Metrics for Numeric.Log:$clog1p from log-domain-0.10.2.1, A

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.9MiB live, 0.9MiB 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 13 to 10 computations (23.1% saved)

sample862.0ms (22.2%)

Memory

48.9MiB live, 1 339.2MiB allocated

Samples

607.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 375.0ms

ival-mult: 244.0ms (65% of total)

ival-add: 119.0ms (31.7% of total)

ival-true: 6.0ms (1.6% of total)

exact: 4.0ms (1.1% of total)

ival-assert: 3.0ms (0.8% of total)

Bogosity

explain119.0ms (3.1%)

Memory

-5.2MiB live, 108.2MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))`
-	-	`(*.f64 x #s(literal 2 binary64))`
-	-	`#s(literal 2 binary64)`
-	-	`y`
-	-	`(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))`
-	-	`(*.f64 y y)`
-	-	`(*.f64 x x)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

30.0ms

512×

valid

Compiler

Compiled 75 to 28 computations (62.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-mult: 10.0ms (68.1% of total)

ival-add: 4.0ms (27.2% of total)

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

exact: 0.0ms (0% of total)

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

preprocess43.0ms (1.1%)

Memory

-35.4MiB live, 30.5MiB allocated

Algorithm

1×	egg-herbie

Rules

266×	`sub-neg`
198×	`unsub-neg`
146×	`cancel-sign-sub-inv`
142×	`associate-+l-`
136×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	51
1	68	49
2	215	46
3	578	45
4	1132	45
5	1396	45
6	1445	45
0	8	11
0	13	9
1	20	9
2	30	9
3	32	9
0	32	8

Stop Event

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

Calls

Call 1

Inputs
(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))

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

Symmetry

(abs y)

Compiler

Compiled 11 to 8 computations (27.3% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify4.0ms (0.1%)

Memory

7.5MiB live, 7.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(*.f64 x #s(literal 2 binary64))
cost-diff	128	(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))
cost-diff	320	(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))

Rules

28×	`lower-fma.f64`
28×	`lower-fma.f32`
28×	`lower-+.f32`
24×	`lower-+.f64`
12×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
0	13	26
1	20	26
2	30	26
3	32	26
0	32	25

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))
(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(*.f64 x x)
(*.f64 y y)
y

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

localize24.0ms (0.6%)

Memory

-17.0MiB live, 57.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	0	(*.f64 x #s(literal 2 binary64))
accuracy	0.00390625	(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))

Samples

15.0ms

256×

valid

Compiler

Compiled 32 to 10 computations (68.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-mult: 5.0ms (70.7% of total)

ival-add: 2.0ms (28.3% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.2%)

Memory

19.2MiB live, 19.2MiB allocated

Counts

5 → 72

Calls

Call 1

Inputs
#s(alt (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (patch (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) #<representation binary64>) () ())
#s(alt (+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (.f64 y y)) (patch (+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (.f64 y y)) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((+ (* x 2) (* x x)) (+ (+ (* x 2) (* x x)) (* y y)) (* x 2) (* x x) (* y y))
1.0ms	x	@	-inf	((+ (* x 2) (* x x)) (+ (+ (* x 2) (* x x)) (* y y)) (* x 2) (* x x) (* y y))
1.0ms	y	@	inf	((+ (* x 2) (* x x)) (+ (+ (* x 2) (* x x)) (* y y)) (* x 2) (* x x) (* y y))
1.0ms	y	@	0	((+ (* x 2) (* x x)) (+ (+ (* x 2) (* x x)) (* y y)) (* x 2) (* x x) (* y y))
1.0ms	x	@	0	((+ (* x 2) (* x x)) (+ (+ (* x 2) (* x x)) (* y y)) (* x 2) (* x x) (* y y))

simplify168.0ms (4.3%)

Memory

-9.3MiB live, 148.5MiB allocated

Algorithm

1×	egg-herbie

Rules

9 938×	`lower-fma.f64`
9 938×	`lower-fma.f32`
3 308×	`lower-*.f64`
3 308×	`lower-*.f32`
1 722×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	334
1	101	334
2	272	334
3	912	334
4	2770	334
5	4863	334
6	7655	334
0	8388	318

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

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

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

rewrite186.0ms (4.8%)

Memory

-1.5MiB live, 271.4MiB allocated

Rules

6 744×	`lower-fma.f64`
6 744×	`lower-fma.f32`
4 716×	`lower-*.f32`
4 710×	`lower-*.f64`
2 642×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	27
0	13	23
1	47	23
2	406	23
3	6148	23
0	8102	22

Stop Event

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

Counts

5 → 219

Calls

Call 1

Inputs
(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))
(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))
(*.f64 x #s(literal 2 binary64))
(*.f64 x x)
(*.f64 y y)

Outputs
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eval33.0ms (0.9%)

Memory: 25.7MiB live, 99.2MiB allocated
Compiler: Compiled 6 579 to 691 computations (89.5% saved)

prune21.0ms (0.5%)

Memory

-24.2MiB live, 28.0MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	286	5	291
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	287	5	292

Accuracy

100.0%

Counts

292 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	81.5%	(+.f64 #s(approx (+ (* x 2) (* x x)) (.f64 x x)) (.f64 y y))
▶	67.2%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 x #s(literal 2 binary64) (*.f64 y y)))
▶	60.2%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
▶	49.1%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
▶	42.3%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))

Compiler

Compiled 58 to 52 computations (10.3% saved)

simplify5.0ms (0.1%)

Memory

15.4MiB live, 15.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 y y)
cost-diff	0	(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
cost-diff	0	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 x #s(literal 2 binary64) (*.f64 y y)))
cost-diff	0	(-.f64 x #s(literal -2 binary64))
cost-diff	0	(*.f64 (-.f64 x #s(literal -2 binary64)) x)
cost-diff	0	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
cost-diff	0	(*.f64 y y)
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (+ (* x 2) (* x x)) (*.f64 x x))
cost-diff	128	(+.f64 #s(approx (+ (* x 2) (* x x)) (.f64 x x)) (.f64 y y))

Rules

32×	`lower-+.f32`
30×	`lower-+.f64`
30×	`lower-fma.f32`
28×	`lower-fma.f64`
14×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	129
0	26	117
1	38	117
2	44	117
0	44	112

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(+.f64 #s(approx (+ (* x 2) (* x x)) (.f64 x x)) (.f64 y y))
#s(approx (+ (* x 2) (* x x)) (*.f64 x x))
(*.f64 x x)
x
(*.f64 y y)
y
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
(*.f64 x x)
x
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
(*.f64 y y)
y
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(-.f64 x #s(literal -2 binary64))
x
#s(literal -2 binary64)
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 x #s(literal 2 binary64) (*.f64 y y)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
x
#s(literal 2 binary64)
(*.f64 y y)
y

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

localize46.0ms (1.2%)

Memory

-3.3MiB live, 70.1MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0.00390625	(fma.f64 x #s(literal 2 binary64) (*.f64 y y))
accuracy	20.965887194190962	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 x #s(literal 2 binary64) (*.f64 y y)))
accuracy	0	(-.f64 x #s(literal -2 binary64))
accuracy	0.00390625	(*.f64 (-.f64 x #s(literal -2 binary64)) x)
accuracy	25.485800064084877	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
accuracy	0	(*.f64 y y)
accuracy	32.59346643468945	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
accuracy	0	(*.f64 x x)
accuracy	36.92370811220308	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
accuracy	0	(+.f64 #s(approx (+ (* x 2) (* x x)) (.f64 x x)) (.f64 y y))
accuracy	0	(*.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	29.835518093145982	#s(approx (+ (* x 2) (* x x)) (*.f64 x x))

Samples

35.0ms

256×

valid

Compiler

Compiled 103 to 14 computations (86.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 6.0ms (55.9% of total)

ival-add: 3.0ms (27.9% of total)

ival-sub: 1.0ms (9.3% of total)

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

exact: 0.0ms (0% of total)

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

series37.0ms (1%)

Memory

-10.6MiB live, 28.3MiB allocated

Counts

11 → 204

Calls

Call 1

Inputs
#s(alt (+.f64 #s(approx (+ (* x 2) (* x x)) (.f64 x x)) (.f64 y y)) (patch (+.f64 #s(approx (+ (* x 2) (* x x)) (.f64 x x)) (.f64 y y)) #<representation binary64>) () ())
#s(alt #s(approx (+ (* x 2) (* x x)) (.f64 x x)) (patch #s(approx (+ ( x 2) (* x x)) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (.f64 x x)) (patch #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (*.f64 x x)) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (.f64 y y)) (patch #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (*.f64 y y)) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (.f64 (-.f64 x #s(literal -2 binary64)) x)) (patch #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x)) #<representation binary64>) () ())
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#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 x #s(literal 2 binary64) (.f64 y y))) (patch #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (fma.f64 x #s(literal 2 binary64) (*.f64 y y))) #<representation binary64>) () ())
#s(alt (fma.f64 x #s(literal 2 binary64) (.f64 y y)) (patch (fma.f64 x #s(literal 2 binary64) (.f64 y y)) #<representation binary64>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x x) (* y y) (+ (+ (* x 2) (* x x)) (* y y)) (+ (+ (* x 2) (* x x)) (* y y)) (+ (+ (* x 2) (* x x)) (* y y)) (* (- x -2) x) (- x -2) (+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* y y)))
1.0ms	x	@	inf	((+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x x) (* y y) (+ (+ (* x 2) (* x x)) (* y y)) (+ (+ (* x 2) (* x x)) (* y y)) (+ (+ (* x 2) (* x x)) (* y y)) (* (- x -2) x) (- x -2) (+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* y y)))
1.0ms	x	@	0	((+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x x) (* y y) (+ (+ (* x 2) (* x x)) (* y y)) (+ (+ (* x 2) (* x x)) (* y y)) (+ (+ (* x 2) (* x x)) (* y y)) (* (- x -2) x) (- x -2) (+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* y y)))
1.0ms	y	@	inf	((+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x x) (* y y) (+ (+ (* x 2) (* x x)) (* y y)) (+ (+ (* x 2) (* x x)) (* y y)) (+ (+ (* x 2) (* x x)) (* y y)) (* (- x -2) x) (- x -2) (+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* y y)))
1.0ms	y	@	-inf	((+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* x x)) (* x x) (* y y) (+ (+ (* x 2) (* x x)) (* y y)) (+ (+ (* x 2) (* x x)) (* y y)) (+ (+ (* x 2) (* x x)) (* y y)) (* (- x -2) x) (- x -2) (+ (+ (* x 2) (* x x)) (* y y)) (+ (* x 2) (* y y)))

simplify130.0ms (3.4%)

Memory

7.8MiB live, 123.7MiB allocated

Algorithm

1×	egg-herbie

Rules

7 768×	`lower-fma.f64`
7 768×	`lower-fma.f32`
3 084×	`lower-*.f64`
3 084×	`lower-*.f32`
2 114×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	1214
1	132	1214
2	353	1214
3	1258	1214
4	3427	1214
5	7448	1214
0	8366	1116

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 202

Calls

Call 1

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

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

rewrite189.0ms (4.9%)

Memory

24.4MiB live, 179.2MiB allocated

Rules

7 744×	`lower-fma.f32`
7 742×	`lower-fma.f64`
5 570×	`lower-*.f32`
5 564×	`lower-*.f64`
4 102×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	111
0	26	99
1	96	99
2	724	99
0	8522	94

Stop Event

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

Counts

11 → 215

Calls

Call 1

Inputs
(+.f64 #s(approx (+ (* x 2) (* x x)) (.f64 x x)) (.f64 y y))
#s(approx (+ (* x 2) (* x x)) (*.f64 x x))
(*.f64 x x)
(*.f64 y y)
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
(*.f64 (-.f64 x #s(literal -2 binary64)) x)
(-.f64 x #s(literal -2 binary64))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 x #s(literal 2 binary64) (*.f64 y y)))
(fma.f64 x #s(literal 2 binary64) (*.f64 y y))

Outputs
#<batchref>
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eval52.0ms (1.3%)

Memory: -13.8MiB live, 114.0MiB allocated
Compiler: Compiled 6 491 to 860 computations (86.8% saved)

prune22.0ms (0.6%)

Memory

-5.8MiB live, 32.2MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	469	2	471
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	470	6	476

Accuracy

100.0%

Counts

476 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	81.5%	(fma.f64 y y #s(approx (+ (* x 2) (* x x)) (*.f64 x x)))
✓	67.2%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 x #s(literal 2 binary64) (*.f64 y y)))
✓	60.2%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
▶	20.8%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
✓	49.1%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
✓	42.3%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))

Compiler

Compiled 33 to 31 computations (6.1% saved)

simplify4.0ms (0.1%)

Memory

5.3MiB live, 5.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (+ (* x 2) (* x x)) (*.f64 x x))
cost-diff	0	(fma.f64 y y #s(approx (+ (* x 2) (* x x)) (*.f64 x x)))
cost-diff	0	#s(approx (- x -2) #s(literal 2 binary64))
cost-diff	0	(*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)
cost-diff	0	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))

Rules

32×	`lower-+.f64`
32×	`lower-+.f32`
30×	`lower-fma.f32`
28×	`lower-fma.f64`
16×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	63
0	19	57
1	30	57
2	39	57
3	41	57
0	41	56

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
(*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)
#s(approx (- x -2) #s(literal 2 binary64))
#s(literal 2 binary64)
x
(fma.f64 y y #s(approx (+ (* x 2) (* x x)) (*.f64 x x)))
y
#s(approx (+ (* x 2) (* x x)) (*.f64 x x))
(*.f64 x x)
x

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

localize43.0ms (1.1%)

Memory

16.9MiB live, 54.3MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 y y #s(approx (+ (* x 2) (* x x)) (*.f64 x x)))
accuracy	0	(*.f64 x x)
accuracy	29.835518093145982	#s(approx (+ (* x 2) (* x x)) (*.f64 x x))
accuracy	0.00390625	(*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)
accuracy	25.485800064084877	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
accuracy	32.43791211379519	#s(approx (- x -2) #s(literal 2 binary64))

Samples

36.0ms

256×

valid

Compiler

Compiled 46 to 14 computations (69.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 6.0ms (53.6% of total)

ival-add: 3.0ms (26.8% of total)

ival-sub: 2.0ms (17.9% of total)

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

exact: 0.0ms (0% of total)

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

series114.0ms (2.9%)

Memory

-40.8MiB live, 33.3MiB allocated

Counts

6 → 96

Calls

Call 1

Inputs
#s(alt #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) (patch #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 #s(approx (- x -2) #s(literal 2 binary64)) x) (patch (.f64 #s(approx (- x -2) #s(literal 2 binary64)) x) #<representation binary64>) () ())
#s(alt #s(approx (- x -2) #s(literal 2 binary64)) (patch #s(approx (- x -2) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 y y #s(approx (+ (* x 2) (* x x)) (.f64 x x))) (patch (fma.f64 y y #s(approx (+ ( x 2) (* x x)) (*.f64 x x))) #<representation binary64>) () ())
#s(alt #s(approx (+ (* x 2) (* x x)) (.f64 x x)) (patch #s(approx (+ ( x 2) (* x x)) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
109.0ms	x	@	-inf	((+ (+ (* x 2) (* x x)) (* y y)) (* (- x -2) x) (- x -2) (+ (* y y) (+ (* x 2) (* x x))) (+ (* x 2) (* x x)) (* x x))
1.0ms	x	@	inf	((+ (+ (* x 2) (* x x)) (* y y)) (* (- x -2) x) (- x -2) (+ (* y y) (+ (* x 2) (* x x))) (+ (* x 2) (* x x)) (* x x))
0.0ms	x	@	0	((+ (+ (* x 2) (* x x)) (* y y)) (* (- x -2) x) (- x -2) (+ (* y y) (+ (* x 2) (* x x))) (+ (* x 2) (* x x)) (* x x))
0.0ms	y	@	-inf	((+ (+ (* x 2) (* x x)) (* y y)) (* (- x -2) x) (- x -2) (+ (* y y) (+ (* x 2) (* x x))) (+ (* x 2) (* x x)) (* x x))
0.0ms	y	@	inf	((+ (+ (* x 2) (* x x)) (* y y)) (* (- x -2) x) (- x -2) (+ (* y y) (+ (* x 2) (* x x))) (+ (* x 2) (* x x)) (* x x))

simplify135.0ms (3.5%)

Memory

-1.6MiB live, 159.0MiB allocated

Algorithm

1×	egg-herbie

Rules

8 130×	`lower-fma.f64`
8 130×	`lower-fma.f32`
4 308×	`lower-*.f64`
4 308×	`lower-*.f32`
1 470×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	518
1	109	518
2	284	518
3	1004	518
4	3129	518
5	6287	518
0	8416	486

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 94

Calls

Call 1

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

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

rewrite314.0ms (8.1%)

Memory

-6.3MiB live, 223.2MiB allocated

Rules

8 536×	`lower-fma.f32`
8 534×	`lower-fma.f64`
5 806×	`lower-*.f32`
5 802×	`lower-*.f64`
3 942×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	59
0	19	53
1	80	53
2	619	53
0	8352	52

Stop Event

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

Counts

6 → 69

Calls

Call 1

Inputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
(*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x)
#s(approx (- x -2) #s(literal 2 binary64))
(fma.f64 y y #s(approx (+ (* x 2) (* x x)) (*.f64 x x)))
#s(approx (+ (* x 2) (* x x)) (*.f64 x x))
(*.f64 x x)

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval15.0ms (0.4%)

Memory: 32.4MiB live, 32.4MiB allocated
Compiler: Compiled 2 567 to 237 computations (90.8% saved)

prune68.0ms (1.7%)

Memory

-23.7MiB live, 14.9MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	163	6	169

Accuracy

100.0%

Counts

169 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	81.5%	(fma.f64 y y #s(approx (+ (* x 2) (* x x)) (*.f64 x x)))
✓	67.2%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 x #s(literal 2 binary64) (*.f64 y y)))
✓	60.2%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
✓	20.8%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
✓	49.1%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
✓	42.3%	#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))

Compiler

Compiled 85 to 53 computations (37.6% saved)

regimes63.0ms (1.6%)

Memory

-18.3MiB live, 28.5MiB allocated

Counts

8 → 1

Calls

Call 1

Inputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 x #s(literal 2 binary64) (*.f64 y y)))
(fma.f64 y y #s(approx (+ (* x 2) (* x x)) (*.f64 x x)))
(+.f64 #s(approx (+ (* x 2) (* x x)) (.f64 x x)) (.f64 y y))
(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))

Outputs
(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))

Calls

5 calls:

3.0ms	x
3.0ms	(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))
3.0ms	y
3.0ms	(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))
3.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))`
100.0%	1	`(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))`
100.0%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes15.0ms (0.4%)

Memory

23.8MiB live, 23.8MiB allocated

Counts

7 → 2

Calls

Call 1

Inputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 x #s(literal 2 binary64) (*.f64 y y)))
(fma.f64 y y #s(approx (+ (* x 2) (* x x)) (*.f64 x x)))
(+.f64 #s(approx (+ (* x 2) (* x x)) (.f64 x x)) (.f64 y y))

Outputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 x #s(literal 2 binary64) (*.f64 y y)))
(fma.f64 y y #s(approx (+ (* x 2) (* x x)) (*.f64 x x)))

Calls

5 calls:

3.0ms	(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))
3.0ms	y
3.0ms	x
3.0ms	(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))
3.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
99.2%	3	`x`
98.0%	2	`y`
99.1%	2	`(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))`
99.2%	2	`(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))`
98.0%	2	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes68.0ms (1.8%)

Memory

-20.2MiB live, 19.5MiB allocated

Counts

5 → 2

Calls

Call 1

Inputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 x #s(literal 2 binary64) (*.f64 y y)))

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

Calls

5 calls:

58.0ms	x
2.0ms	y
2.0ms	(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))
2.0ms	(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))
2.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
92.0%	3	`x`
89.5%	4	`y`
89.5%	4	`(*.f64 y y)`
67.2%	1	`(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))`
91.3%	2	`(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes9.0ms (0.2%)

Memory

14.8MiB live, 14.8MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))

Outputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))

Calls

4 calls:

2.0ms	x
2.0ms	(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))
2.0ms	y
2.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
86.4%	2	`y`
86.4%	2	`(*.f64 y y)`
74.6%	3	`x`
73.4%	2	`(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))`

Compiler

Compiled 12 to 13 computations (-8.3% saved)

regimes6.0ms (0.2%)

Memory

10.4MiB live, 10.4MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))

#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))

#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 #s(approx (- x -2) #s(literal 2 binary64)) x))

Outputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 y y))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))

Calls

3 calls:

2.0ms	(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))
2.0ms	y
2.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
73.4%	2	`(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))`
74.7%	5	`y`
71.9%	4	`(*.f64 y y)`

Compiler

Compiled 11 to 11 computations (0% saved)

regimes7.0ms (0.2%)

Memory

10.5MiB live, 10.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))

Outputs
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))

Calls

5 calls:

1.0ms	(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))
1.0ms	y
1.0ms	(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))
1.0ms	x
1.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
42.3%	1	`(*.f64 y y)`
42.3%	1	`(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))`
42.3%	1	`y`
42.3%	1	`x`
42.3%	1	`(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))`

Compiler

Compiled 23 to 21 computations (8.7% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.5671555347176127e-6	35.05298651026125

Compiler

Compiled 14 to 13 computations (7.1% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0680959872625754e+141	6.673140237949781e+153

Compiler

Compiled 14 to 13 computations (7.1% saved)

bsearch54.0ms (1.4%)

Memory

-20.7MiB live, 19.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
52.0ms	7.791364394693736e-68	5.420911777216145e-52

Samples

7.0ms

160×

valid

Compiler

Compiled 94 to 123 computations (-30.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-mult: 2.0ms (53.2% of total)

ival-add: 1.0ms (26.6% of total)

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

exact: 0.0ms (0% of total)

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

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.0680959872625754e+141	6.673140237949781e+153

Compiler

Compiled 14 to 13 computations (7.1% saved)

simplify39.0ms (1%)

Memory

16.9MiB live, 53.6MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative-binary64-+.f64`
6×	`-commutative-binary64-.f64`
4×	`sub-neg-binary64-neg.f64-+.f64--.f64`
2×	`neg-sub0-binary64--.f64-neg.f64`
2×	`neg-mul-1-binary64-*.f64-neg.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	191
1	39	191
2	44	191
3	46	191
4	47	191

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))
(if (<=.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) #s(literal 5902958103587057/1180591620717411303424 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 x #s(literal 2 binary64) (.f64 y y))) (fma.f64 y y #s(approx (+ ( x 2) (* x x)) (*.f64 x x))))
(if (<=.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) #s(literal 2000000000000000033952438476477919408282090347146213479261202070231995488134433817916524651912510225758816908462311198472918804067301785075712 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 x #s(literal 2 binary64) (.f64 y y))) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x)))
(if (<=.f64 (.f64 y y) #s(literal 5608679322432503/904625697166532776746648320380374280103671755200316906558262375061821325312 binary64)) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (.f64 (-.f64 x #s(literal -2 binary64)) x)) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (*.f64 y y)))
(if (<=.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) #s(literal 2000000000000000033952438476477919408282090347146213479261202070231995488134433817916524651912510225758816908462311198472918804067301785075712 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (.f64 y y)) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (*.f64 x x)))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))

Outputs
(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))
(+.f64 (.f64 y y) (+.f64 (.f64 x x) (*.f64 #s(literal 2 binary64) x)))
(if (<=.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) #s(literal 5902958103587057/1180591620717411303424 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 x #s(literal 2 binary64) (.f64 y y))) (fma.f64 y y #s(approx (+ ( x 2) (* x x)) (*.f64 x x))))
(if (<=.f64 (+.f64 (.f64 x x) (.f64 #s(literal 2 binary64) x)) #s(literal 5902958103587057/1180591620717411303424 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 x #s(literal 2 binary64) (.f64 y y))) (fma.f64 y y #s(approx (+ ( x 2) (* x x)) (*.f64 x x))))
(if (<=.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) #s(literal 2000000000000000033952438476477919408282090347146213479261202070231995488134433817916524651912510225758816908462311198472918804067301785075712 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 x #s(literal 2 binary64) (.f64 y y))) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x)))
(if (<=.f64 (+.f64 (.f64 x x) (.f64 #s(literal 2 binary64) x)) #s(literal 2000000000000000033952438476477919408282090347146213479261202070231995488134433817916524651912510225758816908462311198472918804067301785075712 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (fma.f64 x #s(literal 2 binary64) (.f64 y y))) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (*.f64 (-.f64 x #s(literal -2 binary64)) x)))
(if (<=.f64 (.f64 y y) #s(literal 5608679322432503/904625697166532776746648320380374280103671755200316906558262375061821325312 binary64)) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (.f64 (-.f64 x #s(literal -2 binary64)) x)) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (*.f64 y y)))
(if (<=.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) #s(literal 2000000000000000033952438476477919408282090347146213479261202070231995488134433817916524651912510225758816908462311198472918804067301785075712 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (.f64 y y)) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (*.f64 x x)))
(if (<=.f64 (+.f64 (.f64 x x) (.f64 #s(literal 2 binary64) x)) #s(literal 2000000000000000033952438476477919408282090347146213479261202070231995488134433817916524651912510225758816908462311198472918804067301785075712 binary64)) #s(approx (+ (+ (* x 2) (* x x)) (* y y)) (.f64 y y)) #s(approx (+ (+ ( x 2) (* x x)) (* y y)) (*.f64 x x)))
#s(approx (+ (+ (* x 2) (* x x)) (* y y)) (*.f64 x x))

soundness801.0ms (20.7%)

Memory

-27.6MiB live, 253.9MiB allocated

Rules

9 938×	`lower-fma.f64`
9 938×	`lower-fma.f32`
7 744×	`lower-fma.f32`
7 742×	`lower-fma.f64`
5 570×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	334
1	101	334
2	272	334
3	912	334
4	2770	334
5	4863	334
6	7655	334
0	8388	318
0	20	111
0	26	99
1	96	99
2	724	99
0	8522	94

Stop Event

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

Compiler

Compiled 152 to 72 computations (52.6% saved)

preprocess173.0ms (4.5%)

Memory: 13.2MiB live, 129.5MiB allocated
Remove: (abs y)
Compiler: Compiled 280 to 120 computations (57.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample862.0ms (22.2%)

explain119.0ms (3.1%)

preprocess43.0ms (1.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize24.0ms (0.6%)

series6.0ms (0.2%)

simplify168.0ms (4.3%)

rewrite186.0ms (4.8%)

eval33.0ms (0.9%)

prune21.0ms (0.5%)

simplify5.0ms (0.1%)

localize46.0ms (1.2%)

series37.0ms (1%)

simplify130.0ms (3.4%)

rewrite189.0ms (4.9%)

eval52.0ms (1.3%)

prune22.0ms (0.6%)

simplify4.0ms (0.1%)

localize43.0ms (1.1%)

series114.0ms (2.9%)

simplify135.0ms (3.5%)

rewrite314.0ms (8.1%)

eval15.0ms (0.4%)

prune68.0ms (1.7%)

regimes63.0ms (1.6%)

regimes15.0ms (0.4%)

regimes68.0ms (1.8%)

regimes9.0ms (0.2%)

regimes6.0ms (0.2%)

regimes7.0ms (0.2%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch54.0ms (1.4%)

bsearch0.0ms (0%)

simplify39.0ms (1%)

soundness801.0ms (20.7%)

preprocess173.0ms (4.5%)

end0.0ms (0%)

Profiling