Metrics for Examples.Basics.ProofTests:f4 from sbv-4.4

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample599.0ms (24.7%)

Memory

242.6MiB live, 242.6MiB allocated

Samples

390.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 248.0ms

ival-mult: 178.0ms (71.8% of total)

ival-add: 57.0ms (23% of total)

ival-true: 5.0ms (2% of total)

exact: 4.0ms (1.6% of total)

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

Bogosity

explain129.0ms (5.3%)

Memory

69.4MiB live, 69.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
13	13	(1.237172134480686e+216 8.146341911267927e+227)	-	`(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))`
5	20	(1.237172134480686e+216 8.146341911267927e+227)	-	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`
0	0	-	-	`(*.f64 x #s(literal 2 binary64))`
0	0	-	-	`(*.f64 x x)`
0	0	-	-	`(.f64 (.f64 x #s(literal 2 binary64)) y)`
0	0	-	-	`y`
0	0	-	-	`#s(literal 2 binary64)`
0	0	-	-	`(*.f64 y y)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`+.f64`	`(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))`	nan-rescue	26	0
↳	`(*.f64 x x)`	overflow	67
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	overflow	31
`+.f64`	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`	nan-rescue	25	0
↳	`(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))`	overflow	72
↳	`(*.f64 x x)`	overflow	67
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	overflow	31
↳	`(*.f64 y y)`	overflow	68

Confusion

	Predicted +	Predicted -
+	16	0
-	15	225

Precision

0.5161290322580645

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	16	0	0
-	15	0	225

Precision?

0.5161290322580645

Recall?

1.0

Freqs

test

number	freq
0	225
1	11
2	20

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

30.0ms

512×

valid

Compiler

Compiled 212 to 78 computations (63.2% saved)

Precisions

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

ival-mult: 12.0ms (74.7% of total)

ival-add: 4.0ms (24.9% of total)

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

exact: 0.0ms (0% of total)

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

preprocess33.0ms (1.3%)

Memory

6.1MiB live, 6.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	71
1	77	57
2	250	55
3	638	55
4	1214	55
5	1509	55
6	1539	55
0	9	13
0	15	13
1	23	11
2	43	11
3	51	11
0	51	9

Stop Event

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

Calls

Call 1

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

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

Symmetry

(sort x y)

Compiler

Compiled 13 to 9 computations (30.8% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	93.7%	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify3.0ms (0.1%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 x #s(literal 2 binary64)) y)
cost-diff	0	(*.f64 x x)
cost-diff	128	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
cost-diff	448	(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	39
0	15	39
1	23	35
2	43	35
3	51	35
0	51	32

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize21.0ms (0.9%)

Memory

9.9MiB live, 9.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0	(*.f64 x #s(literal 2 binary64))
accuracy	1.5976562500000002	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
accuracy	2.8554584291510294	(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))

Samples

14.0ms

256×

valid

Compiler

Compiled 80 to 20 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-mult: 6.0ms (75.9% of total)

ival-add: 2.0ms (25.3% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.3%)

Memory

4.0MiB live, 4.0MiB allocated

Counts

5 → 96

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((+ (* x x) (* (* x 2) y)) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x) (* (* x 2) y) (* x 2))
1.0ms	x	@	0	((+ (* x x) (* (* x 2) y)) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x) (* (* x 2) y) (* x 2))
1.0ms	x	@	-inf	((+ (* x x) (* (* x 2) y)) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x) (* (* x 2) y) (* x 2))
1.0ms	y	@	0	((+ (* x x) (* (* x 2) y)) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x) (* (* x 2) y) (* x 2))
1.0ms	y	@	-inf	((+ (* x x) (* (* x 2) y)) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x) (* (* x 2) y) (* x 2))

simplify82.0ms (3.4%)

Memory

22.0MiB live, 22.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	588
1	166	546
2	470	546
3	1334	534
4	3275	534
5	6426	534
0	8157	486

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

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

rewrite129.0ms (5.3%)

Memory

47.2MiB live, 47.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
0	15	33
1	50	29
2	420	29
3	6357	29
0	8219	26

Stop Event

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

Counts

5 → 210

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval26.0ms (1.1%)

Memory: 24.2MiB live, 24.2MiB allocated
Compiler: Compiled 7 504 to 646 computations (91.4% saved)

prune7.0ms (0.3%)

Memory

14.3MiB live, 14.3MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	301	5	306
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	302	5	307

Accuracy

100.0%

Counts

307 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	96.9%	(fma.f64 y y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
▶	55.9%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
▶	60.4%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
▶	60.9%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
▶	57.3%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Compiler

Compiled 62 to 52 computations (16.1% saved)

simplify4.0ms (0.2%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	130
0	29	130
1	43	114
2	58	114
3	61	114
0	61	114

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize37.0ms (1.5%)

Memory

17.2MiB live, 17.2MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 y #s(literal 2 binary64) x)
accuracy	0.01171875	(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
accuracy	28.250817284746727	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
accuracy	0	(fma.f64 #s(literal 2 binary64) x y)
accuracy	0	(*.f64 (fma.f64 #s(literal 2 binary64) x y) y)
accuracy	25.344617736643983	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
accuracy	0	(*.f64 y y)
accuracy	24.99890573303228	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
accuracy	0	(*.f64 x x)
accuracy	27.31042514841954	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
accuracy	0	(fma.f64 y #s(literal 2 binary64) x)
accuracy	0.01171875	(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
accuracy	1.999977980844482	(fma.f64 y y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))

Samples

26.0ms

256×

valid

Compiler

Compiled 196 to 32 computations (83.7% saved)

Precisions

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

ival-mult: 11.0ms (69% of total)

ival-add: 5.0ms (31.4% of total)

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

exact: 0.0ms (0% of total)

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

series12.0ms (0.5%)

Memory

6.5MiB live, 6.5MiB allocated

Counts

11 → 240

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((+ (* y y) (* (+ (* y 2) x) x)) (* (+ (* y 2) x) x) (+ (* y 2) x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (+ (* x x) (* (* x 2) y)) (* y y)))
1.0ms	y	@	-inf	((+ (* y y) (* (+ (* y 2) x) x)) (* (+ (* y 2) x) x) (+ (* y 2) x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (+ (* x x) (* (* x 2) y)) (* y y)))
1.0ms	x	@	-inf	((+ (* y y) (* (+ (* y 2) x) x)) (* (+ (* y 2) x) x) (+ (* y 2) x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (+ (* x x) (* (* x 2) y)) (* y y)))
1.0ms	y	@	inf	((+ (* y y) (* (+ (* y 2) x) x)) (* (+ (* y 2) x) x) (+ (* y 2) x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (+ (* x x) (* (* x 2) y)) (* y y)))
1.0ms	y	@	0	((+ (* y y) (* (+ (* y 2) x) x)) (* (+ (* y 2) x) x) (+ (* y 2) x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 x) y) y) (+ (* 2 x) y) (+ (+ (* x x) (* (* x 2) y)) (* y y)))

simplify96.0ms (4%)

Memory

27.3MiB live, 27.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	82	1602
1	269	1536
2	745	1536
3	2189	1536
4	4585	1536
5	7541	1536
0	8006	1314

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 234

Calls

Call 1

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

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

rewrite170.0ms (7%)

Memory

60.8MiB live, 60.8MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	109
0	29	109
1	102	93
2	857	93
0	8333	93

Stop Event

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

Counts

11 → 353

Calls

Call 1

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

Outputs
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eval87.0ms (3.6%)

Memory: 58.1MiB live, 58.1MiB allocated
Compiler: Compiled 13 467 to 1 209 computations (91% saved)

prune30.0ms (1.3%)

Memory

31.5MiB live, 31.5MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	748	1	749
Fresh	0	0	0
Picked	0	5	5
Done	0	0	0
Total	748	6	754

Accuracy

100.0%

Counts

754 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	96.9%	(fma.f64 y y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
▶	57.3%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (fma.f64 (.f64 y x) #s(literal 2 binary64) (.f64 y y)))
✓	55.9%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
✓	60.4%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
✓	60.9%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
✓	57.3%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Compiler

Compiled 40 to 33 computations (17.5% saved)

simplify4.0ms (0.1%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	39
0	17	38
1	30	35
2	48	35
3	51	35
0	51	31

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize30.0ms (1.2%)

Memory

11.0MiB live, 11.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0	(*.f64 y x)
accuracy	2.3476500574906174	(fma.f64 (.f64 y x) #s(literal 2 binary64) (.f64 y y))
accuracy	25.344617736643983	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (fma.f64 (.f64 y x) #s(literal 2 binary64) (.f64 y y)))

Samples

22.0ms

256×

valid

Compiler

Compiled 59 to 21 computations (64.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-mult: 10.0ms (73.2% of total)

ival-add: 3.0ms (21.9% 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

3.0MiB live, 3.0MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

6 calls:

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

simplify89.0ms (3.7%)

Memory

21.5MiB live, 21.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	456
1	165	450
2	471	450
3	1340	450
4	3287	450
5	6444	450
0	8183	402

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

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

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

rewrite134.0ms (5.5%)

Memory

45.3MiB live, 45.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	36
0	17	35
1	72	32
2	550	32
0	8206	28

Stop Event

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

Counts

4 → 111

Calls

Call 1

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

Outputs
#<batchref>
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eval24.0ms (1%)

Memory: 15.7MiB live, 15.7MiB allocated
Compiler: Compiled 3 819 to 441 computations (88.5% saved)

prune10.0ms (0.4%)

Memory

10.3MiB live, 10.3MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	195	6	201

Accuracy

100.0%

Counts

201 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	96.9%	(fma.f64 y y (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
✓	57.3%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (fma.f64 (.f64 y x) #s(literal 2 binary64) (.f64 y y)))
✓	55.9%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
✓	60.4%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y))
✓	60.9%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
✓	57.3%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Compiler

Compiled 93 to 54 computations (41.9% saved)

regimes10.0ms (0.4%)

Memory

5.9MiB live, 5.9MiB allocated

Counts

7 → 2

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
98.8%	2	`x`
100.0%	2	`y`
98.9%	2	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes9.0ms (0.4%)

Memory

5.5MiB live, 5.5MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
89.0%	2	`x`
63.2%	2	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`
87.6%	2	`y`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes3.0ms (0.1%)

Memory

2.0MiB live, 2.0MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
89.0%	2	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes2.0ms (0.1%)

Memory

1.7MiB live, 1.7MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
88.8%	2	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes5.0ms (0.2%)

Memory

4.3MiB live, 4.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
57.3%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`
57.3%	1	`y`
57.3%	1	`x`

Compiler

Compiled 15 to 13 computations (13.3% saved)

bsearch2.0ms (0.1%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
2.0ms	7.76951726027665e+151	4.773515681727775e+158

Samples

1.0ms

16×

valid

Compiler

Compiled 29 to 26 computations (10.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

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

exact: 0.0ms (0% of total)

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

bsearch15.0ms (0.6%)

Memory

4.5MiB live, 4.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	-1.0674704107050588e-125	-2.2073516525515535e-129

Samples

8.0ms

128×

valid

Compiler

Compiled 120 to 118 computations (1.7% saved)

Precisions

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

ival-mult: 3.0ms (63.5% of total)

ival-add: 1.0ms (21.2% of total)

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-1.0674704107050588e-125	-2.2073516525515535e-129

Compiler

Compiled 104 to 110 computations (-5.8% saved)

bsearch13.0ms (0.5%)

Memory

4.0MiB live, 4.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	-1.0674704107050588e-125	-2.2073516525515535e-129

Samples

7.0ms

112×

valid

Compiler

Compiled 80 to 94 computations (-17.5% saved)

Precisions

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

ival-mult: 3.0ms (71.2% of total)

ival-add: 1.0ms (23.7% of total)

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

exact: 0.0ms (0% of total)

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

simplify28.0ms (1.2%)

Memory

18.7MiB live, 18.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	169
1	35	169

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 y #s(literal 100000000000000004625108135904199474001226272395072688491888727201272553753779650923383419882203425131989662450489690590919397689516441796634752009109504 binary64)) (fma.f64 y y (.f64 (fma.f64 y #s(literal 2 binary64) x) x)) #s(approx (+ (+ ( x x) (* (* x 2) y)) (* y y)) (*.f64 y y)))
(if (<=.f64 x #s(literal -4001264621376699/381072821083495145432323880589986121307201921712032611188861933548019011086397170424842053596617672260721060927906081896416989218663120764928 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 x x)) #s(approx (+ (+ ( x x) (* (* x 2) y)) (* y y)) (fma.f64 (.f64 y x) #s(literal 2 binary64) (.f64 y y))))
(if (<=.f64 x #s(literal -4001264621376699/381072821083495145432323880589986121307201921712032611188861933548019011086397170424842053596617672260721060927906081896416989218663120764928 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 x x)) #s(approx (+ (+ ( x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y)))
(if (<=.f64 x #s(literal -7316598164803107/48777321098687378615337456715518223527321845979140174232174327494146433419058837814379782860367062049372295798771978482741374619988879457910784 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 x x)) #s(approx (+ (+ ( x x) (* (* x 2) y)) (* y y)) (*.f64 y y)))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Outputs
(if (<=.f64 y #s(literal 100000000000000004625108135904199474001226272395072688491888727201272553753779650923383419882203425131989662450489690590919397689516441796634752009109504 binary64)) (fma.f64 y y (.f64 (fma.f64 y #s(literal 2 binary64) x) x)) #s(approx (+ (+ ( x x) (* (* x 2) y)) (* y y)) (*.f64 y y)))
(if (<=.f64 x #s(literal -4001264621376699/381072821083495145432323880589986121307201921712032611188861933548019011086397170424842053596617672260721060927906081896416989218663120764928 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 x x)) #s(approx (+ (+ ( x x) (* (* x 2) y)) (* y y)) (fma.f64 (.f64 y x) #s(literal 2 binary64) (.f64 y y))))
(if (<=.f64 x #s(literal -4001264621376699/381072821083495145432323880589986121307201921712032611188861933548019011086397170424842053596617672260721060927906081896416989218663120764928 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 x x)) #s(approx (+ (+ ( x x) (* (* x 2) y)) (* y y)) (fma.f64 (.f64 x y) #s(literal 2 binary64) (.f64 y y))))
(if (<=.f64 x #s(literal -4001264621376699/381072821083495145432323880589986121307201921712032611188861933548019011086397170424842053596617672260721060927906081896416989218663120764928 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 x x)) #s(approx (+ (+ ( x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) x y) y)))
(if (<=.f64 x #s(literal -7316598164803107/48777321098687378615337456715518223527321845979140174232174327494146433419058837814379782860367062049372295798771978482741374619988879457910784 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (.f64 x x)) #s(approx (+ (+ ( x x) (* (* x 2) y)) (* y y)) (*.f64 y y)))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

soundness495.0ms (20.4%)

Memory

5.6MiB live, 5.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	588
1	166	546
2	470	546
3	1334	534
4	3275	534
5	6426	534
0	8157	486
0	20	109
0	29	109
1	102	93
2	857	93
0	8333	93
0	9	33
0	15	33
1	50	29
2	420	29
3	6357	29
0	8219	26

Stop Event

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

Compiler

Compiled 136 to 73 computations (46.3% saved)

preprocess68.0ms (2.8%)

Memory: 47.5MiB live, 47.5MiB allocated
Compiler: Compiled 216 to 110 computations (49.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample599.0ms (24.7%)

explain129.0ms (5.3%)

preprocess33.0ms (1.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize21.0ms (0.9%)

series8.0ms (0.3%)

simplify82.0ms (3.4%)

rewrite129.0ms (5.3%)

eval26.0ms (1.1%)

prune7.0ms (0.3%)

simplify4.0ms (0.2%)

localize37.0ms (1.5%)

series12.0ms (0.5%)

simplify96.0ms (4%)

rewrite170.0ms (7%)

eval87.0ms (3.6%)

prune30.0ms (1.3%)

simplify4.0ms (0.1%)

localize30.0ms (1.2%)

series6.0ms (0.2%)

simplify89.0ms (3.7%)

rewrite134.0ms (5.5%)

eval24.0ms (1%)

prune10.0ms (0.4%)

regimes10.0ms (0.4%)

regimes9.0ms (0.4%)

regimes3.0ms (0.1%)

regimes2.0ms (0.1%)

regimes5.0ms (0.2%)

bsearch2.0ms (0.1%)

bsearch15.0ms (0.6%)

bsearch1.0ms (0%)

bsearch13.0ms (0.5%)

simplify28.0ms (1.2%)

soundness495.0ms (20.4%)

preprocess68.0ms (2.8%)

end0.0ms (0%)

Profiling