Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, H

Percentage Accurate: 95.7% → 99.2%

Time: 4.0s

Alternatives: 14

Speedup: 1.0×

• 27.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * 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 / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * 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 / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{\frac{t}{y} - y}{z}, 0.3333333333333333, x\right)\\ t_2 := \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+298}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+299}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (/ (- (/ t y) y) z) 0.3333333333333333 x))
        (t_2 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y)))))
   (if (<= t_2 -2e+298) t_1 (if (<= t_2 2e+299) t_2 t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((((t / y) - y) / z), 0.3333333333333333, x);
	double t_2 = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	double tmp;
	if (t_2 <= -2e+298) {
		tmp = t_1;
	} else if (t_2 <= 2e+299) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(Float64(Float64(t / y) - y) / z), 0.3333333333333333, x)
	t_2 = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
	tmp = 0.0
	if (t_2 <= -2e+298)
		tmp = t_1;
	elseif (t_2 <= 2e+299)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision] * 0.3333333333333333 + x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+298], t$95$1, If[LessEqual[t$95$2, 2e+299], t$95$2, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y))) < -1.9999999999999999e298 or 2.0000000000000001e299 < (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y)))

   1. Initial program 88.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around 0

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

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z}\right)} \]

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

         \[\leadsto x + \frac{1}{3} \cdot \color{blue}{\left(\frac{t}{y \cdot z} - \frac{y}{z}\right)} \]

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

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \left(\frac{t}{y \cdot z} - \frac{y}{z}\right)} \]

      4. metadata-eval N/A

         \[\leadsto x - \frac{-1}{3} \cdot \left(\color{blue}{\frac{t}{y \cdot z}} - \frac{y}{z}\right) \]

      5. associate-/r* N/A

         \[\leadsto x - \frac{-1}{3} \cdot \left(\frac{\frac{t}{y}}{z} - \frac{\color{blue}{y}}{z}\right) \]

      6. sub-div N/A

         \[\leadsto x - \frac{-1}{3} \cdot \frac{\frac{t}{y} - y}{\color{blue}{z}} \]

      7. associate-/l* N/A

         \[\leadsto x - \frac{\frac{-1}{3} \cdot \left(\frac{t}{y} - y\right)}{\color{blue}{z}} \]

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

         \[\leadsto x - \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z} \]

      9. *-lft-identity N/A

         \[\leadsto x - 1 \cdot \color{blue}{\frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z}} \]

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

          \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z}} \]

      11. metadata-eval N/A

          \[\leadsto x + -1 \cdot \frac{\color{blue}{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}}{z} \]

      12. +-commutative N/A

          \[\leadsto -1 \cdot \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z} + \color{blue}{x} \]

   4. Applied rewrites 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{t}{y} - y}{z}, 0.3333333333333333, x\right)} \]

   if -1.9999999999999999e298 < (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y))) < 2.0000000000000001e299

   1. Initial program 99.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 99.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{\frac{t}{y} - y}{z}, 0.3333333333333333, x\right)\\ t_2 := x - \frac{y}{z \cdot 3}\\ t_3 := t\_2 + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+298}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+299}:\\ \;\;\;\;t\_2 + \frac{t}{z \cdot y} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (/ (- (/ t y) y) z) 0.3333333333333333 x))
        (t_2 (- x (/ y (* z 3.0))))
        (t_3 (+ t_2 (/ t (* (* z 3.0) y)))))
   (if (<= t_3 -2e+298)
     t_1
     (if (<= t_3 2e+299) (+ t_2 (* (/ t (* z y)) 0.3333333333333333)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((((t / y) - y) / z), 0.3333333333333333, x);
	double t_2 = x - (y / (z * 3.0));
	double t_3 = t_2 + (t / ((z * 3.0) * y));
	double tmp;
	if (t_3 <= -2e+298) {
		tmp = t_1;
	} else if (t_3 <= 2e+299) {
		tmp = t_2 + ((t / (z * y)) * 0.3333333333333333);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(Float64(Float64(t / y) - y) / z), 0.3333333333333333, x)
	t_2 = Float64(x - Float64(y / Float64(z * 3.0)))
	t_3 = Float64(t_2 + Float64(t / Float64(Float64(z * 3.0) * y)))
	tmp = 0.0
	if (t_3 <= -2e+298)
		tmp = t_1;
	elseif (t_3 <= 2e+299)
		tmp = Float64(t_2 + Float64(Float64(t / Float64(z * y)) * 0.3333333333333333));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision] * 0.3333333333333333 + x), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+298], t$95$1, If[LessEqual[t$95$3, 2e+299], N[(t$95$2 + N[(N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y))) < -1.9999999999999999e298 or 2.0000000000000001e299 < (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y)))

   1. Initial program 88.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around 0

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

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z}\right)} \]

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

         \[\leadsto x + \frac{1}{3} \cdot \color{blue}{\left(\frac{t}{y \cdot z} - \frac{y}{z}\right)} \]

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

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \left(\frac{t}{y \cdot z} - \frac{y}{z}\right)} \]

      4. metadata-eval N/A

         \[\leadsto x - \frac{-1}{3} \cdot \left(\color{blue}{\frac{t}{y \cdot z}} - \frac{y}{z}\right) \]

      5. associate-/r* N/A

         \[\leadsto x - \frac{-1}{3} \cdot \left(\frac{\frac{t}{y}}{z} - \frac{\color{blue}{y}}{z}\right) \]

      6. sub-div N/A

         \[\leadsto x - \frac{-1}{3} \cdot \frac{\frac{t}{y} - y}{\color{blue}{z}} \]

      7. associate-/l* N/A

         \[\leadsto x - \frac{\frac{-1}{3} \cdot \left(\frac{t}{y} - y\right)}{\color{blue}{z}} \]

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

         \[\leadsto x - \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z} \]

      9. *-lft-identity N/A

         \[\leadsto x - 1 \cdot \color{blue}{\frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z}} \]

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

          \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z}} \]

      11. metadata-eval N/A

          \[\leadsto x + -1 \cdot \frac{\color{blue}{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}}{z} \]

      12. +-commutative N/A

          \[\leadsto -1 \cdot \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z} + \color{blue}{x} \]

   4. Applied rewrites 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{t}{y} - y}{z}, 0.3333333333333333, x\right)} \]

   if -1.9999999999999999e298 < (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y))) < 2.0000000000000001e299

   1. Initial program 99.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in y around 0

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

      1. *-commutative N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]

      3. lower-/.f64 N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot z} \cdot \frac{1}{3} \]

      4. *-commutative N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot y} \cdot \frac{1}{3} \]

      5. lower-*.f64 99.2

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot y} \cdot 0.3333333333333333 \]

   4. Applied rewrites 99.2%

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{t}{z \cdot y} \cdot 0.3333333333333333} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 96.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{\frac{t}{z}}{3}}{y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ (/ (/ t z) 3.0) y)))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (((t / z) / 3.0) / 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 / (z * 3.0d0))) + (((t / z) / 3.0d0) / y)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (((t / z) / 3.0) / y);
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + (((t / z) / 3.0) / y)

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(Float64(Float64(t / z) / 3.0) / y))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + (((t / z) / 3.0) / y);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t / z), $MachinePrecision] / 3.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.7%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}} \]

   2. lift-*.f64 N/A

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right)} \cdot y} \]

   3. lift-*.f64 N/A

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

   4. associate-/r* N/A

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]

   5. lower-/.f64 N/A

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]

   6. associate-/r* N/A

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{\frac{t}{z}}{3}}}{y} \]

   7. lower-/.f64 N/A

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{\frac{t}{z}}{3}}}{y} \]

   8. lower-/.f64 96.3

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{\color{blue}{\frac{t}{z}}}{3}}{y} \]

3. Applied rewrites 96.3%

   \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{\frac{t}{z}}{3}}{y}} \]
4. Add Preprocessing

Alternative 4: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-56}:\\ \;\;\;\;\frac{t}{z \cdot y} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-164}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{-164}:\\ \;\;\;\;\frac{0.3333333333333333 \cdot t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma -0.3333333333333333 (/ y z) x)))
   (if (<= y -1.8e-5)
     t_1
     (if (<= y -1.1e-56)
       (* (/ t (* z y)) 0.3333333333333333)
       (if (<= y -2.7e-164)
         t_1
         (if (<= y 3.25e-164) (/ (* 0.3333333333333333 t) (* z y)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(-0.3333333333333333, (y / z), x);
	double tmp;
	if (y <= -1.8e-5) {
		tmp = t_1;
	} else if (y <= -1.1e-56) {
		tmp = (t / (z * y)) * 0.3333333333333333;
	} else if (y <= -2.7e-164) {
		tmp = t_1;
	} else if (y <= 3.25e-164) {
		tmp = (0.3333333333333333 * t) / (z * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(-0.3333333333333333, Float64(y / z), x)
	tmp = 0.0
	if (y <= -1.8e-5)
		tmp = t_1;
	elseif (y <= -1.1e-56)
		tmp = Float64(Float64(t / Float64(z * y)) * 0.3333333333333333);
	elseif (y <= -2.7e-164)
		tmp = t_1;
	elseif (y <= 3.25e-164)
		tmp = Float64(Float64(0.3333333333333333 * t) / Float64(z * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -1.8e-5], t$95$1, If[LessEqual[y, -1.1e-56], N[(N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision], If[LessEqual[y, -2.7e-164], t$95$1, If[LessEqual[y, 3.25e-164], N[(N[(0.3333333333333333 * t), $MachinePrecision] / N[(z * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.80000000000000005e-5 or -1.10000000000000002e-56 < y < -2.7000000000000001e-164 or 3.25000000000000002e-164 < y

   1. Initial program 97.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x - \frac{1}{3} \cdot \frac{y}{z}} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]

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

         \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      3. +-commutative N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]

      5. lower-/.f64 77.8

         \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]

   4. Applied rewrites 77.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]

   if -1.80000000000000005e-5 < y < -1.10000000000000002e-56

   1. Initial program 98.1%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{t}{y \cdot z}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{t}{y \cdot z} \cdot \frac{1}{3} \]

      4. *-commutative N/A

         \[\leadsto \frac{t}{z \cdot y} \cdot \frac{1}{3} \]

      5. lower-*.f64 41.0

         \[\leadsto \frac{t}{z \cdot y} \cdot 0.3333333333333333 \]

   4. Applied rewrites 41.0%

      \[\leadsto \color{blue}{\frac{t}{z \cdot y} \cdot 0.3333333333333333} \]

   if -2.7000000000000001e-164 < y < 3.25000000000000002e-164

   1. Initial program 89.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{t}{y \cdot z}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{t}{y \cdot z} \cdot \frac{1}{3} \]

      4. *-commutative N/A

         \[\leadsto \frac{t}{z \cdot y} \cdot \frac{1}{3} \]

      5. lower-*.f64 67.2

         \[\leadsto \frac{t}{z \cdot y} \cdot 0.3333333333333333 \]

   4. Applied rewrites 67.2%

      \[\leadsto \color{blue}{\frac{t}{z \cdot y} \cdot 0.3333333333333333} \]
   5. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \frac{t}{z \cdot y} \cdot \color{blue}{\frac{1}{3}} \]

      2. lift-*.f64 N/A

         \[\leadsto \frac{t}{z \cdot y} \cdot \frac{1}{3} \]

      3. lift-/.f64 N/A

         \[\leadsto \frac{t}{z \cdot y} \cdot \frac{1}{3} \]

      4. associate-*l/ N/A

         \[\leadsto \frac{t \cdot \frac{1}{3}}{\color{blue}{z \cdot y}} \]

      5. *-commutative N/A

         \[\leadsto \frac{\frac{1}{3} \cdot t}{\color{blue}{z} \cdot y} \]

      6. *-commutative N/A

         \[\leadsto \frac{\frac{1}{3} \cdot t}{y \cdot \color{blue}{z}} \]

      7. lower-/.f64 N/A

         \[\leadsto \frac{\frac{1}{3} \cdot t}{\color{blue}{y \cdot z}} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\frac{1}{3} \cdot t}{\color{blue}{y} \cdot z} \]

      9. *-commutative N/A

         \[\leadsto \frac{\frac{1}{3} \cdot t}{z \cdot \color{blue}{y}} \]

      10. lift-*.f64 67.2

          \[\leadsto \frac{0.3333333333333333 \cdot t}{z \cdot \color{blue}{y}} \]

   6. Applied rewrites 67.2%

      \[\leadsto \frac{0.3333333333333333 \cdot t}{\color{blue}{z \cdot y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 5: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{z \cdot y} \cdot 0.3333333333333333\\ t_2 := \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{-5}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-164}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{-164}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ t (* z y)) 0.3333333333333333))
        (t_2 (fma -0.3333333333333333 (/ y z) x)))
   (if (<= y -1.8e-5)
     t_2
     (if (<= y -1.1e-56)
       t_1
       (if (<= y -2.7e-164) t_2 (if (<= y 3.25e-164) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t / (z * y)) * 0.3333333333333333;
	double t_2 = fma(-0.3333333333333333, (y / z), x);
	double tmp;
	if (y <= -1.8e-5) {
		tmp = t_2;
	} else if (y <= -1.1e-56) {
		tmp = t_1;
	} else if (y <= -2.7e-164) {
		tmp = t_2;
	} else if (y <= 3.25e-164) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t / Float64(z * y)) * 0.3333333333333333)
	t_2 = fma(-0.3333333333333333, Float64(y / z), x)
	tmp = 0.0
	if (y <= -1.8e-5)
		tmp = t_2;
	elseif (y <= -1.1e-56)
		tmp = t_1;
	elseif (y <= -2.7e-164)
		tmp = t_2;
	elseif (y <= 3.25e-164)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]}, Block[{t$95$2 = N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -1.8e-5], t$95$2, If[LessEqual[y, -1.1e-56], t$95$1, If[LessEqual[y, -2.7e-164], t$95$2, If[LessEqual[y, 3.25e-164], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.80000000000000005e-5 or -1.10000000000000002e-56 < y < -2.7000000000000001e-164 or 3.25000000000000002e-164 < y

   1. Initial program 97.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x - \frac{1}{3} \cdot \frac{y}{z}} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]

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

         \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      3. +-commutative N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]

      5. lower-/.f64 77.8

         \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]

   4. Applied rewrites 77.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]

   if -1.80000000000000005e-5 < y < -1.10000000000000002e-56 or -2.7000000000000001e-164 < y < 3.25000000000000002e-164

   1. Initial program 91.1%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{t}{y \cdot z}} \]
   3. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]

      2. lower-*.f64 N/A

         \[\leadsto \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]

      3. lower-/.f64 N/A

         \[\leadsto \frac{t}{y \cdot z} \cdot \frac{1}{3} \]

      4. *-commutative N/A

         \[\leadsto \frac{t}{z \cdot y} \cdot \frac{1}{3} \]

      5. lower-*.f64 63.0

         \[\leadsto \frac{t}{z \cdot y} \cdot 0.3333333333333333 \]

   4. Applied rewrites 63.0%

      \[\leadsto \color{blue}{\frac{t}{z \cdot y} \cdot 0.3333333333333333} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{\frac{t}{y} - y}{z}, 0.3333333333333333, x\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 10^{-166}:\\ \;\;\;\;x + \frac{\frac{t}{3 \cdot z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma (/ (- (/ t y) y) z) 0.3333333333333333 x)))
   (if (<= y -7e-40) t_1 (if (<= y 1e-166) (+ x (/ (/ t (* 3.0 z)) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma((((t / y) - y) / z), 0.3333333333333333, x);
	double tmp;
	if (y <= -7e-40) {
		tmp = t_1;
	} else if (y <= 1e-166) {
		tmp = x + ((t / (3.0 * z)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(Float64(Float64(Float64(t / y) - y) / z), 0.3333333333333333, x)
	tmp = 0.0
	if (y <= -7e-40)
		tmp = t_1;
	elseif (y <= 1e-166)
		tmp = Float64(x + Float64(Float64(t / Float64(3.0 * z)) / y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision] * 0.3333333333333333 + x), $MachinePrecision]}, If[LessEqual[y, -7e-40], t$95$1, If[LessEqual[y, 1e-166], N[(x + N[(N[(t / N[(3.0 * z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.0000000000000003e-40 or 1.00000000000000004e-166 < y

   1. Initial program 98.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around 0

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

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z}\right)} \]

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

         \[\leadsto x + \frac{1}{3} \cdot \color{blue}{\left(\frac{t}{y \cdot z} - \frac{y}{z}\right)} \]

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

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \left(\frac{t}{y \cdot z} - \frac{y}{z}\right)} \]

      4. metadata-eval N/A

         \[\leadsto x - \frac{-1}{3} \cdot \left(\color{blue}{\frac{t}{y \cdot z}} - \frac{y}{z}\right) \]

      5. associate-/r* N/A

         \[\leadsto x - \frac{-1}{3} \cdot \left(\frac{\frac{t}{y}}{z} - \frac{\color{blue}{y}}{z}\right) \]

      6. sub-div N/A

         \[\leadsto x - \frac{-1}{3} \cdot \frac{\frac{t}{y} - y}{\color{blue}{z}} \]

      7. associate-/l* N/A

         \[\leadsto x - \frac{\frac{-1}{3} \cdot \left(\frac{t}{y} - y\right)}{\color{blue}{z}} \]

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

         \[\leadsto x - \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z} \]

      9. *-lft-identity N/A

         \[\leadsto x - 1 \cdot \color{blue}{\frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z}} \]

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

          \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z}} \]

      11. metadata-eval N/A

          \[\leadsto x + -1 \cdot \frac{\color{blue}{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}}{z} \]

      12. +-commutative N/A

          \[\leadsto -1 \cdot \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z} + \color{blue}{x} \]

   4. Applied rewrites 98.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{t}{y} - y}{z}, 0.3333333333333333, x\right)} \]

   if -7.0000000000000003e-40 < y < 1.00000000000000004e-166

   1. Initial program 90.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right)} \cdot y} \]

      3. lift-*.f64 N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      4. associate-/r* N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]

      5. lower-/.f64 N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]

      6. associate-/r* N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{\frac{t}{z}}{3}}}{y} \]

      7. lower-/.f64 N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{\frac{t}{z}}{3}}}{y} \]

      8. lower-/.f64 98.5

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{\color{blue}{\frac{t}{z}}}{3}}{y} \]

   3. Applied rewrites 98.5%

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{\frac{t}{z}}{3}}{y}} \]

   4. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} + \frac{\frac{\frac{t}{z}}{3}}{y} \]
   5. Step-by-step derivation

   6. Applied rewrites 96.0%

      \[\leadsto \color{blue}{x} + \frac{\frac{\frac{t}{z}}{3}}{y} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \frac{\frac{\color{blue}{\frac{t}{z}}}{3}}{y} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\frac{\frac{t}{z}}{3}}}{y} \]

      3. associate-/l/ N/A

         \[\leadsto x + \frac{\color{blue}{\frac{t}{z \cdot 3}}}{y} \]

      4. lift-*.f64 N/A

         \[\leadsto x + \frac{\frac{t}{\color{blue}{z \cdot 3}}}{y} \]

      5. lower-/.f64 95.9

         \[\leadsto x + \frac{\color{blue}{\frac{t}{z \cdot 3}}}{y} \]

      6. lift-*.f64 N/A

         \[\leadsto x + \frac{\frac{t}{\color{blue}{z \cdot 3}}}{y} \]

      7. *-commutative N/A

         \[\leadsto x + \frac{\frac{t}{\color{blue}{3 \cdot z}}}{y} \]

      8. lower-*.f64 95.9

         \[\leadsto x + \frac{\frac{t}{\color{blue}{3 \cdot z}}}{y} \]

   8. Applied rewrites 95.9%

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

Alternative 7: 91.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.054:\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+80}:\\ \;\;\;\;x + \frac{\frac{t}{3 \cdot z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{y} - \frac{0.3333333333333333}{z}\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.054)
   (fma -0.3333333333333333 (/ y z) x)
   (if (<= y 1.25e+80)
     (+ x (/ (/ t (* 3.0 z)) y))
     (* (- (/ x y) (/ 0.3333333333333333 z)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.054) {
		tmp = fma(-0.3333333333333333, (y / z), x);
	} else if (y <= 1.25e+80) {
		tmp = x + ((t / (3.0 * z)) / y);
	} else {
		tmp = ((x / y) - (0.3333333333333333 / z)) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.054)
		tmp = fma(-0.3333333333333333, Float64(y / z), x);
	elseif (y <= 1.25e+80)
		tmp = Float64(x + Float64(Float64(t / Float64(3.0 * z)) / y));
	else
		tmp = Float64(Float64(Float64(x / y) - Float64(0.3333333333333333 / z)) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.054], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[y, 1.25e+80], N[(x + N[(N[(t / N[(3.0 * z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] - N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0539999999999999994

   1. Initial program 98.2%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x - \frac{1}{3} \cdot \frac{y}{z}} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]

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

         \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      3. +-commutative N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]

      5. lower-/.f64 91.6

         \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]

   4. Applied rewrites 91.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]

   if -0.0539999999999999994 < y < 1.2499999999999999e80

   1. Initial program 93.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}} \]

      2. lift-*.f64 N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right)} \cdot y} \]

      3. lift-*.f64 N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      4. associate-/r* N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]

      5. lower-/.f64 N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3}}{y}} \]

      6. associate-/r* N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{\frac{t}{z}}{3}}}{y} \]

      7. lower-/.f64 N/A

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\color{blue}{\frac{\frac{t}{z}}{3}}}{y} \]

      8. lower-/.f64 98.4

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{\color{blue}{\frac{t}{z}}}{3}}{y} \]

   3. Applied rewrites 98.4%

      \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{\frac{t}{z}}{3}}{y}} \]

   4. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} + \frac{\frac{\frac{t}{z}}{3}}{y} \]
   5. Step-by-step derivation

   6. Applied rewrites 89.5%

      \[\leadsto \color{blue}{x} + \frac{\frac{\frac{t}{z}}{3}}{y} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto x + \frac{\frac{\color{blue}{\frac{t}{z}}}{3}}{y} \]

      2. lift-/.f64 N/A

         \[\leadsto x + \frac{\color{blue}{\frac{\frac{t}{z}}{3}}}{y} \]

      3. associate-/l/ N/A

         \[\leadsto x + \frac{\color{blue}{\frac{t}{z \cdot 3}}}{y} \]

      4. lift-*.f64 N/A

         \[\leadsto x + \frac{\frac{t}{\color{blue}{z \cdot 3}}}{y} \]

      5. lower-/.f64 89.5

         \[\leadsto x + \frac{\color{blue}{\frac{t}{z \cdot 3}}}{y} \]

      6. lift-*.f64 N/A

         \[\leadsto x + \frac{\frac{t}{\color{blue}{z \cdot 3}}}{y} \]

      7. *-commutative N/A

         \[\leadsto x + \frac{\frac{t}{\color{blue}{3 \cdot z}}}{y} \]

      8. lower-*.f64 89.5

         \[\leadsto x + \frac{\frac{t}{\color{blue}{3 \cdot z}}}{y} \]

   8. Applied rewrites 89.5%

      \[\leadsto x + \frac{\color{blue}{\frac{t}{3 \cdot z}}}{y} \]

   if 1.2499999999999999e80 < y

   1. Initial program 98.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

         \[\leadsto \left(\frac{x}{y} - \frac{1}{3} \cdot \frac{1}{z}\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{x}{y} - \frac{1}{3} \cdot \frac{1}{z}\right) \cdot \color{blue}{y} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\frac{x}{y} - \frac{1}{3} \cdot \frac{1}{z}\right) \cdot y \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{x}{y} - \frac{1}{3} \cdot \frac{1}{z}\right) \cdot y \]

      5. associate-*r/ N/A

         \[\leadsto \left(\frac{x}{y} - \frac{\frac{1}{3} \cdot 1}{z}\right) \cdot y \]

      6. metadata-eval N/A

         \[\leadsto \left(\frac{x}{y} - \frac{\frac{1}{3}}{z}\right) \cdot y \]

      7. lower-/.f64 97.4

         \[\leadsto \left(\frac{x}{y} - \frac{0.3333333333333333}{z}\right) \cdot y \]

   4. Applied rewrites 97.4%

      \[\leadsto \color{blue}{\left(\frac{x}{y} - \frac{0.3333333333333333}{z}\right) \cdot y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 89.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.054:\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+80}:\\ \;\;\;\;x + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{y} - \frac{0.3333333333333333}{z}\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.054)
   (fma -0.3333333333333333 (/ y z) x)
   (if (<= y 1.25e+80)
     (+ x (/ t (* (* z 3.0) y)))
     (* (- (/ x y) (/ 0.3333333333333333 z)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.054) {
		tmp = fma(-0.3333333333333333, (y / z), x);
	} else if (y <= 1.25e+80) {
		tmp = x + (t / ((z * 3.0) * y));
	} else {
		tmp = ((x / y) - (0.3333333333333333 / z)) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.054)
		tmp = fma(-0.3333333333333333, Float64(y / z), x);
	elseif (y <= 1.25e+80)
		tmp = Float64(x + Float64(t / Float64(Float64(z * 3.0) * y)));
	else
		tmp = Float64(Float64(Float64(x / y) - Float64(0.3333333333333333 / z)) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.054], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[y, 1.25e+80], N[(x + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] - N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0539999999999999994

   1. Initial program 98.2%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x - \frac{1}{3} \cdot \frac{y}{z}} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]

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

         \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      3. +-commutative N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]

      5. lower-/.f64 91.6

         \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]

   4. Applied rewrites 91.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]

   if -0.0539999999999999994 < y < 1.2499999999999999e80

   1. Initial program 93.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 85.0%

      \[\leadsto \color{blue}{x} + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   if 1.2499999999999999e80 < y

   1. Initial program 98.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in y around inf

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

      1. *-commutative N/A

         \[\leadsto \left(\frac{x}{y} - \frac{1}{3} \cdot \frac{1}{z}\right) \cdot \color{blue}{y} \]

      2. lower-*.f64 N/A

         \[\leadsto \left(\frac{x}{y} - \frac{1}{3} \cdot \frac{1}{z}\right) \cdot \color{blue}{y} \]

      3. lower--.f64 N/A

         \[\leadsto \left(\frac{x}{y} - \frac{1}{3} \cdot \frac{1}{z}\right) \cdot y \]

      4. lower-/.f64 N/A

         \[\leadsto \left(\frac{x}{y} - \frac{1}{3} \cdot \frac{1}{z}\right) \cdot y \]

      5. associate-*r/ N/A

         \[\leadsto \left(\frac{x}{y} - \frac{\frac{1}{3} \cdot 1}{z}\right) \cdot y \]

      6. metadata-eval N/A

         \[\leadsto \left(\frac{x}{y} - \frac{\frac{1}{3}}{z}\right) \cdot y \]

      7. lower-/.f64 97.4

         \[\leadsto \left(\frac{x}{y} - \frac{0.3333333333333333}{z}\right) \cdot y \]

   4. Applied rewrites 97.4%

      \[\leadsto \color{blue}{\left(\frac{x}{y} - \frac{0.3333333333333333}{z}\right) \cdot y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 89.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \mathbf{if}\;y \leq -0.054:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+80}:\\ \;\;\;\;x + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma -0.3333333333333333 (/ y z) x)))
   (if (<= y -0.054)
     t_1
     (if (<= y 1.25e+80) (+ x (/ t (* (* z 3.0) y))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(-0.3333333333333333, (y / z), x);
	double tmp;
	if (y <= -0.054) {
		tmp = t_1;
	} else if (y <= 1.25e+80) {
		tmp = x + (t / ((z * 3.0) * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(-0.3333333333333333, Float64(y / z), x)
	tmp = 0.0
	if (y <= -0.054)
		tmp = t_1;
	elseif (y <= 1.25e+80)
		tmp = Float64(x + Float64(t / Float64(Float64(z * 3.0) * y)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -0.054], t$95$1, If[LessEqual[y, 1.25e+80], N[(x + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0539999999999999994 or 1.2499999999999999e80 < y

   1. Initial program 98.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x - \frac{1}{3} \cdot \frac{y}{z}} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]

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

         \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      3. +-commutative N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]

      5. lower-/.f64 94.1

         \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]

   4. Applied rewrites 94.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]

   if -0.0539999999999999994 < y < 1.2499999999999999e80

   1. Initial program 93.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 85.0%

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

Alternative 10: 89.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \mathbf{if}\;y \leq -0.054:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{z \cdot y}, 0.3333333333333333, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (fma -0.3333333333333333 (/ y z) x)))
   (if (<= y -0.054)
     t_1
     (if (<= y 1.25e+80) (fma (/ t (* z y)) 0.3333333333333333 x) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(-0.3333333333333333, (y / z), x);
	double tmp;
	if (y <= -0.054) {
		tmp = t_1;
	} else if (y <= 1.25e+80) {
		tmp = fma((t / (z * y)), 0.3333333333333333, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = fma(-0.3333333333333333, Float64(y / z), x)
	tmp = 0.0
	if (y <= -0.054)
		tmp = t_1;
	elseif (y <= 1.25e+80)
		tmp = fma(Float64(t / Float64(z * y)), 0.3333333333333333, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -0.054], t$95$1, If[LessEqual[y, 1.25e+80], N[(N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision] * 0.3333333333333333 + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0539999999999999994 or 1.2499999999999999e80 < y

   1. Initial program 98.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in t around 0

      \[\leadsto \color{blue}{x - \frac{1}{3} \cdot \frac{y}{z}} \]
   3. Step-by-step derivation

      1. metadata-eval N/A

         \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]

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

         \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

      3. +-commutative N/A

         \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

      4. lower-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]

      5. lower-/.f64 94.1

         \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]

   4. Applied rewrites 94.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]

   if -0.0539999999999999994 < y < 1.2499999999999999e80

   1. Initial program 93.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around 0

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

      1. associate--l+ N/A

         \[\leadsto x + \color{blue}{\left(\frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z}\right)} \]

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

         \[\leadsto x + \frac{1}{3} \cdot \color{blue}{\left(\frac{t}{y \cdot z} - \frac{y}{z}\right)} \]

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

         \[\leadsto x - \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \left(\frac{t}{y \cdot z} - \frac{y}{z}\right)} \]

      4. metadata-eval N/A

         \[\leadsto x - \frac{-1}{3} \cdot \left(\color{blue}{\frac{t}{y \cdot z}} - \frac{y}{z}\right) \]

      5. associate-/r* N/A

         \[\leadsto x - \frac{-1}{3} \cdot \left(\frac{\frac{t}{y}}{z} - \frac{\color{blue}{y}}{z}\right) \]

      6. sub-div N/A

         \[\leadsto x - \frac{-1}{3} \cdot \frac{\frac{t}{y} - y}{\color{blue}{z}} \]

      7. associate-/l* N/A

         \[\leadsto x - \frac{\frac{-1}{3} \cdot \left(\frac{t}{y} - y\right)}{\color{blue}{z}} \]

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

         \[\leadsto x - \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z} \]

      9. *-lft-identity N/A

         \[\leadsto x - 1 \cdot \color{blue}{\frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z}} \]

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

          \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z}} \]

      11. metadata-eval N/A

          \[\leadsto x + -1 \cdot \frac{\color{blue}{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}}{z} \]

      12. +-commutative N/A

          \[\leadsto -1 \cdot \frac{\frac{-1}{3} \cdot \frac{t}{y} - \frac{-1}{3} \cdot y}{z} + \color{blue}{x} \]

   4. Applied rewrites 91.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\frac{t}{y} - y}{z}, 0.3333333333333333, x\right)} \]

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{fma}\left(\frac{t}{y \cdot z}, \frac{1}{3}, x\right) \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto \mathsf{fma}\left(\frac{t}{y \cdot z}, \frac{1}{3}, x\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{fma}\left(\frac{t}{z \cdot y}, \frac{1}{3}, x\right) \]

      3. lift-*.f64 84.9

         \[\leadsto \mathsf{fma}\left(\frac{t}{z \cdot y}, 0.3333333333333333, x\right) \]

   7. Applied rewrites 84.9%

      \[\leadsto \mathsf{fma}\left(\frac{t}{z \cdot y}, 0.3333333333333333, x\right) \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 47.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.116:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+139}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333 \cdot y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.116)
   (* -0.3333333333333333 (/ y z))
   (if (<= y 4.7e+139) x (/ (* -0.3333333333333333 y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.116) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 4.7e+139) {
		tmp = x;
	} else {
		tmp = (-0.3333333333333333 * y) / z;
	}
	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 (y <= (-0.116d0)) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else if (y <= 4.7d+139) then
        tmp = x
    else
        tmp = ((-0.3333333333333333d0) * y) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.116) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 4.7e+139) {
		tmp = x;
	} else {
		tmp = (-0.3333333333333333 * y) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.116:
		tmp = -0.3333333333333333 * (y / z)
	elif y <= 4.7e+139:
		tmp = x
	else:
		tmp = (-0.3333333333333333 * y) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.116)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	elseif (y <= 4.7e+139)
		tmp = x;
	else
		tmp = Float64(Float64(-0.3333333333333333 * y) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -0.116)
		tmp = -0.3333333333333333 * (y / z);
	elseif (y <= 4.7e+139)
		tmp = x;
	else
		tmp = (-0.3333333333333333 * y) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.116], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e+139], x, N[(N[(-0.3333333333333333 * y), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.116000000000000006

   1. Initial program 98.2%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{-1}{3} \cdot \color{blue}{\frac{y}{z}} \]

      2. lower-/.f64 63.1

         \[\leadsto -0.3333333333333333 \cdot \frac{y}{\color{blue}{z}} \]

   4. Applied rewrites 63.1%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]

   if -0.116000000000000006 < y < 4.7000000000000001e139

   1. Initial program 93.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 33.0%

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

   if 4.7000000000000001e139 < y

   1. Initial program 99.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{t}{y \cdot z} - \frac{1}{3} \cdot \frac{y}{z}} \]
   3. Step-by-step derivation

      1. associate-/r* N/A

         \[\leadsto \frac{1}{3} \cdot \frac{\frac{t}{y}}{z} - \frac{1}{3} \cdot \frac{y}{z} \]

      2. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{y}}{z} - \color{blue}{\frac{1}{3}} \cdot \frac{y}{z} \]

      3. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{y}}{z} - \frac{\frac{1}{3} \cdot y}{\color{blue}{z}} \]

      4. div-sub N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{y} - \frac{1}{3} \cdot y}{\color{blue}{z}} \]

      5. lower-/.f64 N/A

         \[\leadsto \frac{\frac{1}{3} \cdot \frac{t}{y} - \frac{1}{3} \cdot y}{\color{blue}{z}} \]

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

         \[\leadsto \frac{\frac{1}{3} \cdot \left(\frac{t}{y} - y\right)}{z} \]

      7. *-commutative N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{z} \]

      8. lower-*.f64 N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{z} \]

      9. lower--.f64 N/A

         \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot \frac{1}{3}}{z} \]

      10. lower-/.f64 79.5

          \[\leadsto \frac{\left(\frac{t}{y} - y\right) \cdot 0.3333333333333333}{z} \]

   4. Applied rewrites 79.5%

      \[\leadsto \color{blue}{\frac{\left(\frac{t}{y} - y\right) \cdot 0.3333333333333333}{z}} \]

   5. Taylor expanded in y around inf

      \[\leadsto \frac{\frac{-1}{3} \cdot y}{z} \]
   6. Step-by-step derivation

      1. lower-*.f64 79.4

         \[\leadsto \frac{-0.3333333333333333 \cdot y}{z} \]

   7. Applied rewrites 79.4%

      \[\leadsto \frac{-0.3333333333333333 \cdot y}{z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 12: 47.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{if}\;y \leq -0.116:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+139}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* -0.3333333333333333 (/ y z))))
   (if (<= y -0.116) t_1 (if (<= y 4.7e+139) x t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -0.3333333333333333 * (y / z);
	double tmp;
	if (y <= -0.116) {
		tmp = t_1;
	} else if (y <= 4.7e+139) {
		tmp = 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 = (-0.3333333333333333d0) * (y / z)
    if (y <= (-0.116d0)) then
        tmp = t_1
    else if (y <= 4.7d+139) then
        tmp = 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 = -0.3333333333333333 * (y / z);
	double tmp;
	if (y <= -0.116) {
		tmp = t_1;
	} else if (y <= 4.7e+139) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -0.3333333333333333 * (y / z)
	tmp = 0
	if y <= -0.116:
		tmp = t_1
	elif y <= 4.7e+139:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-0.3333333333333333 * Float64(y / z))
	tmp = 0.0
	if (y <= -0.116)
		tmp = t_1;
	elseif (y <= 4.7e+139)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -0.3333333333333333 * (y / z);
	tmp = 0.0;
	if (y <= -0.116)
		tmp = t_1;
	elseif (y <= 4.7e+139)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.116], t$95$1, If[LessEqual[y, 4.7e+139], x, t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.116000000000000006 or 4.7000000000000001e139 < y

   1. Initial program 98.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]
   3. Step-by-step derivation

      1. lower-*.f64 N/A

         \[\leadsto \frac{-1}{3} \cdot \color{blue}{\frac{y}{z}} \]

      2. lower-/.f64 68.9

         \[\leadsto -0.3333333333333333 \cdot \frac{y}{\color{blue}{z}} \]

   4. Applied rewrites 68.9%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]

   if -0.116000000000000006 < y < 4.7000000000000001e139

   1. Initial program 93.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   3. Step-by-step derivation

   4. Applied rewrites 33.0%

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

Alternative 13: 65.0% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (fma -0.3333333333333333 (/ y z) x))

C

double code(double x, double y, double z, double t) {
	return fma(-0.3333333333333333, (y / z), x);
}

Julia

function code(x, y, z, t)
	return fma(-0.3333333333333333, Float64(y / z), x)
end

Wolfram

code[x_, y_, z_, t_] := N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 95.7%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

2. Taylor expanded in t around 0

   \[\leadsto \color{blue}{x - \frac{1}{3} \cdot \frac{y}{z}} \]
3. Step-by-step derivation

   1. metadata-eval N/A

      \[\leadsto x - \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot \frac{\color{blue}{y}}{z} \]

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

      \[\leadsto x + \color{blue}{\frac{-1}{3} \cdot \frac{y}{z}} \]

   3. +-commutative N/A

      \[\leadsto \frac{-1}{3} \cdot \frac{y}{z} + \color{blue}{x} \]

   4. lower-fma.f64 N/A

      \[\leadsto \mathsf{fma}\left(\frac{-1}{3}, \color{blue}{\frac{y}{z}}, x\right) \]

   5. lower-/.f64 65.0

      \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{\color{blue}{z}}, x\right) \]

4. Applied rewrites 65.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)} \]
5. Add Preprocessing

Alternative 14: 30.7% accurate, 44.0× speedup

Math

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

FPCore

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

C

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

Fortran

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

2. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
3. Step-by-step derivation

4. Applied rewrites 30.7%

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

Developer Target 1: 96.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y)))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / 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 / (z * 3.0d0))) + ((t / (z * 3.0d0)) / y)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y)

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(Float64(t / Float64(z * 3.0)) / y))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2025093 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (- x (/ y (* z 3))) (/ (/ t (* z 3)) y)))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))