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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB 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)

sample868.0ms (15%)

Memory

5.5MiB live, 944.4MiB allocated

Samples

513.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 323.0ms

ival-mult: 230.0ms (71.2% of total)

ival-add: 79.0ms (24.5% of total)

ival-true: 7.0ms (2.2% of total)

exact: 4.0ms (1.2% of total)

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

Bogosity

explain121.0ms (2.1%)

Memory

-23.2MiB live, 147.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
12	-	-	`(.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**	12	0

Confusion

	Predicted +	Predicted -
+	12	0
-	0	244

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	12	0	0
-	0	0	244

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	244
1	12

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

23.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 7.0ms (66.7% of total)

ival-add: 2.0ms (19.1% of total)

ival-true: 1.0ms (9.5% of total)

exact: 0.0ms (0% of total)

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

preprocess142.0ms (2.5%)

Memory

16.4MiB live, 50.4MiB allocated

Algorithm

1×	egg-herbie

Rules

158×	`associate-r`
124×	`distribute-lft-in`
112×	`unsub-neg`
92×	`associate-l`
82×	`distribute-lft-neg-out`

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: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	95.5%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB 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))

Rules

46×	`lower-*.f32`
42×	`lower-*.f64`
22×	`lower-fma.f64`
22×	`lower-fma.f32`
14×	`associate-r`

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

localize328.0ms (5.7%)

Memory

-16.6MiB live, 59.5MiB 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	2.881705463416142	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))

Samples

130.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 123.0ms

ival-mult: 121.0ms (98.4% of total)

ival-add: 1.0ms (0.8% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

16.2MiB live, 16.1MiB 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))

simplify213.0ms (3.7%)

Memory

-12.3MiB live, 152.9MiB allocated

Algorithm

1×	egg-herbie

Rules

9 064×	`lower-fma.f64`
9 064×	`lower-fma.f32`
6 574×	`lower-*.f64`
6 574×	`lower-*.f32`
2 432×	`cube-prod`

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)))

rewrite284.0ms (4.9%)

Memory

-5.8MiB live, 196.1MiB allocated

Rules

5 176×	`lower-fma.f64`
5 176×	`lower-fma.f32`
4 882×	`lower-/.f64`
4 882×	`lower-/.f32`
4 246×	`lower-*.f32`

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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eval63.0ms (1.1%)

Memory: 23.7MiB live, 58.7MiB allocated
Compiler: Compiled 9 642 to 1 119 computations (88.4% saved)

prune31.0ms (0.5%)

Memory

-1.7MiB live, 34.3MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	409	6	415
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	410	6	416

Accuracy

100.0%

Counts

416 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(fma.f64 (*.f64 x y) y x)
▶	95.5%	(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
▶	95.3%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64)))))
	69.3%	(.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))
▶	44.8%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
▶	54.2%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 94 to 76 computations (19.1% saved)

simplify10.0ms (0.2%)

Memory

-20.7MiB live, 17.4MiB 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)

Rules

86×	`lower-*.f32`
76×	`lower-*.f64`
56×	`lower-/.f32`
50×	`lower-/.f64`
26×	`associate-r`

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)

localize49.0ms (0.8%)

Memory

5.7MiB live, 57.7MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 y y #s(literal 1 binary64))
accuracy	0.33988112865271913	(pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))
accuracy	2.7235504300556825	(/.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	0.16796875	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64)))))
accuracy	0.2599828633066067	(/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64))))
accuracy	2.881705463416142	(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
accuracy	0	(*.f64 y y)
accuracy	2.881705463416142	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
accuracy	32.61305288626112	#s(approx (+ 1 (* y y)) (*.f64 y y))
accuracy	2.881705463416142	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))
accuracy	29.486796457446818	#s(approx (+ 1 (* y y)) #s(literal 1 binary64))
accuracy	0	(*.f64 x y)
accuracy	0.05859375	(fma.f64 (*.f64 x y) y x)

Samples

37.0ms

256×

valid

Compiler

Compiled 105 to 18 computations (82.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-mult: 14.0ms (56.4% of total)

ival-div: 5.0ms (20.1% of total)

ival-add: 3.0ms (12.1% of total)

ival-pow: 2.0ms (8.1% of total)

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

exact: 0.0ms (0% of total)

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

series19.0ms (0.3%)

Memory

-10.2MiB live, 27.3MiB 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>) () ())) ())
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#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>) () ())) ())
#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))

simplify237.0ms (4.1%)

Memory

18.7MiB live, 299.5MiB allocated

Algorithm

1×	egg-herbie

Rules

15 520×	`lower-fma.f64`
15 520×	`lower-fma.f32`
3 416×	`lower-*.f64`
3 416×	`lower-*.f32`
3 044×	`lower-+.f64`

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))
(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 (* 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))
(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
(+ 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 x)
(/.f64 #s(literal 1 binary64) x)
(+ (* -1 (/ (pow y 2) x)) (/ 1 x))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (neg.f64 x))
(+ (* (pow y 2) (- (/ (pow y 2) x) (/ 1 x))) (/ 1 x))
(*.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y #s(literal -1 binary64))))
(+ (* (pow y 2) (- (* (pow y 2) (+ (* -1 (/ (pow y 2) x)) (/ 1 x))) (/ 1 x))) (/ 1 x))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1 binary64)) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (neg.f64 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))
(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 (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow y 2)))
(-.f64 #s(literal 1 binary64) (*.f64 y y))
(+ 1 (* (pow y 2) (- (pow y 2) 1)))
(-.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y #s(literal -1 binary64)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))
(.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 y y)))
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ 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 (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(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 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(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))
(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 (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 (* x (pow y 2)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y)) x)
(/ (- (/ 1 x) (/ 1 (* x (pow y 2)))) (pow y 2))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 y #s(literal 4 binary64))) (fma.f64 y y #s(literal -1 binary64)))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (/ 1 (* x (pow y 2)))) (pow y 2))
(/.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 y #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 y y)) (/.f64 #s(literal 1 binary64) x)) (.f64 y y))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6))))) (pow y 2))
(/.f64 (-.f64 (/.f64 (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 6 binary64))) x) (fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 y #s(literal 4 binary64))) (fma.f64 y y #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))) (*.f64 y y))
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(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 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y) y)
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 y y)) #s(literal 1 binary64))) (.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64)))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 y y))) y) y)) (.f64 y y))
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ 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 (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(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 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(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))
(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 (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 (* x (pow y 2)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y)) x)
(/ (- (/ 1 x) (/ 1 (* x (pow y 2)))) (pow y 2))
(*.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 y #s(literal 4 binary64))) (fma.f64 y y #s(literal -1 binary64)))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (/ 1 (* x (pow y 2)))) (pow y 2))
(/.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 y #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (.f64 y y)) (/.f64 #s(literal 1 binary64) x)) (.f64 y y))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6))))) (pow y 2))
(/.f64 (-.f64 (/.f64 (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 6 binary64))) x) (fma.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 y #s(literal 4 binary64))) (fma.f64 y y #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))) (*.f64 y y))
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(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 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y) y)
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 y y)) #s(literal 1 binary64))) (.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64)))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 y y))) y) y)) (.f64 y y))
(* 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 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)
(* 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))))
(/.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))
(* 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)
(* 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 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)
(* 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))))
(/.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))
(* 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)
(* 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)
(* 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))))
(/.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))
(* 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)

rewrite179.0ms (3.1%)

Memory

3.3MiB live, 235.2MiB allocated

Rules

4 514×	`lower-fma.f32`
4 510×	`lower-fma.f64`
3 804×	`lower-*.f32`
3 794×	`lower-*.f64`
2 670×	`lower-/.f32`

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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eval900.0ms (15.6%)

Memory: 14.1MiB live, 369.8MiB allocated
Compiler: Compiled 33 002 to 2 813 computations (91.5% saved)

prune37.0ms (0.6%)

Memory

-11.2MiB live, 112.9MiB allocated

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1 723	3	1 726
Fresh	1	0	1
Picked	2	3	5
Done	0	0	0
Total	1 726	6	1 732

Accuracy

100.0%

Counts

1 732 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (*.f64 x y) y x)
▶	95.4%	(/.f64 (neg.f64 (fma.f64 y y #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x))
▶	44.7%	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y) y)))
▶	44.8%	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
✓	44.8%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
✓	54.2%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 47 to 39 computations (17% saved)

simplify117.0ms (2%)

Memory

-16.5MiB live, 100.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal -1 binary64) x)
cost-diff	0	(fma.f64 y y #s(literal 1 binary64))
cost-diff	0	(neg.f64 (fma.f64 y y #s(literal 1 binary64)))
cost-diff	1216	(/.f64 (neg.f64 (fma.f64 y y #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x))
cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y)
cost-diff	0	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y) y)
cost-diff	0	#s(approx (pow (+ (* y y) 1) -1) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y) y))
cost-diff	0	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y) y)))
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))))

Rules

3 376×	`lower-fma.f32`
3 374×	`lower-fma.f64`
1 408×	`lower-*.f32`
1 406×	`lower-*.f64`
1 328×	`lower--.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	138
0	31	138
1	51	138
2	99	137
3	185	135
4	350	135
5	824	135
6	2199	135
7	3341	135
8	3886	135
9	4495	135
10	5214	135
11	5446	135
12	6606	135
0	8161	135

Stop Event

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

Calls

Call 1

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

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

localize43.0ms (0.7%)

Memory

17.4MiB live, 94.9MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 y y #s(literal 1 binary64))
accuracy	0	(/.f64 #s(literal -1 binary64) x)
accuracy	0	(neg.f64 (fma.f64 y y #s(literal 1 binary64)))
accuracy	2.9660217231845842	(/.f64 (neg.f64 (fma.f64 y y #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x))
accuracy	0.10546875	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y) y)
accuracy	0.41409987865271913	(/.f64 #s(literal 1 binary64) (*.f64 y y))
accuracy	2.7235504300556825	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y) y)))
accuracy	33.5595672956305	#s(approx (pow (+ (* y y) 1) -1) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y) y))
accuracy	0	(*.f64 y y)
accuracy	0.41409987865271913	(/.f64 #s(literal 1 binary64) (*.f64 y y))
accuracy	2.7235504300556825	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
accuracy	32.61849417308409	#s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))

Samples

31.0ms

256×

valid

Compiler

Compiled 111 to 17 computations (84.7% saved)

Precisions

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

ival-div: 10.0ms (52.7% of total)

ival-pow: 3.0ms (15.8% of total)

ival-mult: 2.0ms (10.5% of total)

ival-add: 1.0ms (5.3% of total)

ival-sub: 1.0ms (5.3% of total)

ival-neg: 1.0ms (5.3% of total)

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

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

exact: 0.0ms (0% of total)

series23.0ms (0.4%)

Memory

-29.5MiB live, 29.5MiB allocated

Counts

12 → 180

Calls

Call 1

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

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

Calls

6 calls:

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

simplify182.0ms (3.2%)

Memory

10.4MiB live, 200.6MiB allocated

Algorithm

1×	egg-herbie

Rules

21 642×	`lower-fma.f64`
21 642×	`lower-fma.f32`
4 530×	`lower-*.f64`
4 530×	`lower-*.f32`
1 740×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	1197
1	132	1193
2	316	1176
3	1024	1152
4	2917	1152
5	6325	1152
0	8152	1046

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 177

Calls

Call 1

Inputs
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))
(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
(+ 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 4))
(/ (- (pow y 2) 1) (pow y 4))
(/ (- (pow y 2) 1) (pow y 4))
(/ (- (pow y 2) 1) (pow y 4))
(/ -1 (pow y 3))
(/ (- (pow y 2) 1) (pow y 3))
(/ (- (pow y 2) 1) (pow y 3))
(/ (- (pow y 2) 1) (pow y 3))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
-1
(- (* -1 (pow y 2)) 1)
(- (* -1 (pow y 2)) 1)
(- (* -1 (pow y 2)) 1)
1
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(+ 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))
(/ 1 (pow y 2))
(/ 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 (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 (/ 1 (pow y 2))) (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ 1 y)
(/ (- 1 (/ 1 (pow y 2))) y)
(/ (- 1 (/ 1 (pow y 2))) y)
(/ (- 1 (/ 1 (pow y 2))) 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 (* (pow y 2) (+ 1 (/ 1 (pow y 2)))))
(* -1 (* (pow y 2) (+ 1 (/ 1 (pow y 2)))))
(* -1 (* (pow y 2) (+ 1 (/ 1 (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))
(/ 1 (pow y 2))
(/ 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 (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 (/ 1 (pow y 2))) (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ 1 y)
(* -1 (/ (- (/ 1 (pow y 2)) 1) y))
(* -1 (/ (- (/ 1 (pow y 2)) 1) y))
(* -1 (/ (- (/ 1 (pow y 2)) 1) 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 (* (pow y 2) (+ 1 (/ 1 (pow y 2)))))
(* -1 (* (pow y 2) (+ 1 (/ 1 (pow y 2)))))
(* -1 (* (pow y 2) (+ 1 (/ 1 (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 (+ 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 x)
(/ -1 x)
(/ -1 x)
(* 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 x)
(/ -1 x)
(/ -1 x)
(* 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 x)
(/ -1 x)
(/ -1 x)

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)
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow y 2)))
(-.f64 #s(literal 1 binary64) (*.f64 y y))
(+ 1 (* (pow y 2) (- (pow y 2) 1)))
(fma.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) y) y #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))
(*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 4 binary64))) (fma.f64 y y #s(literal -1 binary64)))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.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)
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 (* -1 (pow y 2)))
(-.f64 #s(literal 1 binary64) (*.f64 y y))
(+ 1 (* (pow y 2) (- (pow y 2) 1)))
(fma.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) y) y #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))
(*.f64 (-.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 4 binary64))) (fma.f64 y y #s(literal -1 binary64)))
(/ -1 (pow y 4))
(/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 4 binary64)))
(/ (- (pow y 2) 1) (pow y 4))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- (pow y 2) 1) (pow y 4))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- (pow y 2) 1) (pow y 4))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ -1 (pow y 3))
(/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 3 binary64)))
(/ (- (pow y 2) 1) (pow y 3))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(/ (- (pow y 2) 1) (pow y 3))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(/ (- (pow y 2) 1) (pow y 3))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 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 (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
-1
#s(literal -1 binary64)
(- (* -1 (pow y 2)) 1)
(-.f64 #s(literal -1 binary64) (*.f64 y y))
(- (* -1 (pow y 2)) 1)
(-.f64 #s(literal -1 binary64) (*.f64 y y))
(- (* -1 (pow y 2)) 1)
(-.f64 #s(literal -1 binary64) (*.f64 y y))
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 (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))) (*.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/.f64 (/.f64 (-.f64 (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64)) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))) y) y)
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.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)
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))) (*.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/.f64 (/.f64 (-.f64 (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64)) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))) y) y)
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ (- 1 (/ 1 (pow y 2))) y)
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(/ (- 1 (/ 1 (pow y 2))) y)
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(/ (- 1 (/ 1 (pow y 2))) y)
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (* (pow y 2) (+ 1 (/ 1 (pow y 2)))))
(-.f64 #s(literal -1 binary64) (*.f64 y y))
(* -1 (* (pow y 2) (+ 1 (/ 1 (pow y 2)))))
(-.f64 #s(literal -1 binary64) (*.f64 y y))
(* -1 (* (pow y 2) (+ 1 (/ 1 (pow y 2)))))
(-.f64 #s(literal -1 binary64) (*.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 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))) (*.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/.f64 (/.f64 (-.f64 (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64)) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))) y) y)
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.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)
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))) (*.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/.f64 (/.f64 (-.f64 (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64)) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))) y) y)
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(* -1 (/ (- (/ 1 (pow y 2)) 1) y))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(* -1 (/ (- (/ 1 (pow y 2)) 1) y))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(* -1 (/ (- (/ 1 (pow y 2)) 1) y))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (* (pow y 2) (+ 1 (/ 1 (pow y 2)))))
(-.f64 #s(literal -1 binary64) (*.f64 y y))
(* -1 (* (pow y 2) (+ 1 (/ 1 (pow y 2)))))
(-.f64 #s(literal -1 binary64) (*.f64 y y))
(* -1 (* (pow y 2) (+ 1 (/ 1 (pow y 2)))))
(-.f64 #s(literal -1 binary64) (*.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 (+ 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)
(* 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)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #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)
(* 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)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #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)
(* 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)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)
(/ -1 x)
(/.f64 #s(literal -1 binary64) x)

rewrite127.0ms (2.2%)

Memory

6.9MiB live, 165.1MiB allocated

Rules

3 318×	`lower-/.f32`
3 304×	`lower-/.f64`
3 286×	`lower-fma.f32`
3 284×	`lower-fma.f64`
3 086×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	113
0	31	113
1	125	98
2	786	90
3	7450	90
0	8062	90

Stop Event

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

Counts

12 → 749

Calls

Call 1

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

Outputs
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eval114.0ms (2%)

Memory: 28.3MiB live, 216.3MiB allocated
Compiler: Compiled 15 705 to 2 917 computations (81.4% saved)

prune51.0ms (0.9%)

Memory

-7.5MiB live, 89.3MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	994	1	995
Fresh	0	0	0
Picked	1	2	3
Done	0	3	3
Total	995	6	1 001

Accuracy

100.0%

Counts

1 001 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (*.f64 x y) y x)
✓	95.4%	(/.f64 (neg.f64 (fma.f64 y y #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x))
▶	45.0%	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)))
✓	44.8%	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
✓	44.8%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
✓	54.2%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 42 to 37 computations (11.9% saved)

simplify374.0ms (6.5%)

Memory

9.9MiB live, 198.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

20 920×	`lower-fma.f64`
20 920×	`lower-fma.f32`
5 176×	`lower-+.f64`
5 176×	`lower-+.f32`
3 176×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	82
0	18	82
1	27	82
2	43	82
3	72	82
4	114	82
5	176	82
6	296	82
7	417	82
8	581	82
9	712	82
10	1209	82
11	1615	82
12	2474	82
13	3560	82
14	4141	82
15	4682	82
16	4868	82
17	4975	82
18	5056	82
19	5062	82
20	5282	82
21	5510	82
22	5546	82
23	5576	82
24	5600	82
25	5608	82
26	5620	82
27	5620	82
0	8604	80

Stop Event

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

Calls

Call 1

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

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

localize32.0ms (0.5%)

Memory

-1.9MiB live, 36.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.10546875	(/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)
accuracy	2.7235504300556825	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)))
accuracy	33.5595672956305	#s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))
accuracy	33.93446521850577	#s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y))

Samples

24.0ms

256×

valid

Compiler

Compiled 44 to 15 computations (65.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-div: 8.0ms (48.6% of total)

ival-mult: 3.0ms (18.2% of total)

ival-pow: 2.0ms (12.1% of total)

ival-sub: 1.0ms (6.1% of total)

ival-add: 1.0ms (6.1% of total)

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

exact: 0.0ms (0% of total)

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

series21.0ms (0.4%)

Memory

-31.5MiB live, 6.8MiB allocated

Counts

4 → 60

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 y) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) #<representation binary64>) () ())) ())
#s(alt (+ x (* x (pow y 2))) (taylor 0 y) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 y) (#s(alt #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) (patch #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* -1 (pow y 2))) (taylor 0 y) (#s(alt #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) (patch #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (pow y 2) 1))) (taylor 0 y) (#s(alt #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) (patch #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1))) (taylor 0 y) (#s(alt #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) (patch #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) #<representation binary64>) () ())) ())
#s(alt (/ -1 (pow y 4)) (taylor 0 y) (#s(alt (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) (patch (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) #<representation binary64>) () ())) ())
#s(alt (/ (- (pow y 2) 1) (pow y 4)) (taylor 0 y) (#s(alt (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) (patch (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) #<representation binary64>) () ())) ())
#s(alt (/ (- (pow y 2) 1) (pow y 4)) (taylor 0 y) (#s(alt (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) (patch (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) #<representation binary64>) () ())) ())
#s(alt (/ (- (pow y 2) 1) (pow y 4)) (taylor 0 y) (#s(alt (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) (patch (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) #<representation binary64>) () ())) ())
#s(alt (/ -1 (pow y 3)) (taylor 0 y) (#s(alt #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) (patch #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (/ (- (pow y 2) 1) (pow y 3)) (taylor 0 y) (#s(alt #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) (patch #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (/ (- (pow y 2) 1) (pow y 3)) (taylor 0 y) (#s(alt #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) (patch #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (/ (- (pow y 2) 1) (pow y 3)) (taylor 0 y) (#s(alt #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) (patch #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* x (pow y 2)) (taylor inf y) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor inf y) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor inf y) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor inf y) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow y 2)) (taylor inf y) (#s(alt #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) (patch #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow y 2))) (pow y 2)) (taylor inf y) (#s(alt #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) (patch #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2)) (taylor inf y) (#s(alt #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) (patch #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2)) (taylor inf y) (#s(alt #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) (patch #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow y 2)) (taylor inf y) (#s(alt (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) (patch (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow y 2))) (pow y 2)) (taylor inf y) (#s(alt (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) (patch (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow y 2))) (pow y 2)) (taylor inf y) (#s(alt (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) (patch (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow y 2))) (pow y 2)) (taylor inf y) (#s(alt (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) (patch (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) #<representation binary64>) () ())) ())
#s(alt (/ 1 y) (taylor inf y) (#s(alt #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) (patch #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow y 2))) y) (taylor inf y) (#s(alt #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) (patch #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow y 2))) y) (taylor inf y) (#s(alt #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) (patch #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow y 2))) y) (taylor inf y) (#s(alt #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) (patch #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* x (pow y 2)) (taylor -inf y) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor -inf y) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor -inf y) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) #<representation binary64>) () ())) ())
#s(alt (* (pow y 2) (+ x (/ x (pow y 2)))) (taylor -inf y) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow y 2)) (taylor -inf y) (#s(alt #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) (patch #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow y 2))) (pow y 2)) (taylor -inf y) (#s(alt #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) (patch #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2)) (taylor -inf y) (#s(alt #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) (patch #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) #<representation binary64>) () ())) ())
#s(alt (/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2)) (taylor -inf y) (#s(alt #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) (patch #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow y 2)) (taylor -inf y) (#s(alt (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) (patch (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow y 2))) (pow y 2)) (taylor -inf y) (#s(alt (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) (patch (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow y 2))) (pow y 2)) (taylor -inf y) (#s(alt (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) (patch (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) #<representation binary64>) () ())) ())
#s(alt (/ (- 1 (/ 1 (pow y 2))) (pow y 2)) (taylor -inf y) (#s(alt (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) (patch (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y) #<representation binary64>) () ())) ())
#s(alt (/ 1 y) (taylor -inf y) (#s(alt #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) (patch #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ 1 (pow y 2)) 1) y)) (taylor -inf y) (#s(alt #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) (patch #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ 1 (pow y 2)) 1) y)) (taylor -inf y) (#s(alt #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) (patch #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (- (/ 1 (pow y 2)) 1) y)) (taylor -inf y) (#s(alt #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) (patch #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (pow y 2))) (taylor 0 x) (#s(alt (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) 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(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) 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(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) 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(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) 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(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) 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(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) 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(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) 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(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) 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(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) (patch (/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	((/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ (/ (- 1 (/ 1 (* y y))) y) y) (/ (- 1 (/ 1 (* y y))) y))
1.0ms	y	@	-inf	((/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ (/ (- 1 (/ 1 (* y y))) y) y) (/ (- 1 (/ 1 (* y y))) y))
0.0ms	y	@	inf	((/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ (/ (- 1 (/ 1 (* y y))) y) y) (/ (- 1 (/ 1 (* y y))) y))
0.0ms	x	@	-inf	((/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ (/ (- 1 (/ 1 (* y y))) y) y) (/ (- 1 (/ 1 (* y y))) y))
0.0ms	x	@	0	((/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ (/ (- 1 (/ 1 (* y y))) y) y) (/ (- 1 (/ 1 (* y y))) y))

simplify195.0ms (3.4%)

Memory

40.8MiB live, 155.7MiB allocated

Algorithm

1×	egg-herbie

Rules

18 756×	`lower-fma.f64`
18 756×	`lower-fma.f32`
3 634×	`lower-*.f64`
3 634×	`lower-*.f32`
2 376×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	490
1	117	488
2	271	484
3	836	472
4	2343	472
5	6809	472
0	8118	426

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 59

Calls

Call 1

Inputs
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 4))
(/ (- (pow y 2) 1) (pow y 4))
(/ (- (pow y 2) 1) (pow y 4))
(/ (- (pow y 2) 1) (pow y 4))
(/ -1 (pow y 3))
(/ (- (pow y 2) 1) (pow y 3))
(/ (- (pow y 2) 1) (pow y 3))
(/ (- (pow y 2) 1) (pow y 3))
(* 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 (/ 1 (pow y 2))) (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ 1 y)
(/ (- 1 (/ 1 (pow y 2))) y)
(/ (- 1 (/ 1 (pow y 2))) y)
(/ (- 1 (/ 1 (pow y 2))) 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 (/ 1 (pow y 2))) (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ 1 y)
(* -1 (/ (- (/ 1 (pow y 2)) 1) y))
(* -1 (/ (- (/ 1 (pow y 2)) 1) y))
(* -1 (/ (- (/ 1 (pow y 2)) 1) 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)))

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)
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow y 2)))
(-.f64 #s(literal 1 binary64) (*.f64 y y))
(+ 1 (* (pow y 2) (- (pow y 2) 1)))
(fma.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) y) y #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))
(.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 y y)))
(/ -1 (pow y 4))
(/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 4 binary64)))
(/ (- (pow y 2) 1) (pow y 4))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- (pow y 2) 1) (pow y 4))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- (pow y 2) 1) (pow y 4))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ -1 (pow y 3))
(/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 3 binary64)))
(/ (- (pow y 2) 1) (pow y 3))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(/ (- (pow y 2) 1) (pow y 3))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(/ (- (pow y 2) 1) (pow y 3))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))) (*.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/.f64 (/.f64 (-.f64 (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64)) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))) y) y)
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(/ (- 1 (/ 1 (pow y 2))) y)
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(/ (- 1 (/ 1 (pow y 2))) y)
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(/ (- 1 (/ 1 (pow y 2))) y)
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))) (*.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/.f64 (/.f64 (-.f64 (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 6 binary64))) #s(literal -1 binary64)) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))) y) y)
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ 1 y)
(/.f64 #s(literal 1 binary64) y)
(* -1 (/ (- (/ 1 (pow y 2)) 1) y))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(* -1 (/ (- (/ 1 (pow y 2)) 1) y))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(* -1 (/ (- (/ 1 (pow y 2)) 1) y))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(* 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)
(* 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)

rewrite142.0ms (2.5%)

Memory

7.3MiB live, 161.9MiB allocated

Rules

3 452×	`lower-fma.f64`
3 452×	`lower-fma.f32`
2 914×	`lower-/.f32`
2 908×	`lower-/.f64`
2 842×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	76
0	18	76
1	89	68
2	597	68
3	6618	68
0	8037	66

Stop Event

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

Counts

4 → 73

Calls

Call 1

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

Outputs
#<batchref>
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eval14.0ms (0.2%)

Memory: -7.8MiB live, 30.0MiB allocated
Compiler: Compiled 1 505 to 276 computations (81.7% saved)

prune48.0ms (0.8%)

Memory

-22.9MiB live, 60.9MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	132	6	138

Accuracy

100.0%

Counts

138 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (*.f64 x y) y x)
✓	95.4%	(/.f64 (neg.f64 (fma.f64 y y #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x))
✓	45.0%	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)))
✓	44.8%	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
✓	44.8%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
✓	54.2%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 136 to 78 computations (42.6% saved)

regimes118.0ms (2%)

Memory

-1.4MiB live, 36.9MiB allocated

Counts

11 → 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 (neg.f64 (fma.f64 y y #s(literal 1 binary64))) (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64)))))
(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)))
(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y) y)))
(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (.f64 y y))) (-.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 4 binary64))))

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

Calls

5 calls:

103.0ms	x
4.0ms	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
4.0ms	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 (0.1%)

Memory

15.5MiB live, 15.5MiB 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	y
2.0ms	x
2.0ms	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
1.0ms	(*.f64 y y)
1.0ms	(+.f64 #s(literal 1 binary64) (*.f64 y y))

Results

Accuracy	Segments	Branch
63.1%	5	`x`
94.2%	2	`y`
77.4%	2	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`
94.2%	2	`(+.f64 #s(literal 1 binary64) (*.f64 y y))`
94.2%	2	`(*.f64 y y)`

Compiler

Compiled 17 to 18 computations (-5.9% saved)

regimes6.0ms (0.1%)

Memory

16.7MiB live, 16.7MiB 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:

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

Results

Accuracy	Segments	Branch
54.2%	1	`x`
54.2%	1	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`
54.2%	1	`y`
54.2%	1	`(+.f64 #s(literal 1 binary64) (*.f64 y y))`
54.2%	1	`(*.f64 y y)`

Compiler

Compiled 17 to 18 computations (-5.9% saved)

bsearch14.0ms (0.2%)

Memory

-21.3MiB live, 16.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	0.965143872794683	283707.08782406745

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 (52.4% of total)

ival-mult: 1.0ms (52.4% of total)

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

exact: 0.0ms (0% of total)

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

simplify27.0ms (0.5%)

Memory

0.9MiB live, 44.5MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`-commutative-binary64-.f64`
2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`

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)

soundness521.0ms (9%)

Memory

-7.2MiB live, 225.1MiB allocated

Rules

9 064×	`lower-fma.f64`
9 064×	`lower-fma.f32`
6 574×	`lower-*.f64`
6 574×	`lower-*.f32`
5 176×	`lower-fma.f64`

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

Stop Event

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

Compiler

Compiled 50 to 32 computations (36% saved)

preprocess109.0ms (1.9%)

Memory

6.7MiB live, 86.9MiB 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	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

start0.0ms (0%)

analyze0.0ms (0%)

sample868.0ms (15%)

explain121.0ms (2.1%)

preprocess142.0ms (2.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize328.0ms (5.7%)

series5.0ms (0.1%)

simplify213.0ms (3.7%)

rewrite284.0ms (4.9%)

eval63.0ms (1.1%)

prune31.0ms (0.5%)

simplify10.0ms (0.2%)

localize49.0ms (0.8%)

series19.0ms (0.3%)

simplify237.0ms (4.1%)

rewrite179.0ms (3.1%)

eval900.0ms (15.6%)

prune37.0ms (0.6%)

simplify117.0ms (2%)

localize43.0ms (0.7%)

series23.0ms (0.4%)

simplify182.0ms (3.2%)

rewrite127.0ms (2.2%)

eval114.0ms (2%)

prune51.0ms (0.9%)

simplify374.0ms (6.5%)

localize32.0ms (0.5%)

series21.0ms (0.4%)

simplify195.0ms (3.4%)

rewrite142.0ms (2.5%)

eval14.0ms (0.2%)

prune48.0ms (0.8%)

regimes118.0ms (2%)

regimes8.0ms (0.1%)

regimes6.0ms (0.1%)

bsearch14.0ms (0.2%)

simplify27.0ms (0.5%)

soundness521.0ms (9%)

preprocess109.0ms (1.9%)

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