Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2

Percentage Accurate: 86.6% → 99.5%

Time: 7.7s

Alternatives: 13

Speedup: 0.7×

• 23.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Python

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 86.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Python

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z)))))
   (if (<= t_1 INFINITY) t_1 (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 x y) (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))) < +inf.0

   1. Initial program 99.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   if +inf.0 < (+.f64 (/.f64 x y) (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)))

   1. Initial program 0.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Applied rewrites 94.3%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 69.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{x}{y} + -2\\ t_3 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+43}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z)))
        (t_2 (+ (/ x y) -2.0))
        (t_3 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (<= t_3 -1e+105)
     t_1
     (if (<= t_3 5e+43)
       t_2
       (if (<= t_3 5e+296) (/ 2.0 t) (if (<= t_3 INFINITY) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) + -2.0;
	double t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_3 <= -1e+105) {
		tmp = t_1;
	} else if (t_3 <= 5e+43) {
		tmp = t_2;
	} else if (t_3 <= 5e+296) {
		tmp = 2.0 / t;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) + -2.0;
	double t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_3 <= -1e+105) {
		tmp = t_1;
	} else if (t_3 <= 5e+43) {
		tmp = t_2;
	} else if (t_3 <= 5e+296) {
		tmp = 2.0 / t;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (x / y) + -2.0
	t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if t_3 <= -1e+105:
		tmp = t_1
	elif t_3 <= 5e+43:
		tmp = t_2
	elif t_3 <= 5e+296:
		tmp = 2.0 / t
	elif t_3 <= math.inf:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(x / y) + -2.0)
	t_3 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if (t_3 <= -1e+105)
		tmp = t_1;
	elseif (t_3 <= 5e+43)
		tmp = t_2;
	elseif (t_3 <= 5e+296)
		tmp = Float64(2.0 / t);
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = (x / y) + -2.0;
	t_3 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if (t_3 <= -1e+105)
		tmp = t_1;
	elseif (t_3 <= 5e+43)
		tmp = t_2;
	elseif (t_3 <= 5e+296)
		tmp = 2.0 / t;
	elseif (t_3 <= Inf)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -1e+105], t$95$1, If[LessEqual[t$95$3, 5e+43], t$95$2, If[LessEqual[t$95$3, 5e+296], N[(2.0 / t), $MachinePrecision], If[LessEqual[t$95$3, Infinity], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -9.9999999999999994e104 or 5.0000000000000001e296 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 97.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{2 + 2 \cdot z}{t \cdot z}} \]

   5. Applied rewrites 97.6%

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{\frac{2}{z} - -2}{t}} \]

   6. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{2}{t \cdot z}} \]
   7. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2}{t \cdot z}} \]

      2. lower-*.f64 66.6

         \[\leadsto \frac{2}{\color{blue}{t \cdot z}} \]

   8. Applied rewrites 66.6%

      \[\leadsto \color{blue}{\frac{2}{t \cdot z}} \]

   if -9.9999999999999994e104 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 5.0000000000000004e43 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 71.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Applied rewrites 88.0%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]

   if 5.0000000000000004e43 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 5.0000000000000001e296

   1. Initial program 99.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} + 2}}{t} \]

      3. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} + \color{blue}{2 \cdot 1}}{t} \]

      4. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - \left(\mathsf{neg}\left(2\right)\right) \cdot 1}}{t} \]

      5. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2} \cdot 1}{t} \]

      6. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2}}{t} \]

      7. lower--.f64 N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - -2}}{t} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\color{blue}{\frac{2 \cdot 1}{z}} - -2}{t} \]

      9. metadata-eval N/A

         \[\leadsto \frac{\frac{\color{blue}{2}}{z} - -2}{t} \]

      10. lower-/.f64 75.4

          \[\leadsto \frac{\color{blue}{\frac{2}{z}} - -2}{t} \]

   5. Applied rewrites 75.4%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t}} \]

   6. Taylor expanded in z around inf

      \[\leadsto \frac{2}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 49.0%

      \[\leadsto \frac{2}{t} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 84.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{elif}\;t\_1 \leq 20 \lor \neg \left(t\_1 \leq \infty\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(-2, t, 2\right), z, 2\right)}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (<= t_1 -1e+37)
     (/ (- (/ 2.0 z) -2.0) t)
     (if (or (<= t_1 20.0) (not (<= t_1 INFINITY)))
       (+ (/ x y) -2.0)
       (/ (fma (fma -2.0 t 2.0) z 2.0) (* t z))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_1 <= -1e+37) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else if ((t_1 <= 20.0) || !(t_1 <= ((double) INFINITY))) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = fma(fma(-2.0, t, 2.0), z, 2.0) / (t * z);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if (t_1 <= -1e+37)
		tmp = Float64(Float64(Float64(2.0 / z) - -2.0) / t);
	elseif ((t_1 <= 20.0) || !(t_1 <= Inf))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(fma(fma(-2.0, t, 2.0), z, 2.0) / Float64(t * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+37], N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[t$95$1, 20.0], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(N[(-2.0 * t + 2.0), $MachinePrecision] * z + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -9.99999999999999954e36

   1. Initial program 98.2%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} + 2}}{t} \]

      3. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} + \color{blue}{2 \cdot 1}}{t} \]

      4. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - \left(\mathsf{neg}\left(2\right)\right) \cdot 1}}{t} \]

      5. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2} \cdot 1}{t} \]

      6. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2}}{t} \]

      7. lower--.f64 N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - -2}}{t} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\color{blue}{\frac{2 \cdot 1}{z}} - -2}{t} \]

      9. metadata-eval N/A

         \[\leadsto \frac{\frac{\color{blue}{2}}{z} - -2}{t} \]

      10. lower-/.f64 81.8

          \[\leadsto \frac{\color{blue}{\frac{2}{z}} - -2}{t} \]

   5. Applied rewrites 81.8%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t}} \]

   if -9.99999999999999954e36 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 20 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 66.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Applied rewrites 98.2%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]

   if 20 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 98.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

      4. distribute-lft-out-- N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

      5. fp-cancel-sub-sign-inv N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

      14. fp-cancel-sub-sign-inv N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 81.0%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t} - 2} \]

   6. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \frac{1}{t} - \color{blue}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 31.4%

      \[\leadsto \frac{2}{t} - \color{blue}{2} \]

   9. Taylor expanded in z around 0

      \[\leadsto \frac{z \cdot \left(2 \cdot \frac{1}{t} - 2\right) + 2 \cdot \frac{1}{t}}{\color{blue}{z}} \]
   10. Step-by-step derivation

   11. Applied rewrites 80.9%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -1 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{elif}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq 20 \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq \infty\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(-2, t, 2\right), z, 2\right)}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+37} \lor \neg \left(t\_1 \leq 20 \lor \neg \left(t\_1 \leq \infty\right)\right):\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (or (<= t_1 -1e+37) (not (or (<= t_1 20.0) (not (<= t_1 INFINITY)))))
     (/ (- (/ 2.0 z) -2.0) t)
     (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if ((t_1 <= -1e+37) || !((t_1 <= 20.0) || !(t_1 <= ((double) INFINITY)))) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if ((t_1 <= -1e+37) || !((t_1 <= 20.0) || !(t_1 <= Double.POSITIVE_INFINITY))) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if (t_1 <= -1e+37) or not ((t_1 <= 20.0) or not (t_1 <= math.inf)):
		tmp = ((2.0 / z) - -2.0) / t
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if ((t_1 <= -1e+37) || !((t_1 <= 20.0) || !(t_1 <= Inf)))
		tmp = Float64(Float64(Float64(2.0 / z) - -2.0) / t);
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if ((t_1 <= -1e+37) || ~(((t_1 <= 20.0) || ~((t_1 <= Inf)))))
		tmp = ((2.0 / z) - -2.0) / t;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+37], N[Not[Or[LessEqual[t$95$1, 20.0], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]]], $MachinePrecision]], N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -9.99999999999999954e36 or 20 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 98.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} + 2}}{t} \]

      3. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} + \color{blue}{2 \cdot 1}}{t} \]

      4. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - \left(\mathsf{neg}\left(2\right)\right) \cdot 1}}{t} \]

      5. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2} \cdot 1}{t} \]

      6. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2}}{t} \]

      7. lower--.f64 N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - -2}}{t} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\color{blue}{\frac{2 \cdot 1}{z}} - -2}{t} \]

      9. metadata-eval N/A

         \[\leadsto \frac{\frac{\color{blue}{2}}{z} - -2}{t} \]

      10. lower-/.f64 80.6

          \[\leadsto \frac{\color{blue}{\frac{2}{z}} - -2}{t} \]

   5. Applied rewrites 80.6%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t}} \]

   if -9.99999999999999954e36 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 20 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 66.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Applied rewrites 98.2%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -1 \cdot 10^{+37} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq 20 \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq \infty\right)\right):\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+37} \lor \neg \left(t\_1 \leq 20 \lor \neg \left(t\_1 \leq \infty\right)\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(z, 2, 2\right)}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (or (<= t_1 -1e+37) (not (or (<= t_1 20.0) (not (<= t_1 INFINITY)))))
     (/ (fma z 2.0 2.0) (* z t))
     (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if ((t_1 <= -1e+37) || !((t_1 <= 20.0) || !(t_1 <= ((double) INFINITY)))) {
		tmp = fma(z, 2.0, 2.0) / (z * t);
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if ((t_1 <= -1e+37) || !((t_1 <= 20.0) || !(t_1 <= Inf)))
		tmp = Float64(fma(z, 2.0, 2.0) / Float64(z * t));
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+37], N[Not[Or[LessEqual[t$95$1, 20.0], N[Not[LessEqual[t$95$1, Infinity]], $MachinePrecision]]], $MachinePrecision]], N[(N[(z * 2.0 + 2.0), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < -9.99999999999999954e36 or 20 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 98.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} + 2}}{t} \]

      3. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} + \color{blue}{2 \cdot 1}}{t} \]

      4. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - \left(\mathsf{neg}\left(2\right)\right) \cdot 1}}{t} \]

      5. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2} \cdot 1}{t} \]

      6. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2}}{t} \]

      7. lower--.f64 N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - -2}}{t} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\color{blue}{\frac{2 \cdot 1}{z}} - -2}{t} \]

      9. metadata-eval N/A

         \[\leadsto \frac{\frac{\color{blue}{2}}{z} - -2}{t} \]

      10. lower-/.f64 80.6

          \[\leadsto \frac{\color{blue}{\frac{2}{z}} - -2}{t} \]

   5. Applied rewrites 80.6%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t}} \]

   6. Taylor expanded in z around 0

      \[\leadsto \frac{2 \cdot \frac{z}{t} + 2 \cdot \frac{1}{t}}{\color{blue}{z}} \]
   7. Step-by-step derivation

   8. Applied rewrites 80.4%

      \[\leadsto \frac{\mathsf{fma}\left(z, 2, 2\right)}{\color{blue}{z \cdot t}} \]

   if -9.99999999999999954e36 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 20 or +inf.0 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 66.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Applied rewrites 98.2%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq -1 \cdot 10^{+37} \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq 20 \lor \neg \left(\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \leq \infty\right)\right):\\ \;\;\;\;\frac{\mathsf{fma}\left(z, 2, 2\right)}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{z} - -2}{t}\\ \mathbf{if}\;\frac{x}{y} \leq -11600:\\ \;\;\;\;\frac{x}{y} + \frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{y} \leq 6.5 \cdot 10^{-15}:\\ \;\;\;\;t\_1 - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- (/ 2.0 z) -2.0) t)))
   (if (<= (/ x y) -11600.0)
     (+ (/ x y) (/ (fma 2.0 z 2.0) (* t z)))
     (if (<= (/ x y) 6.5e-15) (- t_1 2.0) (+ (/ x y) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / z) - -2.0) / t;
	double tmp;
	if ((x / y) <= -11600.0) {
		tmp = (x / y) + (fma(2.0, z, 2.0) / (t * z));
	} else if ((x / y) <= 6.5e-15) {
		tmp = t_1 - 2.0;
	} else {
		tmp = (x / y) + t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(2.0 / z) - -2.0) / t)
	tmp = 0.0
	if (Float64(x / y) <= -11600.0)
		tmp = Float64(Float64(x / y) + Float64(fma(2.0, z, 2.0) / Float64(t * z)));
	elseif (Float64(x / y) <= 6.5e-15)
		tmp = Float64(t_1 - 2.0);
	else
		tmp = Float64(Float64(x / y) + t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -11600.0], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 * z + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 6.5e-15], N[(t$95$1 - 2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -11600

   1. Initial program 84.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

         \[\leadsto \frac{x}{y} + \frac{\color{blue}{2 \cdot z + 2}}{t \cdot z} \]

      2. lower-fma.f64 97.4

         \[\leadsto \frac{x}{y} + \frac{\color{blue}{\mathsf{fma}\left(2, z, 2\right)}}{t \cdot z} \]

   5. Applied rewrites 97.4%

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{\mathsf{fma}\left(2, z, 2\right)}}{t \cdot z} \]

   if -11600 < (/.f64 x y) < 6.49999999999999991e-15

   1. Initial program 89.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

      4. distribute-lft-out-- N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

      5. fp-cancel-sub-sign-inv N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

      14. fp-cancel-sub-sign-inv N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t} - 2} \]

   if 6.49999999999999991e-15 < (/.f64 x y)

   1. Initial program 80.3%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{2 + 2 \cdot z}{t \cdot z}} \]

   5. Applied rewrites 98.2%

      \[\leadsto \frac{x}{y} + \color{blue}{\frac{\frac{2}{z} - -2}{t}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 98.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -11600 \lor \neg \left(\frac{x}{y} \leq 8.2 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y} + \frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -11600.0) (not (<= (/ x y) 8.2e-11)))
   (+ (/ x y) (/ (fma 2.0 z 2.0) (* t z)))
   (- (/ (- (/ 2.0 z) -2.0) t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -11600.0) || !((x / y) <= 8.2e-11)) {
		tmp = (x / y) + (fma(2.0, z, 2.0) / (t * z));
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -11600.0) || !(Float64(x / y) <= 8.2e-11))
		tmp = Float64(Float64(x / y) + Float64(fma(2.0, z, 2.0) / Float64(t * z)));
	else
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -11600.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 8.2e-11]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 * z + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -11600 or 8.2000000000000001e-11 < (/.f64 x y)

   1. Initial program 82.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

         \[\leadsto \frac{x}{y} + \frac{\color{blue}{2 \cdot z + 2}}{t \cdot z} \]

      2. lower-fma.f64 97.7

         \[\leadsto \frac{x}{y} + \frac{\color{blue}{\mathsf{fma}\left(2, z, 2\right)}}{t \cdot z} \]

   5. Applied rewrites 97.7%

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{\mathsf{fma}\left(2, z, 2\right)}}{t \cdot z} \]

   if -11600 < (/.f64 x y) < 8.2000000000000001e-11

   1. Initial program 89.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

      4. distribute-lft-out-- N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

      5. fp-cancel-sub-sign-inv N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

      14. fp-cancel-sub-sign-inv N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -11600 \lor \neg \left(\frac{x}{y} \leq 8.2 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x}{y} + \frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 92.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.6 \cdot 10^{+71} \lor \neg \left(\frac{x}{y} \leq 4.2 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2.6e+71) (not (<= (/ x y) 4.2e+19)))
   (+ (/ x y) (/ 2.0 (* t z)))
   (- (/ (- (/ 2.0 z) -2.0) t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.6e+71) || !((x / y) <= 4.2e+19)) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2.6d+71)) .or. (.not. ((x / y) <= 4.2d+19))) then
        tmp = (x / y) + (2.0d0 / (t * z))
    else
        tmp = (((2.0d0 / z) - (-2.0d0)) / t) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.6e+71) || !((x / y) <= 4.2e+19)) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2.6e+71) or not ((x / y) <= 4.2e+19):
		tmp = (x / y) + (2.0 / (t * z))
	else:
		tmp = (((2.0 / z) - -2.0) / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2.6e+71) || !(Float64(x / y) <= 4.2e+19))
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	else
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2.6e+71) || ~(((x / y) <= 4.2e+19)))
		tmp = (x / y) + (2.0 / (t * z));
	else
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2.6e+71], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4.2e+19]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.59999999999999991e71 or 4.2e19 < (/.f64 x y)

   1. Initial program 80.2%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 91.1%

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{2}}{t \cdot z} \]

   if -2.59999999999999991e71 < (/.f64 x y) < 4.2e19

   1. Initial program 90.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

      4. distribute-lft-out-- N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

      5. fp-cancel-sub-sign-inv N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

      14. fp-cancel-sub-sign-inv N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 97.5%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.6 \cdot 10^{+71} \lor \neg \left(\frac{x}{y} \leq 4.2 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.45 \cdot 10^{+146} \lor \neg \left(\frac{x}{y} \leq 2.05 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1.45e+146) (not (<= (/ x y) 2.05e+30)))
   (/ x y)
   (- (/ (- (/ 2.0 z) -2.0) t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.45e+146) || !((x / y) <= 2.05e+30)) {
		tmp = x / y;
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1.45d+146)) .or. (.not. ((x / y) <= 2.05d+30))) then
        tmp = x / y
    else
        tmp = (((2.0d0 / z) - (-2.0d0)) / t) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.45e+146) || !((x / y) <= 2.05e+30)) {
		tmp = x / y;
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1.45e+146) or not ((x / y) <= 2.05e+30):
		tmp = x / y
	else:
		tmp = (((2.0 / z) - -2.0) / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1.45e+146) || !(Float64(x / y) <= 2.05e+30))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1.45e+146) || ~(((x / y) <= 2.05e+30)))
		tmp = x / y;
	else
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1.45e+146], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2.05e+30]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.4499999999999999e146 or 2.05000000000000003e30 < (/.f64 x y)

   1. Initial program 76.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]

   5. Applied rewrites 74.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{x}{y} - 2, t, \frac{2}{z} - -2\right)}{t}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(-2, t, \frac{2}{z} - -2\right)}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 18.1%

      \[\leadsto \frac{\mathsf{fma}\left(-2, t, \frac{2}{z} - -2\right)}{t} \]

   9. Taylor expanded in x around inf

      \[\leadsto \frac{x}{\color{blue}{y}} \]
   10. Step-by-step derivation

   11. Applied rewrites 86.4%

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

   if -1.4499999999999999e146 < (/.f64 x y) < 2.05000000000000003e30

   1. Initial program 90.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

      4. distribute-lft-out-- N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

      5. fp-cancel-sub-sign-inv N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

      14. fp-cancel-sub-sign-inv N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 93.3%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.45 \cdot 10^{+146} \lor \neg \left(\frac{x}{y} \leq 2.05 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.5 \cdot 10^{+87} \lor \neg \left(\frac{x}{y} \leq 4.2 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4.5e+87) (not (<= (/ x y) 4.2e+19)))
   (/ x y)
   (- (/ 2.0 t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4.5e+87) || !((x / y) <= 4.2e+19)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-4.5d+87)) .or. (.not. ((x / y) <= 4.2d+19))) then
        tmp = x / y
    else
        tmp = (2.0d0 / t) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4.5e+87) || !((x / y) <= 4.2e+19)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -4.5e+87) or not ((x / y) <= 4.2e+19):
		tmp = x / y
	else:
		tmp = (2.0 / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4.5e+87) || !(Float64(x / y) <= 4.2e+19))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(2.0 / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -4.5e+87) || ~(((x / y) <= 4.2e+19)))
		tmp = x / y;
	else
		tmp = (2.0 / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -4.5e+87], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4.2e+19]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.5000000000000003e87 or 4.2e19 < (/.f64 x y)

   1. Initial program 79.2%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]

   5. Applied rewrites 75.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{x}{y} - 2, t, \frac{2}{z} - -2\right)}{t}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(-2, t, \frac{2}{z} - -2\right)}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 24.6%

      \[\leadsto \frac{\mathsf{fma}\left(-2, t, \frac{2}{z} - -2\right)}{t} \]

   9. Taylor expanded in x around inf

      \[\leadsto \frac{x}{\color{blue}{y}} \]
   10. Step-by-step derivation

   11. Applied rewrites 79.7%

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

   if -4.5000000000000003e87 < (/.f64 x y) < 4.2e19

   1. Initial program 90.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

      4. distribute-lft-out-- N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

      5. fp-cancel-sub-sign-inv N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

      14. fp-cancel-sub-sign-inv N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 96.4%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t} - 2} \]

   6. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \frac{1}{t} - \color{blue}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 56.0%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.5 \cdot 10^{+87} \lor \neg \left(\frac{x}{y} \leq 4.2 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.5 \cdot 10^{+87}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -4.5e+87)
   (/ x y)
   (if (<= (/ x y) 4.2e+19) (- (/ 2.0 t) 2.0) (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4.5e+87) {
		tmp = x / y;
	} else if ((x / y) <= 4.2e+19) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-4.5d+87)) then
        tmp = x / y
    else if ((x / y) <= 4.2d+19) then
        tmp = (2.0d0 / t) - 2.0d0
    else
        tmp = (x / y) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -4.5e+87) {
		tmp = x / y;
	} else if ((x / y) <= 4.2e+19) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -4.5e+87:
		tmp = x / y
	elif (x / y) <= 4.2e+19:
		tmp = (2.0 / t) - 2.0
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -4.5e+87)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 4.2e+19)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -4.5e+87)
		tmp = x / y;
	elseif ((x / y) <= 4.2e+19)
		tmp = (2.0 / t) - 2.0;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -4.5e+87], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4.2e+19], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.5000000000000003e87

   1. Initial program 80.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]

   5. Applied rewrites 74.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{x}{y} - 2, t, \frac{2}{z} - -2\right)}{t}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(-2, t, \frac{2}{z} - -2\right)}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 25.6%

      \[\leadsto \frac{\mathsf{fma}\left(-2, t, \frac{2}{z} - -2\right)}{t} \]

   9. Taylor expanded in x around inf

      \[\leadsto \frac{x}{\color{blue}{y}} \]
   10. Step-by-step derivation

   11. Applied rewrites 81.3%

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

   if -4.5000000000000003e87 < (/.f64 x y) < 4.2e19

   1. Initial program 90.7%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{2 \cdot \frac{1 - t}{t} + 2 \cdot \frac{1}{t \cdot z}} \]
   4. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1 - t}{t}} \]

      2. div-sub N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \color{blue}{\left(\frac{1}{t} - \frac{t}{t}\right)} \]

      3. *-inverses N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + 2 \cdot \left(\frac{1}{t} - \color{blue}{1}\right) \]

      4. distribute-lft-out-- N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} - 2 \cdot 1\right)} \]

      5. fp-cancel-sub-sign-inv N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \color{blue}{\left(2 \cdot \frac{1}{t} + \left(\mathsf{neg}\left(2\right)\right) \cdot 1\right)} \]

      6. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2} \cdot 1\right) \]

      7. metadata-eval N/A

         \[\leadsto 2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + \color{blue}{-2}\right) \]

      8. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + -2} \]

      9. +-commutative N/A

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right)} + -2 \]

      10. associate-*r/ N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + -2 \]

      11. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + -2 \]

      12. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{-2 \cdot 1} \]

      13. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \color{blue}{\left(\mathsf{neg}\left(2\right)\right)} \cdot 1 \]

      14. fp-cancel-sub-sign-inv N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2 \cdot 1} \]

      15. metadata-eval N/A

          \[\leadsto \left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - \color{blue}{2} \]

      16. lower--.f64 N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2} \]

   5. Applied rewrites 96.4%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t} - 2} \]

   6. Taylor expanded in z around inf

      \[\leadsto 2 \cdot \frac{1}{t} - \color{blue}{2} \]
   7. Step-by-step derivation

   8. Applied rewrites 56.0%

      \[\leadsto \frac{2}{t} - \color{blue}{2} \]

   if 4.2e19 < (/.f64 x y)

   1. Initial program 77.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
   4. Step-by-step derivation

   5. Applied rewrites 78.1%

      \[\leadsto \frac{x}{y} + \color{blue}{-2} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 46.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.6 \cdot 10^{+71} \lor \neg \left(\frac{x}{y} \leq 4.2 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2.6e+71) (not (<= (/ x y) 4.2e+19))) (/ x y) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.6e+71) || !((x / y) <= 4.2e+19)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2.6d+71)) .or. (.not. ((x / y) <= 4.2d+19))) then
        tmp = x / y
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.6e+71) || !((x / y) <= 4.2e+19)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2.6e+71) or not ((x / y) <= 4.2e+19):
		tmp = x / y
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2.6e+71) || !(Float64(x / y) <= 4.2e+19))
		tmp = Float64(x / y);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2.6e+71) || ~(((x / y) <= 4.2e+19)))
		tmp = x / y;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2.6e+71], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4.2e+19]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.59999999999999991e71 or 4.2e19 < (/.f64 x y)

   1. Initial program 80.2%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]

   5. Applied rewrites 76.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{x}{y} - 2, t, \frac{2}{z} - -2\right)}{t}} \]

   6. Taylor expanded in x around 0

      \[\leadsto \frac{\mathsf{fma}\left(-2, t, \frac{2}{z} - -2\right)}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 26.3%

      \[\leadsto \frac{\mathsf{fma}\left(-2, t, \frac{2}{z} - -2\right)}{t} \]

   9. Taylor expanded in x around inf

      \[\leadsto \frac{x}{\color{blue}{y}} \]
   10. Step-by-step derivation

   11. Applied rewrites 78.0%

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

   if -2.59999999999999991e71 < (/.f64 x y) < 4.2e19

   1. Initial program 90.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]

      2. +-commutative N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} + 2}}{t} \]

      3. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} + \color{blue}{2 \cdot 1}}{t} \]

      4. fp-cancel-sign-sub-inv N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - \left(\mathsf{neg}\left(2\right)\right) \cdot 1}}{t} \]

      5. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2} \cdot 1}{t} \]

      6. metadata-eval N/A

         \[\leadsto \frac{2 \cdot \frac{1}{z} - \color{blue}{-2}}{t} \]

      7. lower--.f64 N/A

         \[\leadsto \frac{\color{blue}{2 \cdot \frac{1}{z} - -2}}{t} \]

      8. associate-*r/ N/A

         \[\leadsto \frac{\color{blue}{\frac{2 \cdot 1}{z}} - -2}{t} \]

      9. metadata-eval N/A

         \[\leadsto \frac{\frac{\color{blue}{2}}{z} - -2}{t} \]

      10. lower-/.f64 69.7

          \[\leadsto \frac{\color{blue}{\frac{2}{z}} - -2}{t} \]

   5. Applied rewrites 69.7%

      \[\leadsto \color{blue}{\frac{\frac{2}{z} - -2}{t}} \]

   6. Taylor expanded in z around inf

      \[\leadsto \frac{2}{t} \]
   7. Step-by-step derivation

   8. Applied rewrites 29.6%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.6 \cdot 10^{+71} \lor \neg \left(\frac{x}{y} \leq 4.2 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 35.2% accurate, 3.9× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(x / y), $MachinePrecision]

Derivation

1. Initial program 86.1%

   \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
2. Add Preprocessing

3. Taylor expanded in t around 0

   \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]
4. Step-by-step derivation

   1. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]

5. Applied rewrites 89.7%

   \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\frac{x}{y} - 2, t, \frac{2}{z} - -2\right)}{t}} \]

6. Taylor expanded in x around 0

   \[\leadsto \frac{\mathsf{fma}\left(-2, t, \frac{2}{z} - -2\right)}{t} \]
7. Step-by-step derivation

8. Applied rewrites 67.7%

   \[\leadsto \frac{\mathsf{fma}\left(-2, t, \frac{2}{z} - -2\right)}{t} \]

9. Taylor expanded in x around inf

   \[\leadsto \frac{x}{\color{blue}{y}} \]
10. Step-by-step derivation

11. Applied rewrites 35.1%

    \[\leadsto \frac{x}{\color{blue}{y}} \]
12. Add Preprocessing

Developer Target 1: 99.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y))))

C

double code(double x, double y, double z, double t) {
	return (((2.0 / z) + 2.0) / t) - (2.0 - (x / y));
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((2.0d0 / z) + 2.0d0) / t) - (2.0d0 - (x / y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((2.0 / z) + 2.0) / t) - (2.0 - (x / y));
}

Python

def code(x, y, z, t):
	return (((2.0 / z) + 2.0) / t) - (2.0 - (x / y))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(2.0 / z) + 2.0) / t) - Float64(2.0 - Float64(x / y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((2.0 / z) + 2.0) / t) - (2.0 - (x / y));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(2.0 / z), $MachinePrecision] + 2.0), $MachinePrecision] / t), $MachinePrecision] - N[(2.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2025008 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y))))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))