Data.Metrics.Snapshot:quantile from metrics-0.3.0.2

Percentage Accurate: 100.0% → 100.0%

Time: 2.7s

Alternatives: 11

Speedup: 1.1×

• 33.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. lift-+.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift--.f64 N/A

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

   5. +-commutative N/A

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

   6. lower-fma.f64 N/A

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

   7. lift--.f64 N/A

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

   8. lift--.f64 100.0

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

3. Applied rewrites 100.0%

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

Alternative 2: 84.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - t\right) \cdot z\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+99}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-95}:\\ \;\;\;\;\mathsf{fma}\left(y - z, t, x\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x t) z)))
   (if (<= z -5.5e+99)
     t_1
     (if (<= z -2.7e-95)
       (fma (- y z) t x)
       (if (<= z 6.6e+27) (fma (- t x) y x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - t) * z;
	double tmp;
	if (z <= -5.5e+99) {
		tmp = t_1;
	} else if (z <= -2.7e-95) {
		tmp = fma((y - z), t, x);
	} else if (z <= 6.6e+27) {
		tmp = fma((t - x), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - t) * z)
	tmp = 0.0
	if (z <= -5.5e+99)
		tmp = t_1;
	elseif (z <= -2.7e-95)
		tmp = fma(Float64(y - z), t, x);
	elseif (z <= 6.6e+27)
		tmp = fma(Float64(t - x), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -5.5e+99], t$95$1, If[LessEqual[z, -2.7e-95], N[(N[(y - z), $MachinePrecision] * t + x), $MachinePrecision], If[LessEqual[z, 6.6e+27], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5000000000000002e99 or 6.5999999999999996e27 < z

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

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

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

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

      10. distribute-rgt-out N/A

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

      11. associate-*r* N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lift--.f64 N/A

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

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

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

      18. lower--.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-lft-identity N/A

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

      21. *-commutative N/A

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

      22. lower-*.f64 N/A

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

      23. lift--.f64 96.0

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

   3. Applied rewrites 96.0%

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

   4. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 83.6

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

   6. Applied rewrites 83.6%

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

   if -5.5000000000000002e99 < z < -2.7e-95

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 100.0

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

   3. Applied rewrites 100.0%

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

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(y - z, \color{blue}{t}, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 61.3%

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

   if -2.7e-95 < z < 6.5999999999999996e27

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 90.6

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

   4. Applied rewrites 90.6%

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

Alternative 3: 83.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - t\right) \cdot z\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+27}:\\ \;\;\;\;\mathsf{fma}\left(t - x, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x t) z)))
   (if (<= z -8.2e+69) t_1 (if (<= z 6.6e+27) (fma (- t x) y x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - t) * z;
	double tmp;
	if (z <= -8.2e+69) {
		tmp = t_1;
	} else if (z <= 6.6e+27) {
		tmp = fma((t - x), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - t) * z)
	tmp = 0.0
	if (z <= -8.2e+69)
		tmp = t_1;
	elseif (z <= 6.6e+27)
		tmp = fma(Float64(t - x), y, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -8.2e+69], t$95$1, If[LessEqual[z, 6.6e+27], N[(N[(t - x), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.1999999999999998e69 or 6.5999999999999996e27 < z

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

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

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

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

      10. distribute-rgt-out N/A

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

      11. associate-*r* N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lift--.f64 N/A

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

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

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

      18. lower--.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-lft-identity N/A

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

      21. *-commutative N/A

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

      22. lower-*.f64 N/A

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

      23. lift--.f64 96.0

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

   3. Applied rewrites 96.0%

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

   4. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 82.7

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

   6. Applied rewrites 82.7%

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

   if -8.1999999999999998e69 < z < 6.5999999999999996e27

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lift--.f64 85.1

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

   4. Applied rewrites 85.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(t - x, y, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 68.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - t\right) \cdot z\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-64}:\\ \;\;\;\;\left(y - z\right) \cdot t\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-272}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+27}:\\ \;\;\;\;\left(t - x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x t) z)))
   (if (<= z -6.8e+93)
     t_1
     (if (<= z -2.6e-64)
       (* (- y z) t)
       (if (<= z 1.25e-272)
         (* (- 1.0 y) x)
         (if (<= z 6.6e+27) (* (- t x) y) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - t) * z;
	double tmp;
	if (z <= -6.8e+93) {
		tmp = t_1;
	} else if (z <= -2.6e-64) {
		tmp = (y - z) * t;
	} else if (z <= 1.25e-272) {
		tmp = (1.0 - y) * x;
	} else if (z <= 6.6e+27) {
		tmp = (t - x) * y;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (x - t) * z
    if (z <= (-6.8d+93)) then
        tmp = t_1
    else if (z <= (-2.6d-64)) then
        tmp = (y - z) * t
    else if (z <= 1.25d-272) then
        tmp = (1.0d0 - y) * x
    else if (z <= 6.6d+27) then
        tmp = (t - x) * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - t) * z;
	double tmp;
	if (z <= -6.8e+93) {
		tmp = t_1;
	} else if (z <= -2.6e-64) {
		tmp = (y - z) * t;
	} else if (z <= 1.25e-272) {
		tmp = (1.0 - y) * x;
	} else if (z <= 6.6e+27) {
		tmp = (t - x) * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - t) * z
	tmp = 0
	if z <= -6.8e+93:
		tmp = t_1
	elif z <= -2.6e-64:
		tmp = (y - z) * t
	elif z <= 1.25e-272:
		tmp = (1.0 - y) * x
	elif z <= 6.6e+27:
		tmp = (t - x) * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - t) * z)
	tmp = 0.0
	if (z <= -6.8e+93)
		tmp = t_1;
	elseif (z <= -2.6e-64)
		tmp = Float64(Float64(y - z) * t);
	elseif (z <= 1.25e-272)
		tmp = Float64(Float64(1.0 - y) * x);
	elseif (z <= 6.6e+27)
		tmp = Float64(Float64(t - x) * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - t) * z;
	tmp = 0.0;
	if (z <= -6.8e+93)
		tmp = t_1;
	elseif (z <= -2.6e-64)
		tmp = (y - z) * t;
	elseif (z <= 1.25e-272)
		tmp = (1.0 - y) * x;
	elseif (z <= 6.6e+27)
		tmp = (t - x) * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - t), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -6.8e+93], t$95$1, If[LessEqual[z, -2.6e-64], N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 1.25e-272], N[(N[(1.0 - y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 6.6e+27], N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.8000000000000001e93 or 6.5999999999999996e27 < z

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

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

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

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

      10. distribute-rgt-out N/A

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

      11. associate-*r* N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lift--.f64 N/A

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

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

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

      18. lower--.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-lft-identity N/A

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

      21. *-commutative N/A

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

      22. lower-*.f64 N/A

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

      23. lift--.f64 96.0

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

   3. Applied rewrites 96.0%

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

   4. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 83.6

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

   6. Applied rewrites 83.6%

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

   if -6.8000000000000001e93 < z < -2.6e-64

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 50.8

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

   4. Applied rewrites 50.8%

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

   if -2.6e-64 < z < 1.24999999999999995e-272

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

      5. *-lft-identity N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      7. lift--.f64 62.2

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   4. Applied rewrites 62.2%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 62.2%

      \[\leadsto \left(1 - y\right) \cdot x \]

   if 1.24999999999999995e-272 < z < 6.5999999999999996e27

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 55.8

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

   4. Applied rewrites 55.8%

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

Alternative 5: 67.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot y\\ \mathbf{if}\;y \leq -4.7:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-101}:\\ \;\;\;\;\mathsf{fma}\left(-z, t, x\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+172}:\\ \;\;\;\;\left(x - t\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t x) y)))
   (if (<= y -4.7)
     t_1
     (if (<= y 4.7e-101)
       (fma (- z) t x)
       (if (<= y 3.4e+172) (* (- x t) z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * y;
	double tmp;
	if (y <= -4.7) {
		tmp = t_1;
	} else if (y <= 4.7e-101) {
		tmp = fma(-z, t, x);
	} else if (y <= 3.4e+172) {
		tmp = (x - t) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t - x) * y)
	tmp = 0.0
	if (y <= -4.7)
		tmp = t_1;
	elseif (y <= 4.7e-101)
		tmp = fma(Float64(-z), t, x);
	elseif (y <= 3.4e+172)
		tmp = Float64(Float64(x - t) * z);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -4.7], t$95$1, If[LessEqual[y, 4.7e-101], N[((-z) * t + x), $MachinePrecision], If[LessEqual[y, 3.4e+172], N[(N[(x - t), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.70000000000000018 or 3.3999999999999998e172 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 82.8

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

   4. Applied rewrites 82.8%

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

   if -4.70000000000000018 < y < 4.6999999999999999e-101

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lift--.f64 100.0

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

   3. Applied rewrites 100.0%

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

   4. Taylor expanded in x around 0

      \[\leadsto \mathsf{fma}\left(y - z, \color{blue}{t}, x\right) \]
   5. Step-by-step derivation

   6. Applied rewrites 76.2%

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

   7. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\color{blue}{-1 \cdot z}, t, x\right) \]
   8. Step-by-step derivation

      1. mul-1-neg N/A

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

      2. lower-neg.f64 69.3

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

   9. Applied rewrites 69.3%

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

   if 4.6999999999999999e-101 < y < 3.3999999999999998e172

   1. Initial program 100.0%

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

      1. lift-+.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. +-commutative N/A

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

      6. *-commutative N/A

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

      7. *-lft-identity N/A

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

      8. metadata-eval N/A

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

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

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

      10. distribute-rgt-out N/A

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

      11. associate-*r* N/A

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

      12. associate-+l+ N/A

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

      13. +-commutative N/A

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

      14. *-commutative N/A

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

      15. lower-fma.f64 N/A

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

      16. lift--.f64 N/A

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

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

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

      18. lower--.f64 N/A

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

      19. metadata-eval N/A

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

      20. *-lft-identity N/A

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

      21. *-commutative N/A

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

      22. lower-*.f64 N/A

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

      23. lift--.f64 99.5

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

   3. Applied rewrites 99.5%

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

   4. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 44.4

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

   6. Applied rewrites 44.4%

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

Alternative 6: 59.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot t\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{-72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-287}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-50}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) t)))
   (if (<= t -8.8e-72)
     t_1
     (if (<= t -4.8e-287) (* z x) (if (<= t 2.4e-50) (* (- 1.0 y) x) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -8.8e-72) {
		tmp = t_1;
	} else if (t <= -4.8e-287) {
		tmp = z * x;
	} else if (t <= 2.4e-50) {
		tmp = (1.0 - y) * x;
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * t
    if (t <= (-8.8d-72)) then
        tmp = t_1
    else if (t <= (-4.8d-287)) then
        tmp = z * x
    else if (t <= 2.4d-50) then
        tmp = (1.0d0 - y) * x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * t;
	double tmp;
	if (t <= -8.8e-72) {
		tmp = t_1;
	} else if (t <= -4.8e-287) {
		tmp = z * x;
	} else if (t <= 2.4e-50) {
		tmp = (1.0 - y) * x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * t
	tmp = 0
	if t <= -8.8e-72:
		tmp = t_1
	elif t <= -4.8e-287:
		tmp = z * x
	elif t <= 2.4e-50:
		tmp = (1.0 - y) * x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * t)
	tmp = 0.0
	if (t <= -8.8e-72)
		tmp = t_1;
	elseif (t <= -4.8e-287)
		tmp = Float64(z * x);
	elseif (t <= 2.4e-50)
		tmp = Float64(Float64(1.0 - y) * x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * t;
	tmp = 0.0;
	if (t <= -8.8e-72)
		tmp = t_1;
	elseif (t <= -4.8e-287)
		tmp = z * x;
	elseif (t <= 2.4e-50)
		tmp = (1.0 - y) * x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -8.8e-72], t$95$1, If[LessEqual[t, -4.8e-287], N[(z * x), $MachinePrecision], If[LessEqual[t, 2.4e-50], N[(N[(1.0 - y), $MachinePrecision] * x), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.8000000000000001e-72 or 2.40000000000000002e-50 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 68.4

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

   4. Applied rewrites 68.4%

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

   if -8.8000000000000001e-72 < t < -4.79999999999999999e-287

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

      5. *-lft-identity N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      7. lift--.f64 82.3

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   4. Applied rewrites 82.3%

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

   5. Taylor expanded in z around inf

      \[\leadsto z \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 32.6%

      \[\leadsto z \cdot x \]

   if -4.79999999999999999e-287 < t < 2.40000000000000002e-50

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

      5. *-lft-identity N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      7. lift--.f64 82.9

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   4. Applied rewrites 82.9%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 55.4%

      \[\leadsto \left(1 - y\right) \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 52.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(t - x\right) \cdot y\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+124}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-272}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t x) y)))
   (if (<= z -2.5e+124)
     (* z x)
     (if (<= z -2.1e-62)
       t_1
       (if (<= z 1.25e-272)
         (* (- 1.0 y) x)
         (if (<= z 2.5e+28) t_1 (* z x)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * y;
	double tmp;
	if (z <= -2.5e+124) {
		tmp = z * x;
	} else if (z <= -2.1e-62) {
		tmp = t_1;
	} else if (z <= 1.25e-272) {
		tmp = (1.0 - y) * x;
	} else if (z <= 2.5e+28) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = (t - x) * y
    if (z <= (-2.5d+124)) then
        tmp = z * x
    else if (z <= (-2.1d-62)) then
        tmp = t_1
    else if (z <= 1.25d-272) then
        tmp = (1.0d0 - y) * x
    else if (z <= 2.5d+28) then
        tmp = t_1
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t - x) * y;
	double tmp;
	if (z <= -2.5e+124) {
		tmp = z * x;
	} else if (z <= -2.1e-62) {
		tmp = t_1;
	} else if (z <= 1.25e-272) {
		tmp = (1.0 - y) * x;
	} else if (z <= 2.5e+28) {
		tmp = t_1;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t - x) * y
	tmp = 0
	if z <= -2.5e+124:
		tmp = z * x
	elif z <= -2.1e-62:
		tmp = t_1
	elif z <= 1.25e-272:
		tmp = (1.0 - y) * x
	elif z <= 2.5e+28:
		tmp = t_1
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t - x) * y)
	tmp = 0.0
	if (z <= -2.5e+124)
		tmp = Float64(z * x);
	elseif (z <= -2.1e-62)
		tmp = t_1;
	elseif (z <= 1.25e-272)
		tmp = Float64(Float64(1.0 - y) * x);
	elseif (z <= 2.5e+28)
		tmp = t_1;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t - x) * y;
	tmp = 0.0;
	if (z <= -2.5e+124)
		tmp = z * x;
	elseif (z <= -2.1e-62)
		tmp = t_1;
	elseif (z <= 1.25e-272)
		tmp = (1.0 - y) * x;
	elseif (z <= 2.5e+28)
		tmp = t_1;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - x), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[z, -2.5e+124], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.1e-62], t$95$1, If[LessEqual[z, 1.25e-272], N[(N[(1.0 - y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 2.5e+28], t$95$1, N[(z * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4999999999999998e124 or 2.49999999999999979e28 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

      5. *-lft-identity N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      7. lift--.f64 54.1

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   4. Applied rewrites 54.1%

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

   5. Taylor expanded in z around inf

      \[\leadsto z \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 45.6%

      \[\leadsto z \cdot x \]

   if -2.4999999999999998e124 < z < -2.0999999999999999e-62 or 1.24999999999999995e-272 < z < 2.49999999999999979e28

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 52.5

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

   4. Applied rewrites 52.5%

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

   if -2.0999999999999999e-62 < z < 1.24999999999999995e-272

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

      5. *-lft-identity N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      7. lift--.f64 62.1

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   4. Applied rewrites 62.1%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 62.1%

      \[\leadsto \left(1 - y\right) \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 50.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+123}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+27}:\\ \;\;\;\;\left(1 - y\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.2e+123) (* z x) (if (<= z 6e+27) (* (- 1.0 y) x) (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e+123) {
		tmp = z * x;
	} else if (z <= 6e+27) {
		tmp = (1.0 - y) * x;
	} else {
		tmp = z * x;
	}
	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 (z <= (-1.2d+123)) then
        tmp = z * x
    else if (z <= 6d+27) then
        tmp = (1.0d0 - y) * x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e+123) {
		tmp = z * x;
	} else if (z <= 6e+27) {
		tmp = (1.0 - y) * x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.2e+123:
		tmp = z * x
	elif z <= 6e+27:
		tmp = (1.0 - y) * x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.2e+123)
		tmp = Float64(z * x);
	elseif (z <= 6e+27)
		tmp = Float64(Float64(1.0 - y) * x);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.2e+123)
		tmp = z * x;
	elseif (z <= 6e+27)
		tmp = (1.0 - y) * x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.2e+123], N[(z * x), $MachinePrecision], If[LessEqual[z, 6e+27], N[(N[(1.0 - y), $MachinePrecision] * x), $MachinePrecision], N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.19999999999999994e123 or 5.99999999999999953e27 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

      5. *-lft-identity N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      7. lift--.f64 54.1

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   4. Applied rewrites 54.1%

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

   5. Taylor expanded in z around inf

      \[\leadsto z \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 45.5%

      \[\leadsto z \cdot x \]

   if -1.19999999999999994e123 < z < 5.99999999999999953e27

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

      5. *-lft-identity N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      7. lift--.f64 58.8

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   4. Applied rewrites 58.8%

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

   5. Taylor expanded in y around inf

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

   7. Applied rewrites 52.8%

      \[\leadsto \left(1 - y\right) \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 38.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+99}:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-62}:\\ \;\;\;\;t \cdot y\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-179}:\\ \;\;\;\;1 \cdot x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+27}:\\ \;\;\;\;t \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.5e+99)
   (* z x)
   (if (<= z -2.1e-62)
     (* t y)
     (if (<= z 8.2e-179) (* 1.0 x) (if (<= z 2.2e+27) (* t y) (* z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e+99) {
		tmp = z * x;
	} else if (z <= -2.1e-62) {
		tmp = t * y;
	} else if (z <= 8.2e-179) {
		tmp = 1.0 * x;
	} else if (z <= 2.2e+27) {
		tmp = t * y;
	} else {
		tmp = z * x;
	}
	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 (z <= (-5.5d+99)) then
        tmp = z * x
    else if (z <= (-2.1d-62)) then
        tmp = t * y
    else if (z <= 8.2d-179) then
        tmp = 1.0d0 * x
    else if (z <= 2.2d+27) then
        tmp = t * y
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.5e+99) {
		tmp = z * x;
	} else if (z <= -2.1e-62) {
		tmp = t * y;
	} else if (z <= 8.2e-179) {
		tmp = 1.0 * x;
	} else if (z <= 2.2e+27) {
		tmp = t * y;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.5e+99:
		tmp = z * x
	elif z <= -2.1e-62:
		tmp = t * y
	elif z <= 8.2e-179:
		tmp = 1.0 * x
	elif z <= 2.2e+27:
		tmp = t * y
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.5e+99)
		tmp = Float64(z * x);
	elseif (z <= -2.1e-62)
		tmp = Float64(t * y);
	elseif (z <= 8.2e-179)
		tmp = Float64(1.0 * x);
	elseif (z <= 2.2e+27)
		tmp = Float64(t * y);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.5e+99)
		tmp = z * x;
	elseif (z <= -2.1e-62)
		tmp = t * y;
	elseif (z <= 8.2e-179)
		tmp = 1.0 * x;
	elseif (z <= 2.2e+27)
		tmp = t * y;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.5e+99], N[(z * x), $MachinePrecision], If[LessEqual[z, -2.1e-62], N[(t * y), $MachinePrecision], If[LessEqual[z, 8.2e-179], N[(1.0 * x), $MachinePrecision], If[LessEqual[z, 2.2e+27], N[(t * y), $MachinePrecision], N[(z * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.5000000000000002e99 or 2.1999999999999999e27 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

      5. *-lft-identity N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      7. lift--.f64 54.0

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   4. Applied rewrites 54.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto z \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 45.1%

      \[\leadsto z \cdot x \]

   if -5.5000000000000002e99 < z < -2.0999999999999999e-62 or 8.2e-179 < z < 2.1999999999999999e27

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lift--.f64 52.3

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

   4. Applied rewrites 52.3%

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

   5. Taylor expanded in x around 0

      \[\leadsto t \cdot y \]
   6. Step-by-step derivation

   7. Applied rewrites 29.4%

      \[\leadsto t \cdot y \]

   if -2.0999999999999999e-62 < z < 8.2e-179

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

      5. *-lft-identity N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      7. lift--.f64 63.0

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   4. Applied rewrites 63.0%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 38.7

         \[\leadsto \left(1 + z\right) \cdot x \]

   7. Applied rewrites 38.7%

      \[\leadsto \left(1 + z\right) \cdot x \]

   8. Taylor expanded in z around 0

      \[\leadsto 1 \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 38.7%

       \[\leadsto 1 \cdot x \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 38.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3100000:\\ \;\;\;\;z \cdot x\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-6}:\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -3100000.0) (* z x) (if (<= z 3.7e-6) (* 1.0 x) (* z x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3100000.0) {
		tmp = z * x;
	} else if (z <= 3.7e-6) {
		tmp = 1.0 * x;
	} else {
		tmp = z * x;
	}
	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 (z <= (-3100000.0d0)) then
        tmp = z * x
    else if (z <= 3.7d-6) then
        tmp = 1.0d0 * x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3100000.0) {
		tmp = z * x;
	} else if (z <= 3.7e-6) {
		tmp = 1.0 * x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -3100000.0:
		tmp = z * x
	elif z <= 3.7e-6:
		tmp = 1.0 * x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3100000.0)
		tmp = Float64(z * x);
	elseif (z <= 3.7e-6)
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3100000.0)
		tmp = z * x;
	elseif (z <= 3.7e-6)
		tmp = 1.0 * x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -3100000.0], N[(z * x), $MachinePrecision], If[LessEqual[z, 3.7e-6], N[(1.0 * x), $MachinePrecision], N[(z * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1e6 or 3.7000000000000002e-6 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

      5. *-lft-identity N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      7. lift--.f64 53.4

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   4. Applied rewrites 53.4%

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

   5. Taylor expanded in z around inf

      \[\leadsto z \cdot x \]
   6. Step-by-step derivation

   7. Applied rewrites 41.8%

      \[\leadsto z \cdot x \]

   if -3.1e6 < z < 3.7000000000000002e-6

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

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

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

      4. metadata-eval N/A

         \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

      5. *-lft-identity N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      6. lower--.f64 N/A

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

      7. lift--.f64 60.6

         \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   4. Applied rewrites 60.6%

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

   5. Taylor expanded in y around 0

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

      1. lower-+.f64 35.5

         \[\leadsto \left(1 + z\right) \cdot x \]

   7. Applied rewrites 35.5%

      \[\leadsto \left(1 + z\right) \cdot x \]

   8. Taylor expanded in z around 0

      \[\leadsto 1 \cdot x \]
   9. Step-by-step derivation

   10. Applied rewrites 34.9%

       \[\leadsto 1 \cdot x \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 22.4% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

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 = z * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

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

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

   4. metadata-eval N/A

      \[\leadsto \left(1 - 1 \cdot \left(y - z\right)\right) \cdot x \]

   5. *-lft-identity N/A

      \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   6. lower--.f64 N/A

      \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

   7. lift--.f64 57.0

      \[\leadsto \left(1 - \left(y - z\right)\right) \cdot x \]

4. Applied rewrites 57.0%

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

5. Taylor expanded in z around inf

   \[\leadsto z \cdot x \]
6. Step-by-step derivation

7. Applied rewrites 22.4%

   \[\leadsto z \cdot x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025111 
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64
  (+ x (* (- y z) (- t x))))