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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample806.0ms (14.9%)

Memory

10.2MiB live, 885.5MiB allocated

Samples

595.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 321.0ms

ival-mult: 216.0ms (67.2% of total)

ival-add: 91.0ms (28.3% of total)

ival-true: 6.0ms (1.9% of total)

exact: 5.0ms (1.6% of total)

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

Bogosity

explain75.0ms (1.4%)

Memory

-48.5MiB live, 177.4MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`*.f64`	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`	*no**	20	0

Confusion

	Predicted +	Predicted -
+	20	0
-	0	236

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	20	0	0
-	0	0	236

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	236
1	20

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

24.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

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

ival-mult: 7.0ms (61.2% of total)

ival-add: 3.0ms (26.2% of total)

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

exact: 0.0ms (0% of total)

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

preprocess26.0ms (0.5%)

Memory

25.9MiB live, 25.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs y)

(negabs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	92.7%	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0.1%)

Memory

3.8MiB live, 3.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize42.0ms (0.8%)

Memory

-30.2MiB live, 8.7MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 #s(literal 1 binary64) (*.f64 y y))
accuracy	0	(*.f64 y y)
accuracy	4.701630162668436	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))

Samples

37.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-mult: 3.0ms (60.8% of total)

ival-add: 1.0ms (20.3% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

2.3MiB live, 2.3MiB allocated

Counts

3 → 48

Calls

Call 1

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

Inputs

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

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

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

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

Calls

6 calls:

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

simplify302.0ms (5.6%)

Memory

4.4MiB live, 83.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

Calls

Call 1

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

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

rewrite327.0ms (6.1%)

Memory

13.3MiB live, 168.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

3 → 368

Calls

Call 1

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

Outputs
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eval125.0ms (2.3%)

Memory: 12.5MiB live, 88.9MiB allocated
Compiler: Compiled 9 642 to 1 119 computations (88.4% saved)

prune49.0ms (0.9%)

Memory

-13.7MiB live, 31.0MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

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

Accuracy

100.0%

Counts

416 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(fma.f64 (*.f64 x y) y x)
▶	92.6%	(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
▶	92.5%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64)))))
▶	46.2%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
▶	51.5%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 68 to 56 computations (17.6% saved)

simplify7.0ms (0.1%)

Memory

13.7MiB live, 13.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize83.0ms (1.5%)

Memory

11.4MiB live, 88.1MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 y y #s(literal 1 binary64))
accuracy	0.900809831718999	(pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64))
accuracy	3.8554908080154986	(/.f64 x (pow.f64 (fma.f64 y y #s(literal 1 binary64)) #s(literal -1 binary64)))
accuracy	0	(fma.f64 y y #s(literal 1 binary64))
accuracy	0.078125	(/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64))))
accuracy	0.16796875	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x (fma.f64 y y #s(literal 1 binary64)))))
accuracy	4.701630162668436	(*.f64 x (fma.f64 y y #s(literal 1 binary64)))
accuracy	0	(*.f64 y y)
accuracy	4.701630162668436	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
accuracy	29.958518180256657	#s(approx (+ 1 (* y y)) (*.f64 y y))
accuracy	4.701630162668436	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))
accuracy	31.35954984079445	#s(approx (+ 1 (* y y)) #s(literal 1 binary64))
accuracy	0	(*.f64 x y)
accuracy	0.07421875	(fma.f64 (*.f64 x y) y x)

Samples

69.0ms

256×

valid

Compiler

Compiled 105 to 18 computations (82.9% saved)

Precisions

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

ival-mult: 8.0ms (42.3% of total)

ival-div: 4.0ms (21.2% of total)

ival-add: 4.0ms (21.2% of total)

ival-pow: 2.0ms (10.6% of total)

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

exact: 0.0ms (0% of total)

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

series102.0ms (1.9%)

Memory

-19.8MiB live, 18.6MiB allocated

Counts

13 → 252

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
88.0ms	y	@	0	((+ (* (* x y) y) x) (* x y) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* y y) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (/ 1 (* x (+ (* y y) 1))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1))
2.0ms	x	@	-inf	((+ (* (* x y) y) x) (* x y) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* y y) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (/ 1 (* x (+ (* y y) 1))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1))
2.0ms	y	@	-inf	((+ (* (* x y) y) x) (* x y) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* y y) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (/ 1 (* x (+ (* y y) 1))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1))
1.0ms	y	@	inf	((+ (* (* x y) y) x) (* x y) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* y y) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (/ 1 (* x (+ (* y y) 1))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1))
1.0ms	x	@	inf	((+ (* (* x y) y) x) (* x y) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* x (+ 1 (* y y))) (+ 1 (* y y)) (* y y) (/ 1 (/ 1 (* x (+ (* y y) 1)))) (/ 1 (* x (+ (* y y) 1))) (* x (+ (* y y) 1)) (+ (* y y) 1) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1))

simplify241.0ms (4.5%)

Memory

5.4MiB live, 245.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 246

Calls

Call 1

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

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

rewrite618.0ms (11.5%)

Memory

7.4MiB live, 325.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

13 → 1 337

Calls

Call 1

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

Outputs
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eval236.0ms (4.4%)

Memory: -4.2MiB live, 540.6MiB allocated
Compiler: Compiled 33 002 to 2 813 computations (91.5% saved)

prune34.0ms (0.6%)

Memory

23.4MiB live, 107.7MiB allocated

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	1 722	4	1 726
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	1 724	7	1 731

Accuracy

100.0%

Counts

1 731 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (*.f64 x y) y x)
▶	46.9%	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y) y)))
▶	46.2%	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
▶	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y x) y x)))
▶	46.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))))
✓	46.2%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
✓	51.5%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 58 to 46 computations (20.7% saved)

simplify172.0ms (3.2%)

Memory

-22.2MiB live, 111.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	201
0	39	193
1	60	193
2	102	193
3	166	193
4	260	193
5	479	193
6	737	193
7	920	193
8	1196	193
9	1534	193
10	2405	193
11	3016	193
12	4260	193
13	5424	193
14	6330	193
15	6679	193
16	6960	193
17	7216	193
0	8194	185

Stop Event

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

Calls

Call 1

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

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

localize57.0ms (1.1%)

Memory

0.9MiB live, 76.3MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.1015625	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y) y)
accuracy	0.959403581718999	(/.f64 #s(literal 1 binary64) (*.f64 y y))
accuracy	3.8554908080154986	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y) y)))
accuracy	31.012383962982646	#s(approx (pow (+ (* y y) 1) -1) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 y y))) y) y))
accuracy	0	(*.f64 y y)
accuracy	0.959403581718999	(/.f64 #s(literal 1 binary64) (*.f64 y y))
accuracy	3.8554908080154986	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
accuracy	29.958707807754234	#s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y)))
accuracy	0	(*.f64 y x)
accuracy	0.07421875	(fma.f64 (*.f64 y x) y x)
accuracy	0.078125	(/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y x) y x))
accuracy	0.16796875	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y x) y x)))
accuracy	0.078125	(/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y))))
accuracy	0.16796875	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))))
accuracy	4.701630162668436	(.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))
accuracy	29.958518180256657	#s(approx (+ (* y y) 1) (*.f64 y y))

Samples

39.0ms

256×

valid

Compiler

Compiled 154 to 22 computations (85.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 26.0ms

ival-div: 13.0ms (49.7% of total)

ival-mult: 6.0ms (23% of total)

ival-add: 2.0ms (7.7% of total)

ival-pow: 2.0ms (7.7% of total)

ival-sub: 1.0ms (3.8% of total)

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

exact: 0.0ms (0% of total)

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

series23.0ms (0.4%)

Memory

-5.9MiB live, 31.6MiB allocated

Counts

16 → 300

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	x	@	-inf	((/ 1 (/ 1 (* x (+ (* y y) 1)))) (* x (+ (* y y) 1)) (+ (* y y) 1) (* y y) (/ 1 (/ 1 (+ (* (* y x) y) x))) (/ 1 (+ (* (* y x) y) x)) (+ (* (* y x) y) x) (* y x) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ 1 (* y y)) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ (/ (- 1 (/ 1 (* y y))) y) y) (/ (- 1 (/ 1 (* y y))) y) (/ 1 (* x (+ (* y y) 1))))
3.0ms	y	@	-inf	((/ 1 (/ 1 (* x (+ (* y y) 1)))) (* x (+ (* y y) 1)) (+ (* y y) 1) (* y y) (/ 1 (/ 1 (+ (* (* y x) y) x))) (/ 1 (+ (* (* y x) y) x)) (+ (* (* y x) y) x) (* y x) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ 1 (* y y)) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ (/ (- 1 (/ 1 (* y y))) y) y) (/ (- 1 (/ 1 (* y y))) y) (/ 1 (* x (+ (* y y) 1))))
1.0ms	y	@	inf	((/ 1 (/ 1 (* x (+ (* y y) 1)))) (* x (+ (* y y) 1)) (+ (* y y) 1) (* y y) (/ 1 (/ 1 (+ (* (* y x) y) x))) (/ 1 (+ (* (* y x) y) x)) (+ (* (* y x) y) x) (* y x) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ 1 (* y y)) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ (/ (- 1 (/ 1 (* y y))) y) y) (/ (- 1 (/ 1 (* y y))) y) (/ 1 (* x (+ (* y y) 1))))
1.0ms	y	@	0	((/ 1 (/ 1 (* x (+ (* y y) 1)))) (* x (+ (* y y) 1)) (+ (* y y) 1) (* y y) (/ 1 (/ 1 (+ (* (* y x) y) x))) (/ 1 (+ (* (* y x) y) x)) (+ (* (* y x) y) x) (* y x) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ 1 (* y y)) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ (/ (- 1 (/ 1 (* y y))) y) y) (/ (- 1 (/ 1 (* y y))) y) (/ 1 (* x (+ (* y y) 1))))
1.0ms	x	@	inf	((/ 1 (/ 1 (* x (+ (* y y) 1)))) (* x (+ (* y y) 1)) (+ (* y y) 1) (* y y) (/ 1 (/ 1 (+ (* (* y x) y) x))) (/ 1 (+ (* (* y x) y) x)) (+ (* (* y x) y) x) (* y x) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ 1 (* y y)) (/ x (pow (+ (* y y) 1) -1)) (pow (+ (* y y) 1) -1) (/ (/ (- 1 (/ 1 (* y y))) y) y) (/ (- 1 (/ 1 (* y y))) y) (/ 1 (* x (+ (* y y) 1))))

simplify131.0ms (2.4%)

Memory

-7.1MiB live, 146.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	2276
1	207	2268
2	517	2252
3	1791	2204
4	4533	2200
0	8140	1999

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 294

Calls

Call 1

Inputs
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
1
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(+ 1 (pow y 2))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(/ 1 x)
(+ (* -1 (/ (pow y 2) x)) (/ 1 x))
(+ (* (pow y 2) (- (/ (pow y 2) x) (/ 1 x))) (/ 1 x))
(+ (* (pow y 2) (- (* (pow y 2) (+ (* -1 (/ (pow y 2) x)) (/ 1 x))) (/ 1 x))) (/ 1 x))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(* x y)
(* x y)
(* x y)
(* x y)
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
1
(+ 1 (* -1 (pow y 2)))
(+ 1 (* (pow y 2) (- (pow y 2) 1)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
1
(+ 1 (* -1 (pow y 2)))
(+ 1 (* (pow y 2) (- (pow y 2) 1)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))
(/ -1 (pow y 4))
(/ (- (pow y 2) 1) (pow y 4))
(/ (- (pow y 2) 1) (pow y 4))
(/ (- (pow y 2) 1) (pow y 4))
(/ -1 (pow y 3))
(/ (- (pow y 2) 1) (pow y 3))
(/ (- (pow y 2) 1) (pow y 3))
(/ (- (pow y 2) 1) (pow y 3))
(/ 1 x)
(+ (* -1 (/ (pow y 2) x)) (/ 1 x))
(+ (* (pow y 2) (- (/ (pow y 2) x) (/ 1 x))) (/ 1 x))
(+ (* (pow y 2) (- (* (pow y 2) (+ (* -1 (/ (pow y 2) x)) (/ 1 x))) (/ 1 x))) (/ 1 x))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (* x (pow y 2)))
(/ (- (/ 1 x) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6))))) (pow y 2))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ 1 y)
(/ (- 1 (/ 1 (pow y 2))) y)
(/ (- 1 (/ 1 (pow y 2))) y)
(/ (- 1 (/ 1 (pow y 2))) y)
(/ 1 (* x (pow y 2)))
(/ (- (/ 1 x) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6))))) (pow y 2))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(pow y 2)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (* x (pow y 2)))
(/ (- (/ 1 x) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6))))) (pow y 2))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ 1 y)
(* -1 (/ (- (/ 1 (pow y 2)) 1) y))
(* -1 (/ (- (/ 1 (pow y 2)) 1) y))
(* -1 (/ (- (/ 1 (pow y 2)) 1) y))
(/ 1 (* x (pow y 2)))
(/ (- (/ 1 x) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (/ 1 (* x (pow y 2)))) (pow y 2))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6))))) (pow y 2))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(/ -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* -1 (* x (- (* -1 (pow y 2)) 1)))
(* x y)
(* x y)
(* x y)
(* x y)
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))
(/ 1 (* x (+ 1 (pow y 2))))

Outputs
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(+ 1 (pow y 2))
(fma.f64 y y #s(literal 1 binary64))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(+ (* -1 (/ (pow y 2) x)) (/ 1 x))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (neg.f64 x))
(+ (* (pow y 2) (- (/ (pow y 2) x) (/ 1 x))) (/ 1 x))
(fma.f64 (/.f64 y x) (-.f64 (pow.f64 y #s(literal 3 binary64)) y) (/.f64 #s(literal 1 binary64) x))
(+ (* (pow y 2) (- (* (pow y 2) (+ (* -1 (/ (pow y 2) x)) (/ 1 x))) (/ 1 x))) (/ 1 x))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1 binary64)) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (neg.f64 x)))
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow y 2)))
(-.f64 #s(literal 1 binary64) (*.f64 y y))
(+ 1 (* (pow y 2) (- (pow y 2) 1)))
(fma.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) y) y #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))
(.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 y y)))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
x
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(+ x (* x (pow y 2)))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* -1 (pow y 2)))
(-.f64 #s(literal 1 binary64) (*.f64 y y))
(+ 1 (* (pow y 2) (- (pow y 2) 1)))
(fma.f64 (-.f64 (pow.f64 y #s(literal 3 binary64)) y) y #s(literal 1 binary64))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))
(.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 y y)))
(/ -1 (pow y 4))
(/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 4 binary64)))
(/ (- (pow y 2) 1) (pow y 4))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- (pow y 2) 1) (pow y 4))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- (pow y 2) 1) (pow y 4))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ -1 (pow y 3))
(/.f64 #s(literal -1 binary64) (pow.f64 y #s(literal 3 binary64)))
(/ (- (pow y 2) 1) (pow y 3))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(/ (- (pow y 2) 1) (pow y 3))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(/ (- (pow y 2) 1) (pow y 3))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 3 binary64)))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(+ (* -1 (/ (pow y 2) x)) (/ 1 x))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (neg.f64 x))
(+ (* (pow y 2) (- (/ (pow y 2) x) (/ 1 x))) (/ 1 x))
(fma.f64 (/.f64 y x) (-.f64 (pow.f64 y #s(literal 3 binary64)) y) (/.f64 #s(literal 1 binary64) x))
(+ (* (pow y 2) (- (* (pow y 2) (+ (* -1 (/ (pow y 2) x)) (/ 1 x))) (/ 1 x))) (/ 1 x))
(*.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1 binary64)) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (neg.f64 x)))
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(* (pow y 2) (+ 1 (/ 1 (pow y 2))))
(fma.f64 y y #s(literal 1 binary64))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 (* x (pow y 2)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y)) x)
(/ (- (/ 1 x) (/ 1 (* x (pow y 2)))) (pow y 2))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 y y))) (/.f64 #s(literal 1 binary64) x)) (*.f64 y y))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (/ 1 (* x (pow y 2)))) (pow y 2))
(/.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 y y))) (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 y #s(literal 4 binary64)))) (.f64 y y))
(/ (- (+ (/ 1 x) (/ 1 (* x (pow y 4)))) (+ (/ 1 (* x (pow y 2))) (/ 1 (* x (pow y 6))))) (pow y 2))
(/.f64 (-.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 y y))) (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 y #s(literal 4 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 y #s(literal 6 binary64)))) (.f64 y y))
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x y)
(*.f64 y x)
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))) (*.f64 y y))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal -1 binary64)) (pow.f64 y #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 6 binary64)))) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(* x (pow y 2))
(.f64 (.f64 y y) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
(*.f64 (fma.f64 y y #s(literal 1 binary64)) x)
(* (pow y 2) (+ x (/ x (pow y 2))))
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rewrite129.0ms (2.4%)

Memory

31.2MiB live, 189.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	171
0	39	163
1	159	149
2	956	143
0	8752	135

Stop Event

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

Counts

16 → 710

Calls

Call 1

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

Outputs
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eval162.0ms (3%)

Memory: -19.0MiB live, 249.9MiB allocated
Compiler: Compiled 17 423 to 2 730 computations (84.3% saved)

prune18.0ms (0.3%)

Memory

22.9MiB live, 62.4MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	1 098	1	1 099
Fresh	0	0	0
Picked	1	3	4
Done	0	3	3
Total	1 099	7	1 106

Accuracy

100.0%

Counts

1 106 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (*.f64 x y) y x)
▶	47.5%	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)))
✓	46.2%	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
✓	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y x) y x)))
✓	46.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))))
✓	46.2%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
✓	51.5%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 53 to 44 computations (17% saved)

simplify361.0ms (6.7%)

Memory

-6.5MiB live, 152.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

localize105.0ms (1.9%)

Memory

-10.3MiB live, 73.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.1015625	(/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)
accuracy	3.8554908080154986	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)))
accuracy	31.012383962982646	#s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y))
accuracy	31.123688752960298	#s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y))

Samples

97.0ms

256×

valid

Compiler

Compiled 44 to 15 computations (65.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

ival-div: 46.0ms (85.5% of total)

ival-mult: 2.0ms (3.7% of total)

ival-pow: 2.0ms (3.7% of total)

ival-sub: 1.0ms (1.9% of total)

ival-add: 1.0ms (1.9% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated

Counts

4 → 60

Calls

Call 1

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

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

Calls

6 calls:

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

simplify218.0ms (4%)

Memory

26.7MiB live, 177.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 59

Calls

Call 1

Inputs
x
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
(+ x (* x (pow y 2)))
1
(+ 1 (* -1 (pow y 2)))
(+ 1 (* (pow y 2) (- (pow y 2) 1)))
(+ 1 (* (pow y 2) (- (* (pow y 2) (+ 1 (* -1 (pow y 2)))) 1)))
(/ -1 (pow y 4))
(/ (- (pow y 2) 1) (pow y 4))
(/ (- (pow y 2) 1) (pow y 4))
(/ (- (pow y 2) 1) (pow y 4))
(/ -1 (pow y 3))
(/ (- (pow y 2) 1) (pow y 3))
(/ (- (pow y 2) 1) (pow y 3))
(/ (- (pow y 2) 1) (pow y 3))
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ 1 y)
(/ (- 1 (/ 1 (pow y 2))) y)
(/ (- 1 (/ 1 (pow y 2))) y)
(/ (- 1 (/ 1 (pow y 2))) y)
(* x (pow y 2))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(* (pow y 2) (+ x (/ x (pow y 2))))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (/ 1 (pow y 2))) (pow y 2))
(/ (- (+ 1 (/ 1 (pow y 4))) (+ (/ 1 (pow y 2)) (/ 1 (pow y 6)))) (pow y 2))
(/ 1 (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ (- 1 (/ 1 (pow y 2))) (pow y 2))
(/ 1 y)
(* -1 (/ (- (/ 1 (pow y 2)) 1) y))
(* -1 (/ (- (/ 1 (pow y 2)) 1) y))
(* -1 (/ (- (/ 1 (pow y 2)) 1) y))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))
(* x (+ 1 (pow y 2)))

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

rewrite145.0ms (2.7%)

Memory

1.6MiB live, 161.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

4 → 73

Calls

Call 1

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

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

eval15.0ms (0.3%)

Memory: -3.6MiB live, 32.6MiB allocated
Compiler: Compiled 1 505 to 276 computations (81.7% saved)

prune8.0ms (0.2%)

Memory

-19.5MiB live, 18.0MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	132	7	139

Accuracy

100.0%

Counts

139 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (*.f64 x y) y x)
✓	47.5%	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(approx (/ (- 1 (/ 1 (* y y))) y) (/.f64 #s(literal 1 binary64) y)) y)))
✓	46.2%	(/.f64 x #s(approx (pow (+ (* y y) 1) -1) (/.f64 #s(literal 1 binary64) (*.f64 y y))))
✓	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 y x) y x)))
✓	46.2%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x #s(approx (+ ( y y) 1) (*.f64 y y)))))
✓	46.2%	(.f64 x #s(approx (+ 1 ( y y)) (*.f64 y y)))
✓	51.5%	(.f64 x #s(approx (+ 1 ( y y)) #s(literal 1 binary64)))

Compiler

Compiled 145 to 84 computations (42.1% saved)

regimes24.0ms (0.4%)

Memory

14.7MiB live, 61.2MiB allocated

Counts

11 → 1

Calls

Call 1

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

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

Calls

5 calls:

8.0ms	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
4.0ms	y
4.0ms	x
4.0ms	(*.f64 y y)
3.0ms	(+.f64 #s(literal 1 binary64) (*.f64 y y))

Results

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

Compiler

Compiled 17 to 18 computations (-5.9% saved)

regimes96.0ms (1.8%)

Memory

-24.4MiB live, 14.2MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

5 calls:

90.0ms	x
2.0ms	(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))
2.0ms	y
1.0ms	(*.f64 y y)
1.0ms	(+.f64 #s(literal 1 binary64) (*.f64 y y))

Results

Accuracy	Segments	Branch
58.1%	4	`x`
92.6%	2	`y`
73.2%	2	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`
92.6%	2	`(+.f64 #s(literal 1 binary64) (*.f64 y y))`
92.6%	2	`(*.f64 y y)`

Compiler

Compiled 17 to 18 computations (-5.9% saved)

regimes7.0ms (0.1%)

Memory

12.5MiB live, 12.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
51.5%	1	`x`
51.5%	1	`(.f64 x (+.f64 #s(literal 1 binary64) (.f64 y y)))`
51.5%	1	`y`
51.5%	1	`(+.f64 #s(literal 1 binary64) (*.f64 y y))`
51.5%	1	`(*.f64 y y)`

Compiler

Compiled 17 to 18 computations (-5.9% saved)

bsearch13.0ms (0.2%)

Memory

22.7MiB live, 22.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	1.4742898065038751e-16	199069986526885.13

Samples

6.0ms

176×

valid

Compiler

Compiled 98 to 132 computations (-34.7% saved)

Precisions

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

ival-add: 1.0ms (43.6% of total)

ival-mult: 1.0ms (43.6% of total)

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

exact: 0.0ms (0% of total)

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

simplify29.0ms (0.5%)

Memory

-31.9MiB live, 44.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	41
1	20	41

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

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

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

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

soundness455.0ms (8.4%)

Memory

11.6MiB live, 212.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Compiler

Compiled 50 to 32 computations (36% saved)

preprocess145.0ms (2.7%)

Memory

-7.1MiB live, 69.7MiB allocated

Remove

(negabs x)

(abs y)

Compiler

Compiled 152 to 94 computations (38.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

start0.0ms (0%)

analyze0.0ms (0%)

sample806.0ms (14.9%)

explain75.0ms (1.4%)

preprocess26.0ms (0.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize42.0ms (0.8%)

series5.0ms (0.1%)

simplify302.0ms (5.6%)

rewrite327.0ms (6.1%)

eval125.0ms (2.3%)

prune49.0ms (0.9%)

simplify7.0ms (0.1%)

localize83.0ms (1.5%)

series102.0ms (1.9%)

simplify241.0ms (4.5%)

rewrite618.0ms (11.5%)

eval236.0ms (4.4%)

prune34.0ms (0.6%)

simplify172.0ms (3.2%)

localize57.0ms (1.1%)

series23.0ms (0.4%)

simplify131.0ms (2.4%)

rewrite129.0ms (2.4%)

eval162.0ms (3%)

prune18.0ms (0.3%)

simplify361.0ms (6.7%)

localize105.0ms (1.9%)

series5.0ms (0.1%)

simplify218.0ms (4%)

rewrite145.0ms (2.7%)

eval15.0ms (0.3%)

prune8.0ms (0.2%)

regimes24.0ms (0.4%)

regimes96.0ms (1.8%)

regimes7.0ms (0.1%)

bsearch13.0ms (0.2%)

simplify29.0ms (0.5%)

soundness455.0ms (8.4%)

preprocess145.0ms (2.7%)

end0.0ms (0%)

Profiling

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