Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B

Percentage Accurate: 100.0% → 100.0%

Time: 1.3s

Alternatives: 6

Speedup: 1.1×

• 79.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	x + ((y - x) * z)
END code

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	x + ((y - x) * z)
END code

Alternative 1: 100.0% accurate, 1.1× speedup

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (fma z (- y x) x))

C

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

Julia

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

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(z * (y - x)) + x
END code

Derivation

1. Initial program 100.0%

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

3. Applied rewrites 100.0%

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

Alternative 2: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := z \cdot \left(y - x\right)\\ \mathbf{if}\;z \leq -28165673201.033638:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 7.845250112058621 \cdot 10^{-9}:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* z (- y x))))
  (if (<= z -28165673201.033638)
    t_0
    (if (<= z 7.845250112058621e-9) (fma z y x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y - x);
	double tmp;
	if (z <= -28165673201.033638) {
		tmp = t_0;
	} else if (z <= 7.845250112058621e-9) {
		tmp = fma(z, y, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y - x))
	tmp = 0.0
	if (z <= -28165673201.033638)
		tmp = t_0;
	elseif (z <= 7.845250112058621e-9)
		tmp = fma(z, y, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -28165673201.033638], t$95$0, If[LessEqual[z, 7.845250112058621e-9], N[(z * y + x), $MachinePrecision], t$95$0]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = (z * (y - x)) IN
		LET tmp_1 = IF (z <= (78452501120586211901078397558915999976392185999429784715175628662109375e-79)) THEN ((z * y) + x) ELSE t_0 ENDIF IN
		LET tmp = IF (z <= (-2816567320103363800048828125e-17)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -28165673201.033638 or 7.8452501120586212e-9 < z

   1. Initial program 100.0%

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

   3. Applied rewrites 100.0%

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

   4. Taylor expanded in x around 0

      \[\leadsto y \cdot z \]
   5. Step-by-step derivation

   6. Applied rewrites 41.4%

      \[\leadsto y \cdot z \]

   7. Taylor expanded in z around inf

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

   9. Applied rewrites 65.0%

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

   if -28165673201.033638 < z < 7.8452501120586212e-9

   1. Initial program 100.0%

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

   3. Applied rewrites 100.0%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 75.7%

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

Alternative 3: 86.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} t_0 := x \cdot \left(1 - z\right)\\ \mathbf{if}\;x \leq -1.9574573609995736 \cdot 10^{+91}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.0005660629841236394:\\ \;\;\;\;\mathsf{fma}\left(z, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (let* ((t_0 (* x (- 1.0 z))))
  (if (<= x -1.9574573609995736e+91)
    t_0
    (if (<= x 0.0005660629841236394) (fma z y x) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - z);
	double tmp;
	if (x <= -1.9574573609995736e+91) {
		tmp = t_0;
	} else if (x <= 0.0005660629841236394) {
		tmp = fma(z, y, x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - z))
	tmp = 0.0
	if (x <= -1.9574573609995736e+91)
		tmp = t_0;
	elseif (x <= 0.0005660629841236394)
		tmp = fma(z, y, x);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.9574573609995736e+91], t$95$0, If[LessEqual[x, 0.0005660629841236394], N[(z * y + x), $MachinePrecision], t$95$0]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET t_0 = (x * ((1) - z)) IN
		LET tmp_1 = IF (x <= (566062984123639448448550570702764161978848278522491455078125e-63)) THEN ((z * y) + x) ELSE t_0 ENDIF IN
		LET tmp = IF (x <= (-19574573609995735600635967846953792076791839711159263895675501474379448978998529820238807040)) THEN t_0 ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if x < -1.9574573609995736e91 or 5.6606298412363945e-4 < x

   1. Initial program 100.0%

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

   3. Applied rewrites 98.9%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 62.4%

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

   if -1.9574573609995736e91 < x < 5.6606298412363945e-4

   1. Initial program 100.0%

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

   3. Applied rewrites 100.0%

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

   4. Taylor expanded in x around 0

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

   6. Applied rewrites 75.7%

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

Alternative 4: 75.7% accurate, 1.5× speedup

Math

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

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (fma z y x))

C

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

Julia

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

Wolfram

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

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	(z * y) + x
END code

Derivation

1. Initial program 100.0%

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

3. Applied rewrites 100.0%

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

4. Taylor expanded in x around 0

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

6. Applied rewrites 75.7%

   \[\leadsto \mathsf{fma}\left(z, y, x\right) \]
7. Add Preprocessing

Alternative 5: 60.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -1.5998878487717716 \cdot 10^{-87}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 1.4132947115915006 \cdot 10^{-40}:\\ \;\;\;\;x \cdot 1\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (if (<= z -1.5998878487717716e-87)
  (* y z)
  (if (<= z 1.4132947115915006e-40) (* x 1.0) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.5998878487717716e-87) {
		tmp = y * z;
	} else if (z <= 1.4132947115915006e-40) {
		tmp = x * 1.0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.5998878487717716d-87)) then
        tmp = y * z
    else if (z <= 1.4132947115915006d-40) then
        tmp = x * 1.0d0
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.5998878487717716e-87) {
		tmp = y * z;
	} else if (z <= 1.4132947115915006e-40) {
		tmp = x * 1.0;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.5998878487717716e-87:
		tmp = y * z
	elif z <= 1.4132947115915006e-40:
		tmp = x * 1.0
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.5998878487717716e-87)
		tmp = Float64(y * z);
	elseif (z <= 1.4132947115915006e-40)
		tmp = Float64(x * 1.0);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.5998878487717716e-87)
		tmp = y * z;
	elseif (z <= 1.4132947115915006e-40)
		tmp = x * 1.0;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.5998878487717716e-87], N[(y * z), $MachinePrecision], If[LessEqual[z, 1.4132947115915006e-40], N[(x * 1.0), $MachinePrecision], N[(y * z), $MachinePrecision]]]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	LET tmp_1 = IF (z <= (14132947115915006468182910235642061199906833362565967651395812855413318177857125598375794078304482317867511731446228395725484006106853485107421875e-185)) THEN (x * (1)) ELSE (y * z) ENDIF IN
	LET tmp = IF (z <= (-159988784877177164685523371169830722870522374072384409119026858684832480050318864005140114871679013601761552483193181404403016128515199488354968070059220853336754264519220820635743157089849151568897638446024723319315030689580225953250192105770111083984375e-341)) THEN (y * z) ELSE tmp_1 ENDIF IN
	tmp
END code

Derivation

1. Split input into 2 regimes

2. if z < -1.5998878487717716e-87 or 1.4132947115915006e-40 < z

   1. Initial program 100.0%

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

   3. Applied rewrites 100.0%

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

   4. Taylor expanded in x around 0

      \[\leadsto y \cdot z \]
   5. Step-by-step derivation

   6. Applied rewrites 41.4%

      \[\leadsto y \cdot z \]

   if -1.5998878487717716e-87 < z < 1.4132947115915006e-40

   1. Initial program 100.0%

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

   3. Applied rewrites 98.9%

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

   4. Taylor expanded in x around inf

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

   6. Applied rewrites 62.4%

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

   7. Taylor expanded in z around 0

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

   9. Applied rewrites 36.6%

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

Alternative 6: 36.6% accurate, 2.3× speedup

Math

\[x \cdot 1 \]

FPCore

(FPCore (x y z)
  :precision binary64
  :pre TRUE
  (* x 1.0))

C

double code(double x, double y, double z) {
	return x * 1.0;
}

Fortran

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

Java

public static double code(double x, double y, double z) {
	return x * 1.0;
}

Python

def code(x, y, z):
	return x * 1.0

Julia

function code(x, y, z)
	return Float64(x * 1.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * 1.0;
end

Wolfram

code[x_, y_, z_] := N[(x * 1.0), $MachinePrecision]

ReFlow

f(x, y, z):
	x in [-inf, +inf],
	y in [-inf, +inf],
	z in [-inf, +inf]
code: THEORY
BEGIN
f(x, y, z: real): real =
	x * (1)
END code

Derivation

1. Initial program 100.0%

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

3. Applied rewrites 98.9%

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

4. Taylor expanded in x around inf

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

6. Applied rewrites 62.4%

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

7. Taylor expanded in z around 0

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

9. Applied rewrites 36.6%

   \[\leadsto x \cdot 1 \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2026092 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))