Metrics for Optimisation.CirclePacking:place from circle-packing-0.1.0.4, I

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 7 to 7 computations (0% saved)

sample1.2s (39.3%)

Memory

26.2MiB live, 895.8MiB allocated

Samples

850.0ms	8 253×	0	valid
0.0ms	1×	2	valid
0.0ms	2×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 251.0ms

ival-add: 242.0ms (96.6% of total)

ival-true: 6.0ms (2.4% of total)

ival-assert: 3.0ms (1.2% of total)

adjust: 0.0ms (0% of total)

Bogosity

explain52.0ms (1.7%)

Memory

1.9MiB live, 85.0MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(+.f64 (+.f64 x y) z)`
-	-	`y`
-	-	`(+.f64 x y)`
-	-	`z`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	1

Precision?

0/0

Recall?

0/0

Samples

20.0ms

512×

valid

Compiler

Compiled 34 to 19 computations (44.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-add: 5.0ms (92.8% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

preprocess28.0ms (0.9%)

Memory

-0.2MiB live, 37.8MiB allocated

Algorithm

1×	egg-herbie

Rules

66×	`associate--r+`
63×	`sub-neg`
60×	`associate-+l-`
56×	`distribute-rgt-in`
53×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	50
1	62	45
2	191	45
3	490	45
4	780	45
5	843	45
6	859	45
0	5	5
0	7	5
1	11	5
2	18	5
3	20	5
0	20	5

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+.f64 (+.f64 x y) z)

Outputs
(+.f64 (+.f64 x y) z)
(+.f64 (+.f64 z x) y)

Symmetry

(sort x y z)

Compiler

Compiled 8 to 5 computations (37.5% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (+.f64 x y) z)

Compiler

Compiled 8 to 5 computations (37.5% saved)

simplify3.0ms (0.1%)

Memory

6.6MiB live, 6.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(+.f64 x y)
cost-diff	0	(+.f64 (+.f64 x y) z)

Rules

12×	`lower-+.f32`
10×	`lower-+.f64`
5×	`+-commutative`
3×	`associate-+l+`
3×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
0	7	11
1	11	11
2	18	11
3	20	11
0	20	11

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(+.f64 (+.f64 x y) z)
(+.f64 x y)
x
y
z

Outputs
(+.f64 (+.f64 x y) z)
(+.f64 (+.f64 z x) y)
(+.f64 x y)
(+.f64 y x)
x
y
z

localize15.0ms (0.5%)

Memory

4.1MiB live, 42.7MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 (+.f64 x y) z)
accuracy	0	(+.f64 x y)

Samples

10.0ms

256×

valid

Compiler

Compiled 13 to 7 computations (46.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-add: 2.0ms (76.7% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series5.0ms (0.2%)

Memory

-31.9MiB live, 13.6MiB allocated

Counts

2 → 60

Calls

Call 1

Inputs
#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())
#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())

Outputs
#s(alt (+ y z) (taylor 0 x) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 x) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 x) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 x) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (/ y x) (/ z x)))) (taylor inf x) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (/ y x) (/ z x)))) (taylor inf x) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (/ y x) (/ z x)))) (taylor inf x) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (+ y z) x)) 1))) (taylor -inf x) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (+ y z) x)) 1))) (taylor -inf x) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (+ y z) x)) 1))) (taylor -inf x) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (+ x z) (taylor 0 y) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 y) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 y) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 y) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (/ x y) (/ z y)))) (taylor inf y) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (/ x y) (/ z y)))) (taylor inf y) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (/ x y) (/ z y)))) (taylor inf y) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (+ x z) y)) 1))) (taylor -inf y) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (+ x z) y)) 1))) (taylor -inf y) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (+ x z) y)) 1))) (taylor -inf y) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 z) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 z) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 z) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 z) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt z (taylor inf z) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (* z (+ 1 (+ (/ x z) (/ y z)))) (taylor inf z) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (* z (+ 1 (+ (/ x z) (/ y z)))) (taylor inf z) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (* z (+ 1 (+ (/ x z) (/ y z)))) (taylor inf z) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt z (taylor -inf z) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ (+ x y) z)) 1))) (taylor -inf z) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ (+ x y) z)) 1))) (taylor -inf z) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ (+ x y) z)) 1))) (taylor -inf z) (#s(alt (+.f64 (+.f64 x y) z) (patch (+.f64 (+.f64 x y) z) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(+ x y)
0.0ms	x	@	inf	(+ (+ x y) z)
0.0ms	z	@	inf	(+ (+ x y) z)
0.0ms	y	@	inf	(+ (+ x y) z)
0.0ms	x	@	-inf	(+ (+ x y) z)

simplify137.0ms (4.5%)

Memory

17.8MiB live, 179.7MiB allocated

Algorithm

1×	egg-herbie

Rules

2 384×	`lower-/.f32`
2 384×	`lower-/.f64`
1 432×	`lower-fma.f64`
1 432×	`lower-fma.f32`
1 080×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	210
1	148	210
2	381	210
3	1185	210
4	2960	210
5	4921	210
6	5879	210
7	6006	210
8	6088	210
9	6102	210
0	8854	210

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 48

Calls

Call 1

Inputs
(+ y z)
(+ x (+ y z))
(+ x (+ y z))
(+ x (+ y z))
x
(* x (+ 1 (+ (/ y x) (/ z x))))
(* x (+ 1 (+ (/ y x) (/ z x))))
(* x (+ 1 (+ (/ y x) (/ z x))))
x
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(+ x z)
(+ x (+ y z))
(+ x (+ y z))
(+ x (+ y z))
y
(* y (+ 1 (+ (/ x y) (/ z y))))
(* y (+ 1 (+ (/ x y) (/ z y))))
(* y (+ 1 (+ (/ x y) (/ z y))))
y
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(+ x y)
(+ x (+ y z))
(+ x (+ y z))
(+ x (+ y z))
z
(* z (+ 1 (+ (/ x z) (/ y z))))
(* z (+ 1 (+ (/ x z) (/ y z))))
(* z (+ 1 (+ (/ x z) (/ y z))))
z
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
y
(+ x y)
(+ x y)
(+ x y)
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
x
(+ x y)
(+ x y)
(+ x y)
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))

Outputs
(+ y z)
(+.f64 z y)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
x
(* x (+ 1 (+ (/ y x) (/ z x))))
(+.f64 (+.f64 x y) z)
(* x (+ 1 (+ (/ y x) (/ z x))))
(+.f64 (+.f64 x y) z)
(* x (+ 1 (+ (/ y x) (/ z x))))
(+.f64 (+.f64 x y) z)
x
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(+.f64 (+.f64 x y) z)
(+ x z)
(+.f64 x z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
y
(* y (+ 1 (+ (/ x y) (/ z y))))
(+.f64 (+.f64 x y) z)
(* y (+ 1 (+ (/ x y) (/ z y))))
(+.f64 (+.f64 x y) z)
(* y (+ 1 (+ (/ x y) (/ z y))))
(+.f64 (+.f64 x y) z)
y
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(+.f64 (+.f64 x y) z)
(+ x y)
(+.f64 x y)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
z
(* z (+ 1 (+ (/ x z) (/ y z))))
(+.f64 (+.f64 x y) z)
(* z (+ 1 (+ (/ x z) (/ y z))))
(+.f64 (+.f64 x y) z)
(* z (+ 1 (+ (/ x z) (/ y z))))
(+.f64 (+.f64 x y) z)
z
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(+.f64 (+.f64 x y) z)
y
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
x
(* x (+ 1 (/ y x)))
(+.f64 x y)
(* x (+ 1 (/ y x)))
(+.f64 x y)
(* x (+ 1 (/ y x)))
(+.f64 x y)
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 x y)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 x y)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 x y)
x
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
y
(* y (+ 1 (/ x y)))
(+.f64 x y)
(* y (+ 1 (/ x y)))
(+.f64 x y)
(* y (+ 1 (/ x y)))
(+.f64 x y)
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 x y)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 x y)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 x y)

rewrite184.0ms (6%)

Memory

5.4MiB live, 318.7MiB allocated

Rules

2 973×	`lower-fma.f64`
2 973×	`lower-fma.f32`
2 393×	`lower-*.f64`
2 393×	`lower-*.f32`
1 186×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
0	7	8
1	36	8
2	318	8
3	5039	8
0	8074	8

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

2 → 212

Calls

Call 1

Inputs
(+.f64 (+.f64 x y) z)
(+.f64 x y)

Outputs
(.f64 (pow.f64 (/.f64 (fma.f64 (+.f64 y x) (-.f64 (+.f64 y x) z) (.f64 z z)) (.f64 (fma.f64 (.f64 (+.f64 y x) (+.f64 y x)) (+.f64 y x) (.f64 (.f64 z z) z)) (fma.f64 (.f64 (+.f64 y x) (+.f64 y x)) (+.f64 y x) (.f64 (.f64 (neg.f64 z) z) z)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (+.f64 y x) (+.f64 y x)) (+.f64 y x) (.f64 (.f64 (neg.f64 z) z) z))))
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(/.f64 (neg.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (neg.f64 (-.f64 y x)))
(/.f64 (neg.f64 (*.f64 (neg.f64 (+.f64 y x)) (-.f64 x y))) (neg.f64 (neg.f64 (-.f64 x y))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)))) (neg.f64 (neg.f64 (fma.f64 (-.f64 y x) y (.f64 x x)))))
(/.f64 (.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal 1 binary64)) (-.f64 x y))
(/.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) #s(literal 1 binary64)) (fma.f64 (-.f64 y x) y (*.f64 x x)))
(/.f64 (.f64 (.f64 (fma.f64 y y (.f64 x x)) (.f64 (-.f64 x y) (+.f64 y x))) #s(literal 1 binary64)) (.f64 (fma.f64 y y (.f64 x x)) (-.f64 x y)))
(/.f64 (.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) (-.f64 x y))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 y y) (fma.f64 y y (.f64 x x)) (.f64 (.f64 (*.f64 x x) x) x)) (-.f64 x y)))
(/.f64 (.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) (-.f64 x y))) #s(literal 1 binary64)) (.f64 (.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) (-.f64 x y)) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 y y)) (.f64 (.f64 y y) y) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 y y) y) (-.f64 (.f64 (.f64 y y) y) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x))) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 x x) (-.f64 x y)) (.f64 (-.f64 x y) (.f64 y y))) (*.f64 (-.f64 x y) (-.f64 x y)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x))))
(/.f64 (.f64 (fma.f64 y y (.f64 x x)) (.f64 (-.f64 x y) (+.f64 y x))) (.f64 (-.f64 x y) (fma.f64 y y (*.f64 x x))))
(/.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) (-.f64 x y))) (.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) (.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) (-.f64 x y))))
(/.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) (-.f64 x y))) (.f64 (-.f64 x y) (fma.f64 (.f64 y y) (fma.f64 y y (.f64 x x)) (.f64 (.f64 (.f64 x x) x) x))))
(/.f64 (*.f64 (+.f64 y x) (-.f64 y x)) (-.f64 y x))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 y x) (*.f64 (+.f64 y x) (-.f64 y x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 y x)))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 y y)) (.f64 (.f64 y y) y) (.f64 (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)) (.f64 (.f64 x x) x))) (.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) (fma.f64 (.f64 (.f64 y y) y) (-.f64 (.f64 (.f64 y y) y) (.f64 (.f64 x x) x)) (.f64 (.f64 (.f64 (.f64 x x) x) x) (.f64 x x)))))
(/.f64 (*.f64 (neg.f64 (+.f64 y x)) (-.f64 x y)) (neg.f64 (-.f64 x y)))
(/.f64 (neg.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x))) (neg.f64 (fma.f64 (-.f64 y x) y (.f64 x x))))
(/.f64 (*.f64 (-.f64 x y) (+.f64 y x)) (-.f64 x y))
(/.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (fma.f64 (-.f64 y x) y (.f64 x x)))
(neg.f64 (neg.f64 (+.f64 y x)))
(fma.f64 (/.f64 (.f64 x x) (.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) (-.f64 x y))) (fma.f64 (+.f64 y x) y (.f64 x x)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))
(fma.f64 (/.f64 (.f64 x x) (.f64 (-.f64 x y) (+.f64 y x))) (+.f64 y x) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))
(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 x y)) (neg.f64 (.f64 y (/.f64 y (-.f64 x y)))))
(fma.f64 x (/.f64 x (-.f64 x y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 x y)))))
(-.f64 (/.f64 (.f64 y y) (-.f64 y x)) (/.f64 (.f64 x x) (-.f64 y x)))
(-.f64 (.f64 x (/.f64 x (-.f64 x y))) (.f64 y (/.f64 y (-.f64 x y))))
(exp.f64 (*.f64 (log.f64 (+.f64 y x)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (+.f64 y x))) #s(literal -1 binary64)))
(+.f64 (.f64 x (/.f64 x (-.f64 x y))) (neg.f64 (.f64 y (/.f64 y (-.f64 x y)))))
(+.f64 y x)
(+.f64 x y)

eval29.0ms (0.9%)

Memory: -13.9MiB live, 61.8MiB allocated
Compiler: Compiled 6 638 to 616 computations (90.7% saved)

prune38.0ms (1.2%)

Memory

-1.2MiB live, 82.7MiB allocated

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	257	3	260
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	257	4	261

Accuracy

100.0%

Counts

261 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (+.f64 x y) z)
▶	52.5%	#s(approx (+ (+ x y) z) (+.f64 z y))
▶	98.2%	#s(approx (+ (+ x y) z) (+.f64 x z))
▶	49.7%	#s(approx (+ (+ x y) z) (+.f64 x y))

Compiler

Compiled 29 to 17 computations (41.4% saved)

simplify4.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(+.f64 z y)
cost-diff	0	#s(approx (+ (+ x y) z) (+.f64 z y))
cost-diff	0	(+.f64 x z)
cost-diff	0	#s(approx (+ (+ x y) z) (+.f64 x z))
cost-diff	0	(+.f64 x y)
cost-diff	0	#s(approx (+ (+ x y) z) (+.f64 x y))

Rules

12×	`lower-+.f32`
9×	`lower-+.f64`
4×	`+-commutative`
3×	`lift-+.f64`
2×	`associate-+l+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	42
0	14	42
1	20	42
2	23	42
0	23	42

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (+ (+ x y) z) (+.f64 x y))
(+.f64 x y)
x
y
#s(approx (+ (+ x y) z) (+.f64 x z))
(+.f64 x z)
x
z
#s(approx (+ (+ x y) z) (+.f64 z y))
(+.f64 z y)
z
y

Outputs
#s(approx (+ (+ x y) z) (+.f64 x y))
#s(approx (+ (+ x y) z) (+.f64 y x))
(+.f64 x y)
(+.f64 y x)
x
y
#s(approx (+ (+ x y) z) (+.f64 x z))
#s(approx (+ (+ x y) z) (+.f64 z x))
(+.f64 x z)
(+.f64 z x)
x
z
#s(approx (+ (+ x y) z) (+.f64 z y))
(+.f64 z y)
z
y

localize22.0ms (0.7%)

Memory

1.7MiB live, 40.6MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 z y)
accuracy	30.389087671900892	#s(approx (+ (+ x y) z) (+.f64 z y))
accuracy	0	(+.f64 x z)
accuracy	1.1206040258934167	#s(approx (+ (+ x y) z) (+.f64 x z))
accuracy	0	(+.f64 x y)
accuracy	32.17068358658673	#s(approx (+ (+ x y) z) (+.f64 x y))

Samples

14.0ms

256×

valid

Compiler

Compiled 32 to 9 computations (71.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-add: 5.0ms (87.8% of total)

ival-true: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

series5.0ms (0.2%)

Memory

7.9MiB live, 7.9MiB allocated

Counts

6 → 180

Calls

Call 1

Inputs
#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())
#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ x y) z) (+.f64 x z)) (patch #s(approx (+ (+ x y) z) (+.f64 x z)) #<representation binary64>) () ())
#s(alt (+.f64 x z) (patch (+.f64 x z) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ x y) z) (+.f64 z y)) (patch #s(approx (+ (+ x y) z) (+.f64 z y)) #<representation binary64>) () ())
#s(alt (+.f64 z y) (patch (+.f64 z y) #<representation binary64>) () ())

Outputs
#s(alt (+ y z) (taylor 0 x) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 x) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 x) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 x) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (/ y x) (/ z x)))) (taylor inf x) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (/ y x) (/ z x)))) (taylor inf x) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (+ (/ y x) (/ z x)))) (taylor inf x) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (+ y z) x)) 1))) (taylor -inf x) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (+ y z) x)) 1))) (taylor -inf x) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (+ y z) x)) 1))) (taylor -inf x) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ x z) (taylor 0 y) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 y) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 y) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 y) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (/ x y) (/ z y)))) (taylor inf y) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (/ x y) (/ z y)))) (taylor inf y) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (+ (/ x y) (/ z y)))) (taylor inf y) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (+ x z) y)) 1))) (taylor -inf y) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (+ x z) y)) 1))) (taylor -inf y) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (+ x z) y)) 1))) (taylor -inf y) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 z) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 z) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 z) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 z) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt z (taylor inf z) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* z (+ 1 (+ (/ x z) (/ y z)))) (taylor inf z) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* z (+ 1 (+ (/ x z) (/ y z)))) (taylor inf z) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* z (+ 1 (+ (/ x z) (/ y z)))) (taylor inf z) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt z (taylor -inf z) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ (+ x y) z)) 1))) (taylor -inf z) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ (+ x y) z)) 1))) (taylor -inf z) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (- (* -1 (/ (+ x y) z)) 1))) (taylor -inf z) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x y)) (patch #s(approx (+ (+ x y) z) (+.f64 x y)) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ y x))) (taylor inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ y x)) 1))) (taylor -inf x) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ x y) (taylor 0 y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt y (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ x y))) (taylor inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt y (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ x y)) 1))) (taylor -inf y) (#s(alt (+.f64 x y) (patch (+.f64 x y) #<representation binary64>) () ())) ())
#s(alt (+ y z) (taylor 0 x) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x z)) (patch #s(approx (+ (+ x y) z) (+.f64 x z)) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 x) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x z)) (patch #s(approx (+ (+ x y) z) (+.f64 x z)) #<representation binary64>) () ())) ())
#s(alt (+ x (+ y z)) (taylor 0 x) (#s(alt #s(approx (+ (+ x y) z) (+.f64 x z)) (patch #s(approx (+ (+ x y) z) (+.f64 x z)) #<representation binary64>) () ())) ())
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#s(alt (* y (+ 1 (/ z y))) (taylor inf y) (#s(alt (+.f64 z y) (patch (+.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* y (+ 1 (/ z y))) (taylor inf y) (#s(alt (+.f64 z y) (patch (+.f64 z y) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* y (- (* -1 (/ z y)) 1))) (taylor -inf y) (#s(alt (+.f64 z y) (patch (+.f64 z y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ z y)) 1))) (taylor -inf y) (#s(alt (+.f64 z y) (patch (+.f64 z y) #<representation binary64>) () ())) ())

Calls

45 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(+ x z)
0.0ms	x	@	-inf	(+ x z)
0.0ms	z	@	-inf	(+ z y)
0.0ms	y	@	-inf	(+ z y)
0.0ms	z	@	-inf	(+ x z)

simplify272.0ms (8.9%)

Memory

-29.1MiB live, 254.9MiB allocated

Algorithm

1×	egg-herbie

Rules

10 400×	`lower-fma.f64`
10 400×	`lower-fma.f32`
2 884×	`lower-/.f32`
2 884×	`lower-/.f64`
1 443×	`associate-/r*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	630
1	227	630
2	564	630
3	1707	630
4	4046	630
5	4678	630
6	5034	630
7	5172	630
8	5196	630
9	5196	630
0	9436	630

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 144

Calls

Call 1

Inputs
(+ y z)
(+ x (+ y z))
(+ x (+ y z))
(+ x (+ y z))
x
(* x (+ 1 (+ (/ y x) (/ z x))))
(* x (+ 1 (+ (/ y x) (/ z x))))
(* x (+ 1 (+ (/ y x) (/ z x))))
x
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(+ x z)
(+ x (+ y z))
(+ x (+ y z))
(+ x (+ y z))
y
(* y (+ 1 (+ (/ x y) (/ z y))))
(* y (+ 1 (+ (/ x y) (/ z y))))
(* y (+ 1 (+ (/ x y) (/ z y))))
y
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(+ x y)
(+ x (+ y z))
(+ x (+ y z))
(+ x (+ y z))
z
(* z (+ 1 (+ (/ x z) (/ y z))))
(* z (+ 1 (+ (/ x z) (/ y z))))
(* z (+ 1 (+ (/ x z) (/ y z))))
z
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
y
(+ x y)
(+ x y)
(+ x y)
x
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
(* x (+ 1 (/ y x)))
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
x
(+ x y)
(+ x y)
(+ x y)
y
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
(* y (+ 1 (/ x y)))
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+ y z)
(+ x (+ y z))
(+ x (+ y z))
(+ x (+ y z))
x
(* x (+ 1 (+ (/ y x) (/ z x))))
(* x (+ 1 (+ (/ y x) (/ z x))))
(* x (+ 1 (+ (/ y x) (/ z x))))
x
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(+ x z)
(+ x (+ y z))
(+ x (+ y z))
(+ x (+ y z))
y
(* y (+ 1 (+ (/ x y) (/ z y))))
(* y (+ 1 (+ (/ x y) (/ z y))))
(* y (+ 1 (+ (/ x y) (/ z y))))
y
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(+ x y)
(+ x (+ y z))
(+ x (+ y z))
(+ x (+ y z))
z
(* z (+ 1 (+ (/ x z) (/ y z))))
(* z (+ 1 (+ (/ x z) (/ y z))))
(* z (+ 1 (+ (/ x z) (/ y z))))
z
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
z
(+ x z)
(+ x z)
(+ x z)
x
(* x (+ 1 (/ z x)))
(* x (+ 1 (/ z x)))
(* x (+ 1 (/ z x)))
x
(* -1 (* x (- (* -1 (/ z x)) 1)))
(* -1 (* x (- (* -1 (/ z x)) 1)))
(* -1 (* x (- (* -1 (/ z x)) 1)))
x
(+ x z)
(+ x z)
(+ x z)
z
(* z (+ 1 (/ x z)))
(* z (+ 1 (/ x z)))
(* z (+ 1 (/ x z)))
z
(* -1 (* z (- (* -1 (/ x z)) 1)))
(* -1 (* z (- (* -1 (/ x z)) 1)))
(* -1 (* z (- (* -1 (/ x z)) 1)))
(+ y z)
(+ x (+ y z))
(+ x (+ y z))
(+ x (+ y z))
x
(* x (+ 1 (+ (/ y x) (/ z x))))
(* x (+ 1 (+ (/ y x) (/ z x))))
(* x (+ 1 (+ (/ y x) (/ z x))))
x
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(+ x z)
(+ x (+ y z))
(+ x (+ y z))
(+ x (+ y z))
y
(* y (+ 1 (+ (/ x y) (/ z y))))
(* y (+ 1 (+ (/ x y) (/ z y))))
(* y (+ 1 (+ (/ x y) (/ z y))))
y
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(+ x y)
(+ x (+ y z))
(+ x (+ y z))
(+ x (+ y z))
z
(* z (+ 1 (+ (/ x z) (/ y z))))
(* z (+ 1 (+ (/ x z) (/ y z))))
(* z (+ 1 (+ (/ x z) (/ y z))))
z
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
y
(+ y z)
(+ y z)
(+ y z)
z
(* z (+ 1 (/ y z)))
(* z (+ 1 (/ y z)))
(* z (+ 1 (/ y z)))
z
(* -1 (* z (- (* -1 (/ y z)) 1)))
(* -1 (* z (- (* -1 (/ y z)) 1)))
(* -1 (* z (- (* -1 (/ y z)) 1)))
z
(+ y z)
(+ y z)
(+ y z)
y
(* y (+ 1 (/ z y)))
(* y (+ 1 (/ z y)))
(* y (+ 1 (/ z y)))
y
(* -1 (* y (- (* -1 (/ z y)) 1)))
(* -1 (* y (- (* -1 (/ z y)) 1)))
(* -1 (* y (- (* -1 (/ z y)) 1)))

Outputs
(+ y z)
(+.f64 z y)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
x
(* x (+ 1 (+ (/ y x) (/ z x))))
(+.f64 (+.f64 x y) z)
(* x (+ 1 (+ (/ y x) (/ z x))))
(+.f64 (+.f64 x y) z)
(* x (+ 1 (+ (/ y x) (/ z x))))
(+.f64 (+.f64 x y) z)
x
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(+.f64 (+.f64 x y) z)
(+ x z)
(+.f64 x z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
y
(* y (+ 1 (+ (/ x y) (/ z y))))
(+.f64 (+.f64 x y) z)
(* y (+ 1 (+ (/ x y) (/ z y))))
(+.f64 (+.f64 x y) z)
(* y (+ 1 (+ (/ x y) (/ z y))))
(+.f64 (+.f64 x y) z)
y
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(+.f64 (+.f64 x y) z)
(+ x y)
(+.f64 x y)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
z
(* z (+ 1 (+ (/ x z) (/ y z))))
(+.f64 (+.f64 x y) z)
(* z (+ 1 (+ (/ x z) (/ y z))))
(+.f64 (+.f64 x y) z)
(* z (+ 1 (+ (/ x z) (/ y z))))
(+.f64 (+.f64 x y) z)
z
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(+.f64 (+.f64 x y) z)
y
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
x
(* x (+ 1 (/ y x)))
(+.f64 x y)
(* x (+ 1 (/ y x)))
(+.f64 x y)
(* x (+ 1 (/ y x)))
(+.f64 x y)
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 x y)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 x y)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 x y)
x
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
(+ x y)
(+.f64 x y)
y
(* y (+ 1 (/ x y)))
(+.f64 x y)
(* y (+ 1 (/ x y)))
(+.f64 x y)
(* y (+ 1 (/ x y)))
(+.f64 x y)
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 x y)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 x y)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 x y)
(+ y z)
(+.f64 z y)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
x
(* x (+ 1 (+ (/ y x) (/ z x))))
(+.f64 (+.f64 x y) z)
(* x (+ 1 (+ (/ y x) (/ z x))))
(+.f64 (+.f64 x y) z)
(* x (+ 1 (+ (/ y x) (/ z x))))
(+.f64 (+.f64 x y) z)
x
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(+.f64 (+.f64 x y) z)
(+ x z)
(+.f64 x z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
y
(* y (+ 1 (+ (/ x y) (/ z y))))
(+.f64 (+.f64 x y) z)
(* y (+ 1 (+ (/ x y) (/ z y))))
(+.f64 (+.f64 x y) z)
(* y (+ 1 (+ (/ x y) (/ z y))))
(+.f64 (+.f64 x y) z)
y
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(+.f64 (+.f64 x y) z)
(+ x y)
(+.f64 x y)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
z
(* z (+ 1 (+ (/ x z) (/ y z))))
(+.f64 (+.f64 x y) z)
(* z (+ 1 (+ (/ x z) (/ y z))))
(+.f64 (+.f64 x y) z)
(* z (+ 1 (+ (/ x z) (/ y z))))
(+.f64 (+.f64 x y) z)
z
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(+.f64 (+.f64 x y) z)
z
(+ x z)
(+.f64 x z)
(+ x z)
(+.f64 x z)
(+ x z)
(+.f64 x z)
x
(* x (+ 1 (/ z x)))
(+.f64 x z)
(* x (+ 1 (/ z x)))
(+.f64 x z)
(* x (+ 1 (/ z x)))
(+.f64 x z)
x
(* -1 (* x (- (* -1 (/ z x)) 1)))
(+.f64 x z)
(* -1 (* x (- (* -1 (/ z x)) 1)))
(+.f64 x z)
(* -1 (* x (- (* -1 (/ z x)) 1)))
(+.f64 x z)
x
(+ x z)
(+.f64 x z)
(+ x z)
(+.f64 x z)
(+ x z)
(+.f64 x z)
z
(* z (+ 1 (/ x z)))
(+.f64 x z)
(* z (+ 1 (/ x z)))
(+.f64 x z)
(* z (+ 1 (/ x z)))
(+.f64 x z)
z
(* -1 (* z (- (* -1 (/ x z)) 1)))
(+.f64 x z)
(* -1 (* z (- (* -1 (/ x z)) 1)))
(+.f64 x z)
(* -1 (* z (- (* -1 (/ x z)) 1)))
(+.f64 x z)
(+ y z)
(+.f64 z y)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
x
(* x (+ 1 (+ (/ y x) (/ z x))))
(+.f64 (+.f64 x y) z)
(* x (+ 1 (+ (/ y x) (/ z x))))
(+.f64 (+.f64 x y) z)
(* x (+ 1 (+ (/ y x) (/ z x))))
(+.f64 (+.f64 x y) z)
x
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* x (- (* -1 (/ (+ y z) x)) 1)))
(+.f64 (+.f64 x y) z)
(+ x z)
(+.f64 x z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
y
(* y (+ 1 (+ (/ x y) (/ z y))))
(+.f64 (+.f64 x y) z)
(* y (+ 1 (+ (/ x y) (/ z y))))
(+.f64 (+.f64 x y) z)
(* y (+ 1 (+ (/ x y) (/ z y))))
(+.f64 (+.f64 x y) z)
y
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* y (- (* -1 (/ (+ x z) y)) 1)))
(+.f64 (+.f64 x y) z)
(+ x y)
(+.f64 x y)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
(+ x (+ y z))
(+.f64 (+.f64 x y) z)
z
(* z (+ 1 (+ (/ x z) (/ y z))))
(+.f64 (+.f64 x y) z)
(* z (+ 1 (+ (/ x z) (/ y z))))
(+.f64 (+.f64 x y) z)
(* z (+ 1 (+ (/ x z) (/ y z))))
(+.f64 (+.f64 x y) z)
z
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(+.f64 (+.f64 x y) z)
(* -1 (* z (- (* -1 (/ (+ x y) z)) 1)))
(+.f64 (+.f64 x y) z)
y
(+ y z)
(+.f64 z y)
(+ y z)
(+.f64 z y)
(+ y z)
(+.f64 z y)
z
(* z (+ 1 (/ y z)))
(+.f64 z y)
(* z (+ 1 (/ y z)))
(+.f64 z y)
(* z (+ 1 (/ y z)))
(+.f64 z y)
z
(* -1 (* z (- (* -1 (/ y z)) 1)))
(+.f64 z y)
(* -1 (* z (- (* -1 (/ y z)) 1)))
(+.f64 z y)
(* -1 (* z (- (* -1 (/ y z)) 1)))
(+.f64 z y)
z
(+ y z)
(+.f64 z y)
(+ y z)
(+.f64 z y)
(+ y z)
(+.f64 z y)
y
(* y (+ 1 (/ z y)))
(+.f64 z y)
(* y (+ 1 (/ z y)))
(+.f64 z y)
(* y (+ 1 (/ z y)))
(+.f64 z y)
y
(* -1 (* y (- (* -1 (/ z y)) 1)))
(+.f64 z y)
(* -1 (* y (- (* -1 (/ z y)) 1)))
(+.f64 z y)
(* -1 (* y (- (* -1 (/ z y)) 1)))
(+.f64 z y)

rewrite361.0ms (11.8%)

Memory

46.2MiB live, 236.0MiB allocated

Rules

2 251×	`lower-*.f64`
2 251×	`lower-*.f32`
2 235×	`lower-fma.f64`
2 235×	`lower-fma.f32`
1 810×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	36
0	14	36
1	61	36
2	486	36
3	7205	36
0	8325	36

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

6 → 177

Calls

Call 1

Inputs
#s(approx (+ (+ x y) z) (+.f64 x y))
(+.f64 x y)
#s(approx (+ (+ x y) z) (+.f64 x z))
(+.f64 x z)
#s(approx (+ (+ x y) z) (+.f64 z y))
(+.f64 z y)

Outputs
#s(approx (+ (+ x y) z) (+.f64 y x))
(.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) (-.f64 x y))) (fma.f64 (+.f64 y x) y (*.f64 x x)))
(.f64 (/.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) (-.f64 (.f64 x x) (.f64 (-.f64 y x) y)))) (-.f64 (.f64 x x) (.f64 (-.f64 y x) y)))
(.f64 (/.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 x x)) x (.f64 (.f64 (.f64 (-.f64 y x) y) (.f64 (-.f64 y x) y)) (.f64 (-.f64 y x) y)))) (fma.f64 (.f64 (-.f64 y x) y) (-.f64 (.f64 (-.f64 y x) y) (.f64 x x)) (.f64 (.f64 x x) (*.f64 x x))))
(.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (*.f64 (-.f64 x y) (+.f64 y x))) (+.f64 y x))
(.f64 (.f64 (+.f64 y x) (-.f64 y x)) (/.f64 #s(literal 1 binary64) (-.f64 y x)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x y)) (.f64 (-.f64 x y) (+.f64 y x)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 y x) y (.f64 x x))) (fma.f64 (.f64 y y) y (.f64 (*.f64 x x) x)))
(*.f64 #s(literal 1 binary64) (+.f64 y x))
(.f64 (.f64 (neg.f64 (+.f64 y x)) (-.f64 x y)) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x y))))
(.f64 (neg.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 y x) y (*.f64 x x)))))
(.f64 (.f64 (-.f64 x y) (+.f64 y x)) (/.f64 #s(literal 1 binary64) (-.f64 x y)))
(.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) (/.f64 (+.f64 y x) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(.f64 (fma.f64 (-.f64 y x) y (.f64 x x)) (.f64 (+.f64 y x) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 y x) y (.f64 x x)))))
(.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 y x) y (*.f64 x x))))
(*.f64 (+.f64 y x) (/.f64 (-.f64 x y) (-.f64 x y)))
(.f64 (+.f64 y x) (.f64 (-.f64 x y) (/.f64 #s(literal 1 binary64) (-.f64 x y))))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 y x)) #s(literal -1 binary64))
(/.f64 (.f64 (.f64 (fma.f64 y y (.f64 x x)) (.f64 (-.f64 x y) (+.f64 y x))) (/.f64 #s(literal 1 binary64) (-.f64 x y))) (fma.f64 y y (*.f64 x x)))
(/.f64 (.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) (-.f64 x y))) (/.f64 #s(literal 1 binary64) (-.f64 x y))) (fma.f64 (.f64 y y) (fma.f64 y y (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))))
(/.f64 (.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)) (.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) (-.f64 x y))) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 y x) y (.f64 x x)))) (.f64 (fma.f64 (+.f64 y x) y (.f64 x x)) (-.f64 x y)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 y y)) (.f64 (.f64 y y) y) (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) (.f64 (.f64 x x) x))) (/.f64 #s(literal 1 binary64) (fma.f64 (-.f64 y x) y (.f64 x x)))) (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 x x)) x (.f64 (.f64 (.f64 y y) y) (-.f64 (.f64 (.f64 y y) y) (.f64 (.f64 x x) x)))))
(/.f64 (-.f64 (.f64 (.f64 x (/.f64 x (-.f64 x y))) (.f64 x (/.f64 x (-.f64 x y)))) (.f64 (.f64 y (/.f64 y (-.f64 x y))) (.f64 y (/.f64 y (-.f64 x y))))) (fma.f64 x (/.f64 x (-.f64 x y)) (*.f64 y (/.f64 y (-.f64 x y)))))
(/.f64 (-.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 x y))) #s(literal 3 binary64)) (pow.f64 (.f64 y (/.f64 y (-.f64 x y))) #s(literal 3 binary64))) (fma.f64 (.f64 x (/.f64 x (-.f64 x y))) (.f64 x (/.f64 x (-.f64 x y))) (fma.f64 (.f64 y (/.f64 y (-.f64 x y))) (.f64 y (/.f64 y (-.f64 x y))) (.f64 (.f64 x (/.f64 x (-.f64 x y))) (*.f64 y (/.f64 y (-.f64 x y)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 y x) (-.f64 y x))) (neg.f64 (-.f64 y x)))
(/.f64 (neg.f64 (*.f64 (neg.f64 (+.f64 y x)) (-.f64 x y))) (neg.f64 (neg.f64 (-.f64 x y))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 x x) x)))) (neg.f64 (neg.f64 (fma.f64 (-.f64 y x) y (.f64 x x)))))
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(/.f64 (.f64 (.f64 (-.f64 z y) (+.f64 z y)) #s(literal 1 binary64)) (-.f64 z y))
(/.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 z z) z)) #s(literal 1 binary64)) (fma.f64 (-.f64 y z) y (*.f64 z z)))
(/.f64 (.f64 (.f64 (fma.f64 z z (.f64 y y)) (.f64 (-.f64 z y) (+.f64 z y))) #s(literal 1 binary64)) (.f64 (fma.f64 z z (.f64 y y)) (-.f64 z y)))
(/.f64 (.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 z z) z)) (.f64 (fma.f64 y (+.f64 z y) (.f64 z z)) (-.f64 z y))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 y y) (fma.f64 z z (.f64 y y)) (.f64 (.f64 z z) (*.f64 z z))) (-.f64 z y)))
(/.f64 (.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 z z) z)) (.f64 (fma.f64 y (+.f64 z y) (.f64 z z)) (-.f64 z y))) #s(literal 1 binary64)) (.f64 (.f64 (fma.f64 y (+.f64 z y) (.f64 z z)) (-.f64 z y)) (fma.f64 (-.f64 y z) y (*.f64 z z))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 y y)) (.f64 (.f64 y y) y) (.f64 (.f64 (.f64 (.f64 z z) (.f64 z z)) (.f64 z z)) (.f64 (.f64 z z) z))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 y y) y) (-.f64 (.f64 (.f64 y y) y) (.f64 (.f64 z z) z)) (.f64 (.f64 (.f64 z z) (.f64 z z)) (.f64 z z))) (fma.f64 (-.f64 y z) y (*.f64 z z))))
(/.f64 (-.f64 (.f64 (.f64 z z) (-.f64 z y)) (.f64 (-.f64 z y) (.f64 y y))) (*.f64 (-.f64 z y) (-.f64 z y)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 z y))))
(/.f64 (.f64 (fma.f64 z z (.f64 y y)) (.f64 (-.f64 z y) (+.f64 z y))) (.f64 (-.f64 z y) (fma.f64 z z (*.f64 y y))))
(/.f64 (*.f64 (+.f64 z y) (-.f64 y z)) (-.f64 y z))
(/.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 z z) z)) (.f64 (fma.f64 y (+.f64 z y) (.f64 z z)) (-.f64 z y))) (.f64 (-.f64 z y) (fma.f64 (.f64 y y) (fma.f64 z z (.f64 y y)) (.f64 (.f64 z z) (.f64 z z)))))
(/.f64 (.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 z z) z)) (.f64 (fma.f64 y (+.f64 z y) (.f64 z z)) (-.f64 z y))) (.f64 (fma.f64 (-.f64 y z) y (.f64 z z)) (.f64 (fma.f64 y (+.f64 z y) (.f64 z z)) (-.f64 z y))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 y z) (*.f64 (+.f64 z y) (-.f64 y z))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 z y)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 z y)))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 y y)) (.f64 (.f64 y y) y) (.f64 (.f64 (.f64 (.f64 z z) (.f64 z z)) (.f64 z z)) (.f64 (.f64 z z) z))) (.f64 (fma.f64 (-.f64 y z) y (.f64 z z)) (fma.f64 (.f64 (.f64 y y) y) (-.f64 (.f64 (.f64 y y) y) (.f64 (.f64 z z) z)) (.f64 (.f64 (.f64 z z) (.f64 z z)) (.f64 z z)))))
(/.f64 (*.f64 (neg.f64 (+.f64 z y)) (-.f64 z y)) (neg.f64 (-.f64 z y)))
(/.f64 (neg.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 z z) z))) (neg.f64 (fma.f64 (-.f64 y z) y (.f64 z z))))
(/.f64 (*.f64 (-.f64 z y) (+.f64 z y)) (-.f64 z y))
(/.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 z z) z)) (fma.f64 (-.f64 y z) y (.f64 z z)))
(neg.f64 (/.f64 (*.f64 (neg.f64 (+.f64 z y)) (-.f64 z y)) (-.f64 z y)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 z z) z))) (fma.f64 (-.f64 y z) y (.f64 z z))))
(neg.f64 (/.f64 (*.f64 (-.f64 z y) (+.f64 z y)) (neg.f64 (-.f64 z y))))
(neg.f64 (/.f64 (fma.f64 (.f64 y y) y (.f64 (.f64 z z) z)) (neg.f64 (fma.f64 (-.f64 y z) y (.f64 z z)))))
(fma.f64 (/.f64 (.f64 z z) (.f64 (fma.f64 y (+.f64 z y) (.f64 z z)) (-.f64 z y))) (fma.f64 y (+.f64 z y) (.f64 z z)) (neg.f64 (*.f64 y (/.f64 y (-.f64 z y)))))
(fma.f64 (/.f64 (.f64 z z) (.f64 (-.f64 z y) (+.f64 z y))) (+.f64 z y) (neg.f64 (*.f64 y (/.f64 y (-.f64 z y)))))
(fma.f64 (.f64 z z) (/.f64 #s(literal 1 binary64) (-.f64 z y)) (neg.f64 (.f64 y (/.f64 y (-.f64 z y)))))
(fma.f64 z (/.f64 z (-.f64 z y)) (neg.f64 (*.f64 y (/.f64 y (-.f64 z y)))))
(-.f64 (/.f64 (.f64 y y) (-.f64 y z)) (/.f64 (.f64 z z) (-.f64 y z)))
(-.f64 (.f64 z (/.f64 z (-.f64 z y))) (.f64 y (/.f64 y (-.f64 z y))))
(+.f64 (.f64 z (/.f64 z (-.f64 z y))) (neg.f64 (.f64 y (/.f64 y (-.f64 z y)))))
(+.f64 z y)
(+.f64 y z)

eval58.0ms (1.9%)

Memory: -15.7MiB live, 59.2MiB allocated
Compiler: Compiled 5 310 to 481 computations (90.9% saved)

prune34.0ms (1.1%)

Memory

3.9MiB live, 50.1MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	321	0	321
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	321	4	325

Accuracy

100.0%

Counts

325 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (+.f64 x y) z)
✓	52.5%	#s(approx (+ (+ x y) z) (+.f64 z y))
✓	98.2%	#s(approx (+ (+ x y) z) (+.f64 x z))
✓	49.7%	#s(approx (+ (+ x y) z) (+.f64 x y))

Compiler

Compiled 49 to 24 computations (51% saved)

regimes34.0ms (1.1%)

Memory

-19.0MiB live, 19.4MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (+ (+ x y) z) (+.f64 x y))
#s(approx (+ (+ x y) z) (+.f64 x z))
#s(approx (+ (+ x y) z) (+.f64 z y))
(+.f64 (+.f64 x y) z)

Outputs
(+.f64 (+.f64 x y) z)

Calls

5 calls:

25.0ms	y
2.0ms	(+.f64 x y)
2.0ms	x
2.0ms	(+.f64 (+.f64 x y) z)
2.0ms	z

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`z`
100.0%	1	`(+.f64 (+.f64 x y) z)`
100.0%	1	`(+.f64 x y)`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes10.0ms (0.3%)

Memory

15.6MiB live, 15.6MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs
#s(approx (+ (+ x y) z) (+.f64 x y))
#s(approx (+ (+ x y) z) (+.f64 x z))
#s(approx (+ (+ x y) z) (+.f64 z y))

Outputs
#s(approx (+ (+ x y) z) (+.f64 x z))

Calls

5 calls:

2.0ms	(+.f64 x y)
2.0ms	y
2.0ms	x
2.0ms	z
2.0ms	(+.f64 (+.f64 x y) z)

Results

Accuracy	Segments	Branch
98.2%	1	`x`
98.2%	1	`y`
98.2%	1	`z`
98.2%	1	`(+.f64 (+.f64 x y) z)`
98.2%	1	`(+.f64 x y)`

Compiler

Compiled 26 to 18 computations (30.8% saved)

regimes7.0ms (0.2%)

Memory

12.2MiB live, 12.2MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (+ (+ x y) z) (+.f64 x y))

Outputs
#s(approx (+ (+ x y) z) (+.f64 x y))

Calls

5 calls:

1.0ms	(+.f64 (+.f64 x y) z)
1.0ms	x
1.0ms	(+.f64 x y)
1.0ms	y
1.0ms	z

Results

Accuracy	Segments	Branch
49.7%	1	`x`
49.7%	1	`y`
49.7%	1	`z`
49.7%	1	`(+.f64 (+.f64 x y) z)`
49.7%	1	`(+.f64 x y)`

Compiler

Compiled 26 to 18 computations (30.8% saved)

simplify27.0ms (0.9%)

Memory

-30.7MiB live, 8.0MiB allocated

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	13	23

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (+.f64 x y) z)
#s(approx (+ (+ x y) z) (+.f64 x z))
#s(approx (+ (+ x y) z) (+.f64 x y))

Outputs
(+.f64 (+.f64 x y) z)
(+.f64 z (+.f64 y x))
#s(approx (+ (+ x y) z) (+.f64 x z))
#s(approx (+ (+ x y) z) (+.f64 z x))
#s(approx (+ (+ x y) z) (+.f64 x y))
#s(approx (+ (+ x y) z) (+.f64 y x))

soundness491.0ms (16%)

Memory

30.5MiB live, 158.0MiB allocated

Rules

2 384×	`lower-/.f32`
2 384×	`lower-/.f64`
1 432×	`lower-fma.f64`
1 432×	`lower-fma.f32`
1 080×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	210
1	148	210
2	381	210
3	1185	210
4	2960	210
5	4921	210
6	5879	210
7	6006	210
8	6088	210
9	6102	210
0	8854	210

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 28 to 14 computations (50% saved)

preprocess44.0ms (1.4%)

Memory: -14.3MiB live, 105.1MiB allocated
Remove: (sort x y z)
Compiler: Compiled 112 to 62 computations (44.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	21	50
1	62	45
2	191	45
3	490	45
4	780	45
5	843	45
6	859	45
0	5	5
0	7	5
1	11	5
2	18	5
3	20	5
0	20	5

Iter	Nodes	Cost
0	21	50
1	62	45
2	191	45
3	490	45
4	780	45
5	843	45
6	859	45
0	5	5
0	7	5
1	11	5
2	18	5
3	20	5
0	20	5

start0.0ms (0%)

analyze0.0ms (0%)

sample1.2s (39.3%)

explain52.0ms (1.7%)

preprocess28.0ms (0.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize15.0ms (0.5%)

series5.0ms (0.2%)

simplify137.0ms (4.5%)

rewrite184.0ms (6%)

eval29.0ms (0.9%)

prune38.0ms (1.2%)

simplify4.0ms (0.1%)

localize22.0ms (0.7%)

series5.0ms (0.2%)

simplify272.0ms (8.9%)

rewrite361.0ms (11.8%)

eval58.0ms (1.9%)

prune34.0ms (1.1%)

regimes34.0ms (1.1%)

regimes10.0ms (0.3%)

regimes7.0ms (0.2%)

simplify27.0ms (0.9%)

soundness491.0ms (16%)

preprocess44.0ms (1.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	21	50
1	62	45
2	191	45
3	490	45
4	780	45
5	843	45
6	859	45
0	5	5
0	7	5
1	11	5
2	18	5
3	20	5
0	20	5