Metrics for Numeric.Integration.TanhSinh:everywhere from integration-0.2.1

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB 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 9 to 8 computations (11.1% saved)

sample890.0ms (18.6%)

Memory

-18.4MiB live, 742.8MiB allocated

Samples

555.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 348.0ms

ival-mult: 173.0ms (49.7% of total)

ival-add: 160.0ms (45.9% of total)

ival-true: 6.0ms (1.7% of total)

exact: 5.0ms (1.4% of total)

ival-assert: 3.0ms (0.9% of total)

Bogosity

explain83.0ms (1.7%)

Memory

28.3MiB live, 151.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
14	-	-	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`
0	-	-	`y`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(*.f64 y y)`
0	-	-	`(+.f64 #s(literal 1 binary64) (*.f64 y y))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`*.f64`	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`	*no**	14	0

Confusion

	Predicted +	Predicted -
+	14	0
-	0	242

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	14	0	0
-	0	0	242

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	242
1	14

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

45.0ms

512×

valid

Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-mult: 24.0ms (86.7% of total)

ival-add: 2.0ms (7.2% of total)

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

exact: 0.0ms (0% of total)

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

preprocess39.0ms (0.8%)

Memory

-5.0MiB live, 33.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	37
1	65	37
2	194	35
3	463	35
4	639	35
5	762	35
6	789	35
0	6	7
0	9	7
1	19	7
2	27	7
3	49	7
4	49	7
0	49	6

Stop Event

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

Calls

Call 1

Inputs
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))

Outputs
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)

Symmetry

(abs y)

(negabs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	94.7%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0.1%)

Memory

5.4MiB live, 5.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 y y)
cost-diff	0	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
cost-diff	128	(+.f64 #s(literal 1 binary64) (*.f64 y y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	9	18
1	19	18
2	27	18
3	49	18
4	49	18
0	49	16

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
x
(+.f64 #s(literal 1 binary64) (*.f64 y y))
#s(literal 1 binary64)
(*.f64 y y)
y

Outputs
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
x
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(fma.f64 y y #s(literal 1 binary64))
#s(literal 1 binary64)
(*.f64 y y)
y

localize30.0ms (0.6%)

Memory

-4.6MiB live, 32.5MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 #s(literal 1 binary64) (*.f64 y y))
accuracy	0	(*.f64 y y)
accuracy	3.361592420394443	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))

Samples

25.0ms

256×

valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

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

ival-mult: 3.0ms (60.3% of total)

ival-add: 1.0ms (20.1% of total)

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

exact: 0.0ms (0% of total)

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

series18.0ms (0.4%)

Memory

-25.4MiB live, 11.9MiB allocated

Counts

3 → 48

Calls

Call 1

Inputs
#s(alt (+.f64 #s(literal 1 binary64) (.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (.f64 y y)) #<representation binary64>) () ())
#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())
#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())

Inputs

#s(alt (+.f64 #s(literal 1 binary64) (*.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (*.f64 y y)) #<representation binary64>) () ())

#s(alt (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) (patch (*.f64 x (+.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())

#s(alt (*.f64 y y) (patch (*.f64 y y) #<representation binary64>) () ())

Outputs
#s(alt 1 (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt (+.f64 #s(literal 1 binary64) (.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ 1 (pow y 2)))) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ 1 (pow y 2)))) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ 1 (pow y 2)))) (taylor inf y) (#s(alt (+.f64 #s(literal 1 binary64) (.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* x (pow y 2)) (taylor inf y) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor inf y) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor inf y) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor inf y) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ 1 (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ 1 (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ 1 (/ 1 (pow y 2)))) (taylor -inf y) (#s(alt (+.f64 #s(literal 1 binary64) (.f64 y y)) (patch (+.f64 #s(literal 1 binary64) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* x (pow y 2)) (taylor -inf y) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor -inf y) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor -inf y) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor -inf y) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor -inf y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) (patch (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((+ 1 (* y y)) (* x (+ 1 (* y y))) (* y y))
1.0ms	y	@	inf	((+ 1 (* y y)) (* x (+ 1 (* y y))) (* y y))
1.0ms	x	@	0	((+ 1 (* y y)) (* x (+ 1 (* y y))) (* y y))
1.0ms	y	@	0	((+ 1 (* y y)) (* x (+ 1 (* y y))) (* y y))
1.0ms	x	@	-inf	((+ 1 (* y y)) (* x (+ 1 (* y y))) (* y y))

simplify517.0ms (10.8%)

Memory

12.8MiB live, 254.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	246
1	42	246
2	74	246
3	214	246
4	721	246
5	1940	246
6	2658	246
7	3752	246
8	5094	246
9	5986	246
10	6927	246
11	7270	246
12	7376	246
13	7453	246
14	7522	246
15	7669	246
0	8207	216

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

Calls

Call 1

Inputs
1
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(+ 1 (pow y 2))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))

Outputs
1
#s(literal 1 binary64)
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
x
(+ x (* x (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(+ x (* x (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(+ x (* x (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(* x (+ 1 (pow y 2)))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))

rewrite200.0ms (4.2%)

Memory

9.0MiB live, 291.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	9	15
1	34	15
2	209	15
3	1404	15
0	8269	13

Stop Event

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

Counts

3 → 368

Calls

Call 1

Inputs
(+.f64 #s(literal 1 binary64) (*.f64 y y))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
(*.f64 y y)

Outputs
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eval89.0ms (1.9%)

Memory: -1.2MiB live, 72.3MiB allocated
Compiler: Compiled 9 642 to 1 119 computations (88.4% saved)

prune12.0ms (0.2%)

Memory

-9.1MiB live, 28.0MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	410	5	415
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	411	5	416

Accuracy

100.0%

Counts

416 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(fma.f64 (*.f64 x y) y x)
▶	94.8%	(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
▶	94.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64)))))
▶	50.0%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
▶	48.9%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 68 to 56 computations (17.6% saved)

simplify7.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 y y #s(literal 1 binary64))
cost-diff	0	(pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))
cost-diff	6848	(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
cost-diff	0	(fma.f64 y y #s(literal 1 binary64))
cost-diff	0	(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64))))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64)))))
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (+ 1 (* y y)) (*.f64 y y))
cost-diff	0	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
cost-diff	0	#s(approx (+ 1 (* y y)) #s(literal 1 binary64))
cost-diff	0	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))
cost-diff	0	(*.f64 x y)
cost-diff	0	(fma.f64 (*.f64 x y) y x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	107
0	31	97
1	53	97
2	74	97
3	123	97
4	142	97
5	160	97
6	160	97
0	160	97

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(fma.f64 (*.f64 x y) y x)
(*.f64 x y)
x
y
(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))
x
#s(approx (+ 1 (* y y)) #s(literal 1 binary64))
#s(literal 1 binary64)
(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
x
#s(approx (+ 1 (* y y)) (*.f64 y y))
(*.f64 y y)
y
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64)))))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64))))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
x
(fma.f64 y y #s(literal 1 binary64))
y
(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
x
(pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 y y #s(literal 1 binary64))
y
#s(literal 1 binary64)
#s(literal -1 binary64)

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

localize56.0ms (1.2%)

Memory

-8.6MiB live, 70.3MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 y y #s(literal 1 binary64))
accuracy	0.32303312426513964	(pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))
accuracy	3.062734143599982	(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
accuracy	0	(fma.f64 y y #s(literal 1 binary64))
accuracy	0.10546875	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64)))))
accuracy	0.43623513965377736	(/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64))))
accuracy	3.361592420394443	(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
accuracy	0	(*.f64 y y)
accuracy	3.361592420394443	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
accuracy	28.881848530500605	#s(approx (+ 1 (* y y)) (*.f64 y y))
accuracy	3.361592420394443	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))
accuracy	32.97285515130103	#s(approx (+ 1 (* y y)) #s(literal 1 binary64))
accuracy	0	(*.f64 x y)
accuracy	0.04296875	(fma.f64 (*.f64 x y) y x)

Samples

40.0ms

256×

valid

Compiler

Compiled 192 to 35 computations (81.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-mult: 8.0ms (41.3% of total)

ival-div: 5.0ms (25.8% of total)

ival-add: 4.0ms (20.7% of total)

ival-pow: 3.0ms (15.5% of total)

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

exact: 0.0ms (0% of total)

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

series20.0ms (0.4%)

Memory

3.0MiB live, 39.9MiB allocated

Counts

13 → 252

Calls

Call 1

Inputs
#s(alt (fma.f64 (.f64 x y) y x) (patch (fma.f64 (.f64 x y) y x) #<representation binary64>) () ())
#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())
#s(alt (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) (patch (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) (patch #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x #s(approx (+ 1 ( y y)) (.f64 y y))) (patch (.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) #<representation binary64>) () ())
#s(alt #s(approx (+ 1 (* y y)) (.f64 y y)) (patch #s(approx (+ 1 ( y y)) (*.f64 y y)) #<representation binary64>) () ())
#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64))))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 x (fma.f64 y y #s(literal 1 binary64))) (patch (.f64 x (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 y y #s(literal 1 binary64)) (patch (fma.f64 y y #s(literal 1 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) (patch (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 y) (#s(alt (fma.f64 (.f64 x y) y x) (patch (fma.f64 (.f64 x y) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (.f64 x y) y x) (patch (fma.f64 (.f64 x y) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (.f64 x y) y x) (patch (fma.f64 (.f64 x y) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (.f64 x y) y x) (patch (fma.f64 (.f64 x y) y x) #<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 (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) (patch (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) (patch (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) (patch (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) (patch (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) (patch #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) (patch #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) (patch #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) (patch #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) (.f64 y y))) (patch (.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) (.f64 y y))) (patch (.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) (.f64 y y))) (patch (.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) (.f64 y y))) (patch (.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (+ 1 (* y y)) (.f64 y y)) (patch #s(approx (+ 1 ( y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ 1 (* y y)) (.f64 y y)) (patch #s(approx (+ 1 ( y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ 1 (* y y)) (.f64 y y)) (patch #s(approx (+ 1 ( y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ 1 (* y y)) (.f64 y y)) (patch #s(approx (+ 1 ( y y)) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
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#s(alt (/ 1 (* x (+ 1 (pow y 2)))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (.f64 x (fma.f64 y y #s(literal 1 binary64))) (patch (.f64 x (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (.f64 x (fma.f64 y y #s(literal 1 binary64))) (patch (.f64 x (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (.f64 x (fma.f64 y y #s(literal 1 binary64))) (patch (.f64 x (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (.f64 x (fma.f64 y y #s(literal 1 binary64))) (patch (.f64 x (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) (patch (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) (patch (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) (patch (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) (patch (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x y) y x) (patch (fma.f64 (.f64 x y) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x y) y x) (patch (fma.f64 (.f64 x y) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x y) y x) (patch (fma.f64 (.f64 x y) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x y) y x) (patch (fma.f64 (.f64 x y) y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) (patch (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) (patch (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) (patch (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) (patch (.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) (.f64 y y))) (patch (.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) (.f64 y y))) (patch (.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) (.f64 y y))) (patch (.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x #s(approx (+ 1 ( y y)) (.f64 y y))) (patch (.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64))))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* x (+ 1 (pow y 2)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* x (+ 1 (pow y 2)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* x (+ 1 (pow y 2)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* x (+ 1 (pow y 2)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64)))) (patch (/.f64 #s(literal 1 binary64) (.f64 x (fma.f64 y y #s(literal 1 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x (fma.f64 y y #s(literal 1 binary64))) (patch (.f64 x (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x (fma.f64 y y #s(literal 1 binary64))) (patch (.f64 x (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x (fma.f64 y y #s(literal 1 binary64))) (patch (.f64 x (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x (fma.f64 y y #s(literal 1 binary64))) (patch (.f64 x (fma.f64 y y #s(literal 1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) (patch (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) (patch (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) (patch (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) (patch (/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((+ (* (* x y) y) x) (* x y) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* y y) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (/ 1 (* x (+ (* y y) 1))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1))
2.0ms	y	@	-inf	((+ (* (* x y) y) x) (* x y) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* y y) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (/ 1 (* x (+ (* y y) 1))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1))
1.0ms	x	@	inf	((+ (* (* x y) y) x) (* x y) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* y y) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (/ 1 (* x (+ (* y y) 1))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1))
1.0ms	y	@	inf	((+ (* (* x y) y) x) (* x y) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* y y) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (/ 1 (* x (+ (* y y) 1))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1))
1.0ms	x	@	0	((+ (* (* x y) y) x) (* x y) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* y y) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (/ 1 (* x (+ (* y y) 1))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1))

simplify213.0ms (4.5%)

Memory

4.0MiB live, 293.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	1676
1	178	1672
2	453	1664
3	1511	1648
4	3765	1634
0	8122	1459

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 246

Calls

Call 1

Inputs
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(* x y)
(* x y)
(* x y)
(* x y)
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
1
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(+ 1 (pow y 2))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
1
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(/ 1 x)
(+ (* -1 (/ (pow y 2) x)) (/ 1 x))
(+ (* (pow y 2) (- (/ (pow y 2) x) (/ 1 x))) (/ 1 x))
(+ (* (pow y 2) (- (* (pow y 2) (+ (* -1 (/ (pow y 2) x)) (/ 1 x))) (/ 1 x))) (/ 1 x))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
1
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(+ 1 (pow y 2))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
1
(+ 1 (* -1 (pow y 2)))
(+ 1 (* (pow y 2) (- (pow y 2) 1)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (* x (pow y 2)))
(/ (- (/ 1 x) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6))))) (pow y 2))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (* x (pow y 2)))
(/ (- (/ 1 x) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6))))) (pow y 2))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))

Outputs
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
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(/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y y #s(literal 1 binary64)) x))
(/ 1 (* x (+ 1 (pow y 2))))
(/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y y #s(literal 1 binary64)) x))
(/ 1 (* x (+ 1 (pow y 2))))
(/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y y #s(literal 1 binary64)) x))
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)

rewrite177.0ms (3.7%)

Memory

26.7MiB live, 212.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	90
0	31	80
1	115	80
2	665	80
3	6753	80
0	9374	80

Stop Event

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

Counts

13 → 1 337

Calls

Call 1

Inputs
(fma.f64 (*.f64 x y) y x)
(*.f64 x y)
(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))
#s(approx (+ 1 (* y y)) #s(literal 1 binary64))
(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
#s(approx (+ 1 (* y y)) (*.f64 y y))
(*.f64 y y)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64))))
(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
(fma.f64 y y #s(literal 1 binary64))
(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
(pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))

Outputs
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eval225.0ms (4.7%)

Memory: -1.3MiB live, 343.5MiB allocated
Compiler: Compiled 33 002 to 2 813 computations (91.5% saved)

prune333.0ms (7%)

Memory

-3.1MiB live, 91.6MiB allocated

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1 723	3	1 726
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	1 725	6	1 731

Accuracy

100.0%

Counts

1 731 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (*.f64 x y) y x)
▶	50.0%	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
▶	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y x) y x)))
▶	50.0%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))))
✓	50.0%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
✓	48.9%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 44 to 36 computations (18.2% saved)

simplify9.0ms (0.2%)

Memory

7.0MiB live, 7.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 y y)
cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 y y))
cost-diff	0	#s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))
cost-diff	0	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
cost-diff	0	(*.f64 y x)
cost-diff	0	(fma.f64 (*.f64 y x) y x)
cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y x) y x))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y x) y x)))
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (+ (* y y) 1) (*.f64 y y))
cost-diff	0	(.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))
cost-diff	1792	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	123
0	30	115
1	46	115
2	68	115
3	94	115
4	125	115
5	175	115
6	198	115
7	200	115
8	203	115
0	203	109

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y))))
(.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))
x
#s(approx (+ (* y y) 1) (*.f64 y y))
(*.f64 y y)
y
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y x) y x)))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y x) y x))
(fma.f64 (*.f64 y x) y x)
(*.f64 y x)
y
x
(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
x
#s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
#s(literal 1 binary64)
(*.f64 y y)
y

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

localize208.0ms (4.4%)

Memory

9.9MiB live, 48.5MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0.37772062426513964	(/.f64 #s(literal 1 binary64) (*.f64 y y))
accuracy	3.062734143599982	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
accuracy	28.88224524168983	#s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))
accuracy	0	(*.f64 y x)
accuracy	0.04296875	(fma.f64 (*.f64 y x) y x)
accuracy	0.10546875	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y x) y x)))
accuracy	0.43623513965377736	(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y x) y x))
accuracy	0.10546875	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))))
accuracy	0.43623513965377736	(/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y))))
accuracy	3.361592420394443	(.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))
accuracy	28.881848530500605	#s(approx (+ (* y y) 1) (*.f64 y y))

Samples

196.0ms

256×

valid

Compiler

Compiled 189 to 34 computations (82% saved)

Precisions

Click to see histograms. Total time spent on operations: 185.0ms

ival-div: 173.0ms (93.3% of total)

ival-mult: 6.0ms (3.2% of total)

ival-add: 3.0ms (1.6% of total)

ival-pow: 2.0ms (1.1% of total)

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

exact: 0.0ms (0% of total)

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

series176.0ms (3.7%)

Memory

-21.3MiB live, 17.0MiB allocated

Counts

12 → 240

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (.f64 y y))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y))))) #<representation binary64>) () ())
#s(alt (.f64 x #s(approx (+ ( y y) 1) (.f64 y y))) (patch (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* y y) 1) (.f64 y y)) (patch #s(approx (+ ( y y) 1) (*.f64 y y)) #<representation binary64>) () ())
#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())
#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())
#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (.f64 y y)))) (patch (/.f64 x #s(approx (pow (+ ( y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) #<representation binary64>) () ())
#s(alt #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (.f64 y y))) (patch #s(approx (pow (+ ( y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (.f64 y y)) (patch (/.f64 #s(literal 1 binary64) (.f64 y y)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (.f64 y y)))) (patch (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y)))) #<representation binary64>) () ())

Outputs
#s(alt x (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (.f64 y y))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (.f64 y y))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (.f64 y y))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (.f64 y y))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (.f64 x #s(approx (+ ( y y) 1) (.f64 y y))) (patch (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (.f64 x #s(approx (+ ( y y) 1) (.f64 y y))) (patch (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (.f64 x #s(approx (+ ( y y) 1) (.f64 y y))) (patch (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (.f64 x #s(approx (+ ( y y) 1) (.f64 y y))) (patch (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (+ (* y y) 1) (.f64 y y)) (patch #s(approx (+ ( y y) 1) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* y y) 1) (.f64 y y)) (patch #s(approx (+ ( y y) 1) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* y y) 1) (.f64 y y)) (patch #s(approx (+ ( y y) 1) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (pow y 2)) (taylor 0 y) (#s(alt #s(approx (+ (* y y) 1) (.f64 y y)) (patch #s(approx (+ ( y y) 1) (*.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt (pow y 2) (taylor 0 y) (#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x))) #<representation binary64>) () ())) ())
#s(alt (/ 1 x) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (/ (pow y 2) x)) (/ 1 x)) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow y 2) (- (/ (pow y 2) x) (/ 1 x))) (/ 1 x)) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow y 2) (- (* (pow y 2) (+ (* -1 (/ (pow y 2) x)) (/ 1 x))) (/ 1 x))) (/ 1 x)) (taylor 0 y) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 y) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
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#s(alt (* x y) (taylor inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (.f64 y y)))) (patch (/.f64 x #s(approx (pow (+ ( y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (.f64 y y)))) (patch (/.f64 x #s(approx (pow (+ ( y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (.f64 y y)))) (patch (/.f64 x #s(approx (pow (+ ( y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor inf x) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (.f64 y y)))) (patch (/.f64 x #s(approx (pow (+ ( y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* x (+ 1 (pow y 2)))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (.f64 y y)))) (patch (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* x (+ 1 (pow y 2)))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (.f64 y y)))) (patch (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* x (+ 1 (pow y 2)))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (.f64 y y)))) (patch (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* x (+ 1 (pow y 2)))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (.f64 y y)))) (patch (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (.f64 y y))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (.f64 y y))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (.f64 y y))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (.f64 y y))))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x #s(approx (+ ( y y) 1) (.f64 y y))) (patch (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x #s(approx (+ ( y y) 1) (.f64 y y))) (patch (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x #s(approx (+ ( y y) 1) (.f64 y y))) (patch (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (.f64 x #s(approx (+ ( y y) 1) (.f64 y y))) (patch (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x))) #<representation binary64>) () ())) ())
#s(alt (/ -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x)) #<representation binary64>) () ())) ())
#s(alt (/ -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x)) #<representation binary64>) () ())) ())
#s(alt (/ -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x)) #<representation binary64>) () ())) ())
#s(alt (/ -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x)) (patch (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 y x) y x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (pow y 2)) 1))) (taylor -inf x) (#s(alt (fma.f64 (.f64 y x) y x) (patch (fma.f64 (.f64 y x) y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor -inf x) (#s(alt (.f64 y x) (patch (.f64 y x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (.f64 y y)))) (patch (/.f64 x #s(approx (pow (+ ( y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (.f64 y y)))) (patch (/.f64 x #s(approx (pow (+ ( y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (.f64 y y)))) (patch (/.f64 x #s(approx (pow (+ ( y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor -inf x) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (.f64 y y)))) (patch (/.f64 x #s(approx (pow (+ ( y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* x (+ 1 (pow y 2)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (.f64 y y)))) (patch (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* x (+ 1 (pow y 2)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (.f64 y y)))) (patch (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* x (+ 1 (pow y 2)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (.f64 y y)))) (patch (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (* x (+ 1 (pow y 2)))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (.f64 y y)))) (patch (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ (* y y) 1) (*.f64 y y)))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
164.0ms	y	@	0	((/ 1 (/ 1 (* x (+ (* y y) 1)))) (* x (+ (* y y) 1)) (+ (* y y) 1) (* y y) (/ 1 (/ 1 (+ (* (* y x) y) x))) (/ 1 (+ (* (* y x) y) x)) (+ (* (* y x) y) x) (* y x) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ 1 (* y y)) (/ 1 (* x (+ (* y y) 1))))
2.0ms	x	@	-inf	((/ 1 (/ 1 (* x (+ (* y y) 1)))) (* x (+ (* y y) 1)) (+ (* y y) 1) (* y y) (/ 1 (/ 1 (+ (* (* y x) y) x))) (/ 1 (+ (* (* y x) y) x)) (+ (* (* y x) y) x) (* y x) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ 1 (* y y)) (/ 1 (* x (+ (* y y) 1))))
1.0ms	x	@	inf	((/ 1 (/ 1 (* x (+ (* y y) 1)))) (* x (+ (* y y) 1)) (+ (* y y) 1) (* y y) (/ 1 (/ 1 (+ (* (* y x) y) x))) (/ 1 (+ (* (* y x) y) x)) (+ (* (* y x) y) x) (* y x) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ 1 (* y y)) (/ 1 (* x (+ (* y y) 1))))
1.0ms	x	@	0	((/ 1 (/ 1 (* x (+ (* y y) 1)))) (* x (+ (* y y) 1)) (+ (* y y) 1) (* y y) (/ 1 (/ 1 (+ (* (* y x) y) x))) (/ 1 (+ (* (* y x) y) x)) (+ (* (* y x) y) x) (* y x) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ 1 (* y y)) (/ 1 (* x (+ (* y y) 1))))
1.0ms	y	@	-inf	((/ 1 (/ 1 (* x (+ (* y y) 1)))) (* x (+ (* y y) 1)) (+ (* y y) 1) (* y y) (/ 1 (/ 1 (+ (* (* y x) y) x))) (/ 1 (+ (* (* y x) y) x)) (+ (* (* y x) y) x) (* y x) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ 1 (* y y)) (/ 1 (* x (+ (* y y) 1))))

simplify325.0ms (6.8%)

Memory

14.5MiB live, 245.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	1790
1	181	1784
2	458	1772
3	1532	1744
4	3823	1716
0	8171	1559

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 235

Calls

Call 1

Inputs
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
1
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(/ 1 x)
(+ (* -1 (/ (pow y 2) x)) (/ 1 x))
(+ (* (pow y 2) (- (/ (pow y 2) x) (/ 1 x))) (/ 1 x))
(+ (* (pow y 2) (- (* (pow y 2) (+ (* -1 (/ (pow y 2) x)) (/ 1 x))) (/ 1 x))) (/ 1 x))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(* x y)
(* x y)
(* x y)
(* x y)
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
1
(+ 1 (* -1 (pow y 2)))
(+ 1 (* (pow y 2) (- (pow y 2) 1)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 x)
(+ (* -1 (/ (pow y 2) x)) (/ 1 x))
(+ (* (pow y 2) (- (/ (pow y 2) x) (/ 1 x))) (/ 1 x))
(+ (* (pow y 2) (- (* (pow y 2) (+ (* -1 (/ (pow y 2) x)) (/ 1 x))) (/ 1 x))) (/ 1 x))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (* x (pow y 2)))
(/ (- (/ 1 x) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6))))) (pow y 2))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (* x (pow y 2)))
(/ (- (/ 1 x) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6))))) (pow y 2))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (* x (pow y 2)))
(/ (- (/ 1 x) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6))))) (pow y 2))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (* x (pow y 2)))
(/ (- (/ 1 x) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6))))) (pow y 2))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))

Outputs
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(/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y y #s(literal 1 binary64)) x))
(/ 1 (* x (+ 1 (pow y 2))))
(/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y y #s(literal 1 binary64)) x))
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y y #s(literal 1 binary64)) x))
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y y #s(literal 1 binary64)) x))
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y y #s(literal 1 binary64)) x))
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y y #s(literal 1 binary64)) x))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (+ 1 (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 (* x (+ 1 (pow y 2))))
(/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y y #s(literal 1 binary64)) x))
(/ 1 (* x (+ 1 (pow y 2))))
(/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y y #s(literal 1 binary64)) x))
(/ 1 (* x (+ 1 (pow y 2))))
(/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y y #s(literal 1 binary64)) x))
(/ 1 (* x (+ 1 (pow y 2))))
(/.f64 #s(literal 1 binary64) (*.f64 (fma.f64 y y #s(literal 1 binary64)) x))

rewrite146.0ms (3.1%)

Memory

-11.6MiB live, 224.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	111
0	30	103
1	118	97
2	611	97
3	4828	97
0	8195	91

Stop Event

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

Counts

12 → 578

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))))
(.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))
#s(approx (+ (* y y) 1) (*.f64 y y))
(*.f64 y y)
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y x) y x)))
(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y x) y x))
(fma.f64 (*.f64 y x) y x)
(*.f64 y x)
(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
#s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y))))

Outputs
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eval216.0ms (4.5%)

Memory: -20.7MiB live, 155.0MiB allocated
Compiler: Compiled 14 026 to 1 642 computations (88.3% saved)

prune18.0ms (0.4%)

Memory

0.9MiB live, 51.1MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	858	0	858
Fresh	0	0	0
Picked	0	3	3
Done	0	3	3
Total	858	6	864

Accuracy

100.0%

Counts

864 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (*.f64 x y) y x)
✓	50.0%	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
✓	99.8%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y x) y x)))
✓	50.0%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))))
✓	50.0%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
✓	48.9%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 113 to 66 computations (41.6% saved)

regimes18.0ms (0.4%)

Memory

4.7MiB live, 43.6MiB allocated

Counts

9 → 1

Calls

Call 1

Inputs
(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))
(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
(fma.f64 (*.f64 x y) y x)
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y x) y x)))
(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))

Outputs
(fma.f64 (*.f64 x y) y x)

Calls

5 calls:

5.0ms	y
3.0ms	x
3.0ms	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
3.0ms	(*.f64 y y)
3.0ms	(+.f64 #s(literal 1 binary64) (*.f64 y y))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`
99.9%	1	`(+.f64 #s(literal 1 binary64) (*.f64 y y))`
99.9%	1	`(*.f64 y y)`

Compiler

Compiled 17 to 18 computations (-5.9% saved)

regimes8.0ms (0.2%)

Memory

20.5MiB live, 20.5MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))
(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))

Outputs
(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))
(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))

Calls

5 calls:

2.0ms	x
2.0ms	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
2.0ms	y
1.0ms	(*.f64 y y)
1.0ms	(+.f64 #s(literal 1 binary64) (*.f64 y y))

Results

Accuracy	Segments	Branch
58.6%	4	`x`
93.6%	2	`y`
73.5%	2	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`
93.6%	2	`(+.f64 #s(literal 1 binary64) (*.f64 y y))`
93.6%	2	`(*.f64 y y)`

Compiler

Compiled 17 to 18 computations (-5.9% saved)

regimes45.0ms (0.9%)

Memory

-23.2MiB live, 15.8MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Outputs
(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Calls

5 calls:

39.0ms	(+.f64 #s(literal 1 binary64) (*.f64 y y))
1.0ms	y
1.0ms	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
1.0ms	x
1.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
48.9%	1	`x`
48.9%	1	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`
48.9%	1	`y`
48.9%	1	`(+.f64 #s(literal 1 binary64) (*.f64 y y))`
48.9%	1	`(*.f64 y y)`

Compiler

Compiled 17 to 18 computations (-5.9% saved)

bsearch11.0ms (0.2%)

Memory

11.7MiB live, 11.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.0003940218516783747	30523.24157998987

Samples

5.0ms

144×

valid

Compiler

Compiled 82 to 110 computations (-34.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-add: 1.0ms (48.7% of total)

ival-mult: 1.0ms (48.7% of total)

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

exact: 0.0ms (0% of total)

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

simplify25.0ms (0.5%)

Memory

1.3MiB live, 40.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	41
1	20	41

Stop Event

1×

saturated

Calls

Call 1

Inputs

(fma.f64 (*.f64 x y) y x)

(if (<=.f64 (*.f64 y y) #s(literal 1 binary64)) (*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) (*.f64 x #s(approx (+ 1 (* y y)) (*.f64 y y))))

(*.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64)))

Outputs
(fma.f64 (*.f64 x y) y x)
(fma.f64 (*.f64 y x) y x)
(if (<=.f64 (.f64 y y) #s(literal 1 binary64)) (.f64 x #s(approx (+ 1 (* y y)) #s(literal 1 binary64))) (.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y))))
(if (<=.f64 (.f64 y y) #s(literal 1 binary64)) (.f64 #s(approx (+ 1 (* y y)) #s(literal 1 binary64)) x) (.f64 #s(approx (+ 1 ( y y)) (*.f64 y y)) x))
(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))
(.f64 #s(approx (+ 1 ( y y)) #s(literal 1 binary64)) x)

soundness486.0ms (10.2%)

Memory

14.3MiB live, 245.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	9	15
1	34	15
2	209	15
3	1404	15
0	8269	13
0	15	246
1	42	246
2	74	246
3	214	246
4	721	246
5	1940	246
6	2658	246
7	3752	246
8	5094	246
9	5986	246
10	6927	246
11	7270	246
12	7376	246
13	7453	246
14	7522	246
15	7669	246
0	8207	216

Stop Event

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

Compiler

Compiled 50 to 32 computations (36% saved)

preprocess170.0ms (3.6%)

Memory

-20.5MiB live, 149.7MiB allocated

Remove

(negabs x)

(abs y)

Compiler

Compiled 152 to 94 computations (38.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	16	37
1	65	37
2	194	35
3	463	35
4	639	35
5	762	35
6	789	35
0	6	7
0	9	7
1	19	7
2	27	7
3	49	7
4	49	7
0	49	6

Iter	Nodes	Cost
0	19	123
0	30	115
1	46	115
2	68	115
3	94	115
4	125	115
5	175	115
6	198	115
7	200	115
8	203	115
0	203	109

Iter	Nodes	Cost
0	16	37
1	65	37
2	194	35
3	463	35
4	639	35
5	762	35
6	789	35
0	6	7
0	9	7
1	19	7
2	27	7
3	49	7
4	49	7
0	49	6

Iter	Nodes	Cost
0	19	123
0	30	115
1	46	115
2	68	115
3	94	115
4	125	115
5	175	115
6	198	115
7	200	115
8	203	115
0	203	109

start0.0ms (0%)

analyze0.0ms (0%)

sample890.0ms (18.6%)

explain83.0ms (1.7%)

preprocess39.0ms (0.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize30.0ms (0.6%)

series18.0ms (0.4%)

simplify517.0ms (10.8%)

rewrite200.0ms (4.2%)

eval89.0ms (1.9%)

prune12.0ms (0.2%)

simplify7.0ms (0.1%)

localize56.0ms (1.2%)

series20.0ms (0.4%)

simplify213.0ms (4.5%)

rewrite177.0ms (3.7%)

eval225.0ms (4.7%)

prune333.0ms (7%)

simplify9.0ms (0.2%)

localize208.0ms (4.4%)

series176.0ms (3.7%)

simplify325.0ms (6.8%)

rewrite146.0ms (3.1%)

eval216.0ms (4.5%)

prune18.0ms (0.4%)

regimes18.0ms (0.4%)

regimes8.0ms (0.2%)

regimes45.0ms (0.9%)

bsearch11.0ms (0.2%)

simplify25.0ms (0.5%)

soundness486.0ms (10.2%)

preprocess170.0ms (3.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	16	37
1	65	37
2	194	35
3	463	35
4	639	35
5	762	35
6	789	35
0	6	7
0	9	7
1	19	7
2	27	7
3	49	7
4	49	7
0	49	6

Iter	Nodes	Cost
0	19	123
0	30	115
1	46	115
2	68	115
3	94	115
4	125	115
5	175	115
6	198	115
7	200	115
8	203	115
0	203	109