -5.5e-53)
         (* y t)
         (if (<= y -1.2e-126)
           x
           (if (<= y 1.7e-80) t_1 (if (<= y 0.0018) x (* y (- x))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * -t;
	double tmp;
	if (y <= -1.7e-12) {
		tmp = y * t;
	} else if (y <= -1.4e-39) {
		tmp = t_1;
	} else if (y <= -5.5e-53) {
		tmp = y * t;
	} else if (y <= -1.2e-126) {
		tmp = x;
	} else if (y <= 1.7e-80) {
		tmp = t_1;
	} else if (y <= 0.0018) {
		tmp = x;
	} 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 <= (-1.7d-12)) then
        tmp = y * t
    else if (y <= (-1.4d-39)) then
        tmp = t_1
    else if (y <= (-5.5d-53)) then
        tmp = y * t
    else if (y <= (-1.2d-126)) then
        tmp = x
    else if (y <= 1.7d-80) then
        tmp = t_1
    else if (y <= 0.0018d0) then
        tmp = x
    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 <= -1.7e-12) {
		tmp = y * t;
	} else if (y <= -1.4e-39) {
		tmp = t_1;
	} else if (y <= -5.5e-53) {
		tmp = y * t;
	} else if (y <= -1.2e-126) {
		tmp = x;
	} else if (y <= 1.7e-80) {
		tmp = t_1;
	} else if (y <= 0.0018) {
		tmp = x;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * -t
	tmp = 0
	if y <= -1.7e-12:
		tmp = y * t
	elif y <= -1.4e-39:
		tmp = t_1
	elif y <= -5.5e-53:
		tmp = y * t
	elif y <= -1.2e-126:
		tmp = x
	elif y <= 1.7e-80:
		tmp = t_1
	elif y <= 0.0018:
		tmp = x
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-t))
	tmp = 0.0
	if (y <= -1.7e-12)
		tmp = Float64(y * t);
	elseif (y <= -1.4e-39)
		tmp = t_1;
	elseif (y <= -5.5e-53)
		tmp = Float64(y * t);
	elseif (y <= -1.2e-126)
		tmp = x;
	elseif (y <= 1.7e-80)
		tmp = t_1;
	elseif (y <= 0.0018)
		tmp = x;
	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 <= -1.7e-12)
		tmp = y * t;
	elseif (y <= -1.4e-39)
		tmp = t_1;
	elseif (y <= -5.5e-53)
		tmp = y * t;
	elseif (y <= -1.2e-126)
		tmp = x;
	elseif (y <= 1.7e-80)
		tmp = t_1;
	elseif (y <= 0.0018)
		tmp = x;
	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, -1.7e-12], N[(y * t), $MachinePrecision], If[LessEqual[y, -1.4e-39], t$95$1, If[LessEqual[y, -5.5e-53], N[(y * t), $MachinePrecision], If[LessEqual[y, -1.2e-126], x, If[LessEqual[y, 1.7e-80], t$95$1, If[LessEqual[y, 0.0018], x, N[(y * (-x)), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.7e-12 or -1.4000000000000001e-39 < y < -5.50000000000000023e-53

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 89.7%

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

      4. fma-def 95.6%

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

   3. Applied egg-rr 95.6%

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

   4. Taylor expanded in x around 0 50.4%

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

      1. associate-+r+ 50.4%

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

      2. mul-1-neg 50.4%

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

      3. *-commutative 50.4%

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

      4. sub-neg 50.4%

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

      5. associate-+l- 50.4%

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

      6. *-commutative 50.4%

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

   6. Applied egg-rr 50.4%

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

   7. Taylor expanded in y around inf 51.5%

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

   if -1.7e-12 < y < -1.4000000000000001e-39 or -1.20000000000000003e-126 < y < 1.7e-80

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 80.1%

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

   3. Taylor expanded in y around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. unsub-neg 76.9%

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

      3. *-commutative 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in x around 0 51.1%

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

      1. associate-*r* 51.1%

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

      2. neg-mul-1 51.1%

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

   8. Simplified 51.1%

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

   if -5.50000000000000023e-53 < y < -1.20000000000000003e-126 or 1.7e-80 < y < 0.0018

   1. Initial program 99.9%

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

   2. Taylor expanded in t around inf 78.6%

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

   3. Taylor expanded in x around inf 47.3%

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

   if 0.0018 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. unsub-neg 61.5%

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

   4. Simplified 61.5%

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

   5. Taylor expanded in y around inf 50.9%

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

      1. mul-1-neg 50.9%

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

      2. distribute-lft-neg-out 50.9%

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

      3. *-commutative 50.9%

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

   7. Simplified 50.9%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-12}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-39}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-53}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-126}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 0.0018:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 4: 71.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-79}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 800000000:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -1.9e-11)
     t_1
     (if (<= y 4.7e-79)
       (- x (* z t))
       (if (<= y 800000000.0)
         (* x (+ z 1.0))
         (if (<= y 4.8e+19) (* z (- t)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -1.9e-11) {
		tmp = t_1;
	} else if (y <= 4.7e-79) {
		tmp = x - (z * t);
	} else if (y <= 800000000.0) {
		tmp = x * (z + 1.0);
	} else if (y <= 4.8e+19) {
		tmp = z * -t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t - x)
    if (y <= (-1.9d-11)) then
        tmp = t_1
    else if (y <= 4.7d-79) then
        tmp = x - (z * t)
    else if (y <= 800000000.0d0) then
        tmp = x * (z + 1.0d0)
    else if (y <= 4.8d+19) then
        tmp = z * -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 * (t - x);
	double tmp;
	if (y <= -1.9e-11) {
		tmp = t_1;
	} else if (y <= 4.7e-79) {
		tmp = x - (z * t);
	} else if (y <= 800000000.0) {
		tmp = x * (z + 1.0);
	} else if (y <= 4.8e+19) {
		tmp = z * -t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -1.9e-11:
		tmp = t_1
	elif y <= 4.7e-79:
		tmp = x - (z * t)
	elif y <= 800000000.0:
		tmp = x * (z + 1.0)
	elif y <= 4.8e+19:
		tmp = z * -t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -1.9e-11)
		tmp = t_1;
	elseif (y <= 4.7e-79)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 800000000.0)
		tmp = Float64(x * Float64(z + 1.0));
	elseif (y <= 4.8e+19)
		tmp = Float64(z * Float64(-t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -1.9e-11)
		tmp = t_1;
	elseif (y <= 4.7e-79)
		tmp = x - (z * t);
	elseif (y <= 800000000.0)
		tmp = x * (z + 1.0);
	elseif (y <= 4.8e+19)
		tmp = z * -t;
	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]}, If[LessEqual[y, -1.9e-11], t$95$1, If[LessEqual[y, 4.7e-79], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 800000000.0], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+19], N[(z * (-t)), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.8999999999999999e-11 or 4.8e19 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 85.0%

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

      1. *-commutative 85.0%

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

   4. Simplified 85.0%

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

   5. Taylor expanded in x around -inf 78.3%

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

      1. +-commutative 78.3%

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

      2. mul-1-neg 78.3%

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

      3. unsub-neg 78.3%

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

      4. *-commutative 78.3%

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

      5. sub-neg 78.3%

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

      6. metadata-eval 78.3%

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

      7. +-commutative 78.3%

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

   7. Simplified 78.3%

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

   8. Taylor expanded in y around inf 85.0%

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

   if -1.8999999999999999e-11 < y < 4.7000000000000002e-79

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 81.1%

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

   3. Taylor expanded in y around 0 74.8%

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

      1. mul-1-neg 74.8%

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

      2. unsub-neg 74.8%

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

      3. *-commutative 74.8%

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

   5. Simplified 74.8%

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

   if 4.7000000000000002e-79 < y < 8e8

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 67.8%

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

      1. mul-1-neg 67.8%

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

      2. unsub-neg 67.8%

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

   4. Simplified 67.8%

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

   5. Taylor expanded in y around 0 65.6%

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

      1. +-commutative 65.6%

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

   7. Simplified 65.6%

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

   if 8e8 < y < 4.8e19

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 75.7%

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

   3. Taylor expanded in y around 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. unsub-neg 75.7%

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

      3. *-commutative 75.7%

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

   5. Simplified 75.7%

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

   6. Taylor expanded in x around 0 76.1%

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

      1. associate-*r* 76.1%

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

      2. neg-mul-1 76.1%

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

   8. Simplified 76.1%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-79}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 800000000:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 5: 72.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(t - x\right)\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-80}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (- t x))))
   (if (<= y -4.8e-12)
     t_1
     (if (<= y 2.9e-80)
       (- x (* z t))
       (if (<= y 9e+25) (* x (+ (- z y) 1.0)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -4.8e-12) {
		tmp = t_1;
	} else if (y <= 2.9e-80) {
		tmp = x - (z * t);
	} else if (y <= 9e+25) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (t - x)
    if (y <= (-4.8d-12)) then
        tmp = t_1
    else if (y <= 2.9d-80) then
        tmp = x - (z * t)
    else if (y <= 9d+25) then
        tmp = x * ((z - y) + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (t - x);
	double tmp;
	if (y <= -4.8e-12) {
		tmp = t_1;
	} else if (y <= 2.9e-80) {
		tmp = x - (z * t);
	} else if (y <= 9e+25) {
		tmp = x * ((z - y) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (t - x)
	tmp = 0
	if y <= -4.8e-12:
		tmp = t_1
	elif y <= 2.9e-80:
		tmp = x - (z * t)
	elif y <= 9e+25:
		tmp = x * ((z - y) + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(t - x))
	tmp = 0.0
	if (y <= -4.8e-12)
		tmp = t_1;
	elseif (y <= 2.9e-80)
		tmp = Float64(x - Float64(z * t));
	elseif (y <= 9e+25)
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (t - x);
	tmp = 0.0;
	if (y <= -4.8e-12)
		tmp = t_1;
	elseif (y <= 2.9e-80)
		tmp = x - (z * t);
	elseif (y <= 9e+25)
		tmp = x * ((z - y) + 1.0);
	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]}, If[LessEqual[y, -4.8e-12], t$95$1, If[LessEqual[y, 2.9e-80], N[(x - N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+25], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.79999999999999974e-12 or 9.0000000000000006e25 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 86.1%

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

      1. *-commutative 86.1%

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

   4. Simplified 86.1%

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

   5. Taylor expanded in x around -inf 79.3%

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

      1. +-commutative 79.3%

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

      2. mul-1-neg 79.3%

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

      3. unsub-neg 79.3%

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

      4. *-commutative 79.3%

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

      5. sub-neg 79.3%

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

      6. metadata-eval 79.3%

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

      7. +-commutative 79.3%

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

   7. Simplified 79.3%

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

   8. Taylor expanded in y around inf 86.1%

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

   if -4.79999999999999974e-12 < y < 2.89999999999999998e-80

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 81.1%

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

   3. Taylor expanded in y around 0 74.8%

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

      1. mul-1-neg 74.8%

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

      2. unsub-neg 74.8%

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

      3. *-commutative 74.8%

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

   5. Simplified 74.8%

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

   if 2.89999999999999998e-80 < y < 9.0000000000000006e25

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 64.3%

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

      1. mul-1-neg 64.3%

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

      2. unsub-neg 64.3%

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

   4. Simplified 64.3%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-12}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-80}:\\ \;\;\;\;x - z \cdot t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+25}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t - x\right)\\ \end{array} \]

Alternative 6: 78.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-131} \lor \neg \left(t \leq 6.2 \cdot 10^{-142}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -5.2e-131) (not (<= t 6.2e-142)))
   (- x (* t (- z y)))
   (* x (+ (- z y) 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.2e-131) || !(t <= 6.2e-142)) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	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 ((t <= (-5.2d-131)) .or. (.not. (t <= 6.2d-142))) then
        tmp = x - (t * (z - y))
    else
        tmp = x * ((z - y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -5.2e-131) || !(t <= 6.2e-142)) {
		tmp = x - (t * (z - y));
	} else {
		tmp = x * ((z - y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -5.2e-131) or not (t <= 6.2e-142):
		tmp = x - (t * (z - y))
	else:
		tmp = x * ((z - y) + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -5.2e-131) || !(t <= 6.2e-142))
		tmp = Float64(x - Float64(t * Float64(z - y)));
	else
		tmp = Float64(x * Float64(Float64(z - y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -5.2e-131) || ~((t <= 6.2e-142)))
		tmp = x - (t * (z - y));
	else
		tmp = x * ((z - y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -5.2e-131], N[Not[LessEqual[t, 6.2e-142]], $MachinePrecision]], N[(x - N[(t * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.19999999999999993e-131 or 6.2e-142 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 79.0%

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

   if -5.19999999999999993e-131 < t < 6.2e-142

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 93.9%

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

      1. mul-1-neg 93.9%

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

      2. unsub-neg 93.9%

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

   4. Simplified 93.9%

      \[\leadsto \color{blue}{x \cdot \left(1 - \left(y - z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-131} \lor \neg \left(t \leq 6.2 \cdot 10^{-142}\right):\\ \;\;\;\;x - t \cdot \left(z - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z - y\right) + 1\right)\\ \end{array} \]

Alternative 7: 53.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-156} \lor \neg \left(t \leq 2.95 \cdot 10^{-195}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.5e-156) (not (<= t 2.95e-195))) (* (- y z) t) (* y (- x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.5e-156) || !(t <= 2.95e-195)) {
		tmp = (y - z) * 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 ((t <= (-2.5d-156)) .or. (.not. (t <= 2.95d-195))) then
        tmp = (y - z) * 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 ((t <= -2.5e-156) || !(t <= 2.95e-195)) {
		tmp = (y - z) * t;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.5e-156) or not (t <= 2.95e-195):
		tmp = (y - z) * t
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.5e-156) || !(t <= 2.95e-195))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.5e-156) || ~((t <= 2.95e-195)))
		tmp = (y - z) * t;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.5e-156], N[Not[LessEqual[t, 2.95e-195]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(y * (-x)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.50000000000000004e-156 or 2.95000000000000003e-195 < t

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 95.7%

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

      4. fma-def 97.9%

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

   3. Applied egg-rr 97.9%

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

   4. Taylor expanded in x around 0 75.4%

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

      1. associate-+r+ 75.4%

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

      2. mul-1-neg 75.4%

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

      3. *-commutative 75.4%

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

      4. sub-neg 75.4%

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

      5. associate-+l- 75.4%

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

      6. *-commutative 75.4%

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

   6. Applied egg-rr 75.4%

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

   7. Taylor expanded in x around 0 62.4%

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

      1. distribute-lft-out-- 65.0%

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

   9. Simplified 65.0%

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

   if -2.50000000000000004e-156 < t < 2.95000000000000003e-195

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 97.0%

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

      1. mul-1-neg 97.0%

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

      2. unsub-neg 97.0%

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

   4. Simplified 97.0%

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

   5. Taylor expanded in y around inf 49.3%

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

      1. mul-1-neg 49.3%

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

      2. distribute-lft-neg-out 49.3%

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

      3. *-commutative 49.3%

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

   7. Simplified 49.3%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-156} \lor \neg \left(t \leq 2.95 \cdot 10^{-195}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 8: 60.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{-119} \lor \neg \left(t \leq 4.6 \cdot 10^{-142}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.35e-119) (not (<= t 4.6e-142)))
   (* (- y z) t)
   (* x (+ z 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.35e-119) || !(t <= 4.6e-142)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (z + 1.0);
	}
	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 ((t <= (-2.35d-119)) .or. (.not. (t <= 4.6d-142))) then
        tmp = (y - z) * t
    else
        tmp = x * (z + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.35e-119) || !(t <= 4.6e-142)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (z + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.35e-119) or not (t <= 4.6e-142):
		tmp = (y - z) * t
	else:
		tmp = x * (z + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.35e-119) || !(t <= 4.6e-142))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(z + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.35e-119) || ~((t <= 4.6e-142)))
		tmp = (y - z) * t;
	else
		tmp = x * (z + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.35e-119], N[Not[LessEqual[t, 4.6e-142]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.35000000000000001e-119 or 4.60000000000000005e-142 < t

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 95.3%

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

      4. fma-def 97.7%

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

   3. Applied egg-rr 97.7%

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

   4. Taylor expanded in x around 0 76.3%

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

      1. associate-+r+ 76.3%

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

      2. mul-1-neg 76.3%

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

      3. *-commutative 76.3%

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

      4. sub-neg 76.3%

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

      5. associate-+l- 76.3%

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

      6. *-commutative 76.3%

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

   6. Applied egg-rr 76.3%

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

   7. Taylor expanded in x around 0 65.7%

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

      1. distribute-lft-out-- 68.6%

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

   9. Simplified 68.6%

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

   if -2.35000000000000001e-119 < t < 4.60000000000000005e-142

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 93.0%

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

      1. mul-1-neg 93.0%

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

      2. unsub-neg 93.0%

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

   4. Simplified 93.0%

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

   5. Taylor expanded in y around 0 55.1%

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

      1. +-commutative 55.1%

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

   7. Simplified 55.1%

      \[\leadsto \color{blue}{x \cdot \left(z + 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{-119} \lor \neg \left(t \leq 4.6 \cdot 10^{-142}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z + 1\right)\\ \end{array} \]

Alternative 9: 60.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-150} \lor \neg \left(t \leq 9.6 \cdot 10^{-127}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.2e-150) (not (<= t 9.6e-127)))
   (* (- y z) t)
   (* x (- 1.0 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.2e-150) || !(t <= 9.6e-127)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-6.2d-150)) .or. (.not. (t <= 9.6d-127))) then
        tmp = (y - z) * t
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.2e-150) || !(t <= 9.6e-127)) {
		tmp = (y - z) * t;
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.2e-150) or not (t <= 9.6e-127):
		tmp = (y - z) * t
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.2e-150) || !(t <= 9.6e-127))
		tmp = Float64(Float64(y - z) * t);
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6.2e-150) || ~((t <= 9.6e-127)))
		tmp = (y - z) * t;
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.2e-150], N[Not[LessEqual[t, 9.6e-127]], $MachinePrecision]], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.19999999999999996e-150 or 9.59999999999999929e-127 < t

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 95.4%

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

      4. fma-def 97.7%

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

   3. Applied egg-rr 97.7%

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

   4. Taylor expanded in x around 0 76.1%

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

      1. associate-+r+ 76.1%

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

      2. mul-1-neg 76.1%

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

      3. *-commutative 76.1%

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

      4. sub-neg 76.1%

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

      5. associate-+l- 76.1%

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

      6. *-commutative 76.1%

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

   6. Applied egg-rr 76.1%

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

   7. Taylor expanded in x around 0 65.1%

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

      1. distribute-lft-out-- 67.9%

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

   9. Simplified 67.9%

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

   if -6.19999999999999996e-150 < t < 9.59999999999999929e-127

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 93.9%

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

      1. mul-1-neg 93.9%

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

      2. unsub-neg 93.9%

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

   4. Simplified 93.9%

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

   5. Taylor expanded in z around 0 68.5%

      \[\leadsto \color{blue}{x \cdot \left(1 - y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-150} \lor \neg \left(t \leq 9.6 \cdot 10^{-127}\right):\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 10: 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 11: 36.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-40}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 0.0017:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.3e-40) (* y t) (if (<= y 0.0017) x (* y (- x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e-40) {
		tmp = y * t;
	} else if (y <= 0.0017) {
		tmp = x;
	} 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 <= (-1.3d-40)) then
        tmp = y * t
    else if (y <= 0.0017d0) then
        tmp = x
    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 <= -1.3e-40) {
		tmp = y * t;
	} else if (y <= 0.0017) {
		tmp = x;
	} else {
		tmp = y * -x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.3e-40:
		tmp = y * t
	elif y <= 0.0017:
		tmp = x
	else:
		tmp = y * -x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.3e-40)
		tmp = Float64(y * t);
	elseif (y <= 0.0017)
		tmp = x;
	else
		tmp = Float64(y * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.3e-40)
		tmp = y * t;
	elseif (y <= 0.0017)
		tmp = x;
	else
		tmp = y * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.3e-40], N[(y * t), $MachinePrecision], If[LessEqual[y, 0.0017], x, N[(y * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3000000000000001e-40

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 90.8%

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

      4. fma-def 96.1%

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

   3. Applied egg-rr 96.1%

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

   4. Taylor expanded in x around 0 54.3%

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

      1. associate-+r+ 54.3%

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

      2. mul-1-neg 54.3%

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

      3. *-commutative 54.3%

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

      4. sub-neg 54.3%

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

      5. associate-+l- 54.3%

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

      6. *-commutative 54.3%

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

   6. Applied egg-rr 54.3%

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

   7. Taylor expanded in y around inf 47.7%

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

   if -1.3000000000000001e-40 < y < 0.00169999999999999991

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 79.1%

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

   3. Taylor expanded in x around inf 35.7%

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

   if 0.00169999999999999991 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. unsub-neg 61.5%

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

   4. Simplified 61.5%

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

   5. Taylor expanded in y around inf 50.9%

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

      1. mul-1-neg 50.9%

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

      2. distribute-lft-neg-out 50.9%

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

      3. *-commutative 50.9%

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

   7. Simplified 50.9%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-40}:\\ \;\;\;\;y \cdot t\\ \mathbf{elif}\;y \leq 0.0017:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \end{array} \]

Alternative 12: 36.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-48} \lor \neg \left(y \leq 4.7 \cdot 10^{-55}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.15e-48) (not (<= y 4.7e-55))) (* y t) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.15e-48) || !(y <= 4.7e-55)) {
		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-48)) .or. (.not. (y <= 4.7d-55))) 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-48) || !(y <= 4.7e-55)) {
		tmp = y * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.15e-48) or not (y <= 4.7e-55):
		tmp = y * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.15e-48) || !(y <= 4.7e-55))
		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-48) || ~((y <= 4.7e-55)))
		tmp = y * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.15e-48], N[Not[LessEqual[y, 4.7e-55]], $MachinePrecision]], N[(y * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e-48 or 4.7e-55 < y

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-lft-in 93.8%

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

      4. fma-def 96.6%

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

   3. Applied egg-rr 96.6%

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

   4. Taylor expanded in x around 0 50.7%

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

      1. associate-+r+ 50.7%

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

      2. mul-1-neg 50.7%

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

      3. *-commutative 50.7%

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

      4. sub-neg 50.7%

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

      5. associate-+l- 50.7%

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

      6. *-commutative 50.7%

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

   6. Applied egg-rr 50.7%

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

   7. Taylor expanded in y around inf 41.8%

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

   if -1.15e-48 < y < 4.7e-55

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 78.8%

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

   3. Taylor expanded in x around inf 37.1%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-48} \lor \neg \left(y \leq 4.7 \cdot 10^{-55}\right):\\ \;\;\;\;y \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 17.6% 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 64.7%

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

3. Taylor expanded in x around inf 18.0%

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

4. Final simplification 18.0%

   \[\leadsto x \]

Developer target: 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 2023320 
(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))))