Metrics for Examples.Basics.BasicTests:f2 from sbv-4.4

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample528.0ms (13%)

Memory

35.3MiB live, 1 175.3MiB allocated

Samples

331.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 171.0ms

ival-mult: 124.0ms (72.3% of total)

ival-sub: 37.0ms (21.6% of total)

ival-true: 6.0ms (3.5% of total)

ival-assert: 3.0ms (1.8% of total)

Bogosity

explain72.0ms (1.8%)

Memory

-0.4MiB live, 129.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
12	-	-	`(-.f64 (.f64 x x) (.f64 y y))`
0	-	-	`y`
0	-	-	`(*.f64 y y)`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (.f64 x x) (.f64 y y))`	nan-rescue	12	0
↳	`(*.f64 x x)`	overflow	66
↳	`(*.f64 y y)`	overflow	56

Confusion

	Predicted +	Predicted -
+	12	0
-	0	244

Precision

1.0

Recall

1.0

Confusion?

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

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	244
1	12

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

22.0ms

512×

valid

Compiler

Compiled 41 to 19 computations (53.7% saved)

Precisions

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

ival-mult: 7.0ms (69.1% of total)

ival-sub: 2.0ms (19.8% of total)

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

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

preprocess714.0ms (17.5%)

Memory

-22.5MiB live, 335.1MiB allocated

Algorithm

1×	egg-herbie

Rules

24 584×	`lower-fma.f64`
24 584×	`lower-fma.f32`
5 200×	`lower-+.f64`
5 200×	`lower-+.f32`
3 934×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	38
1	51	35
2	144	35
3	366	35
4	892	35
5	1223	35
6	1754	35
7	2340	35
8	4152	35
9	4727	35
10	4840	35
11	4954	35
12	5034	35
13	5034	35
14	6415	35
15	7393	35
16	7877	35
17	7893	35
18	7893	35
0	5	7
0	8	7
1	16	7
2	27	7
3	53	7
4	114	7
5	315	7
6	567	7
7	1238	7
8	2495	7
9	4124	7
10	4997	7
11	5366	7
12	5596	7
13	5710	7
14	5710	7
15	6670	7
16	6830	7
17	7150	7
18	7150	7
19	7550	7
20	7710	7
21	7790	7
22	7790	7
23	7790	7
0	10268	7

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (.f64 y y))

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

Symmetry

(abs y)

(abs x)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	95.3%	(-.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify332.0ms (8.2%)

Memory

41.1MiB live, 227.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 y y)
cost-diff	0	(*.f64 x x)
cost-diff	0	(-.f64 (.f64 x x) (.f64 y y))

Rules

24 584×	`lower-fma.f64`
24 584×	`lower-fma.f32`
5 200×	`lower-+.f64`
5 200×	`lower-+.f32`
3 934×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	16	15
2	27	15
3	53	15
4	114	15
5	315	15
6	567	15
7	1238	15
8	2495	15
9	4124	15
10	4997	15
11	5366	15
12	5596	15
13	5710	15
14	5710	15
15	6670	15
16	6830	15
17	7150	15
18	7150	15
19	7550	15
20	7710	15
21	7790	15
22	7790	15
23	7790	15
0	10268	15

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (.f64 y y))
(*.f64 x x)
x
(*.f64 y y)
y

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

localize87.0ms (2.1%)

Memory

-18.5MiB live, 20.6MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	2.546868807490618	(-.f64 (.f64 x x) (.f64 y y))

Samples

10.0ms

256×

valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

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

ival-mult: 3.0ms (65.7% of total)

ival-sub: 1.0ms (21.9% of total)

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

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

series4.0ms (0.1%)

Memory

4.4MiB live, 4.4MiB allocated

Counts

3 → 48

Calls

Call 1

Inputs
#s(alt (-.f64 (.f64 x x) (.f64 y y)) (patch (-.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (.f64 y y) (patch (.f64 y y) #<representation binary64>) () ())

Inputs

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

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

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

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

Calls

6 calls:

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

simplify257.0ms (6.3%)

Memory

15.5MiB live, 175.3MiB allocated

Algorithm

1×	egg-herbie

Rules

12 540×	`lower-fma.f64`
12 540×	`lower-fma.f32`
3 658×	`lower-*.f64`
3 658×	`lower-*.f32`
1 136×	`lower-neg.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	219
1	39	219
2	113	219
3	469	219
4	1679	219
5	2846	219
6	5006	219
0	8448	219

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

Outputs
(pow x 2)
(*.f64 x x)
(+ (* -1 (pow y 2)) (pow x 2))
(*.f64 (-.f64 x y) (+.f64 y x))
(+ (* -1 (pow y 2)) (pow x 2))
(*.f64 (-.f64 x y) (+.f64 y x))
(+ (* -1 (pow y 2)) (pow x 2))
(*.f64 (-.f64 x y) (+.f64 y x))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(*.f64 (-.f64 x y) (+.f64 y x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(*.f64 (-.f64 x y) (+.f64 y x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(*.f64 (-.f64 x y) (+.f64 y x))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(*.f64 (-.f64 x y) (+.f64 y x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(*.f64 (-.f64 x y) (+.f64 y x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(*.f64 (-.f64 x y) (+.f64 y x))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(- (pow x 2) (pow y 2))
(*.f64 (-.f64 x y) (+.f64 y x))
(- (pow x 2) (pow y 2))
(*.f64 (-.f64 x y) (+.f64 y x))
(- (pow x 2) (pow y 2))
(*.f64 (-.f64 x y) (+.f64 y x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(*.f64 (-.f64 x y) (+.f64 y x))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(*.f64 (-.f64 x y) (+.f64 y x))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(*.f64 (-.f64 x y) (+.f64 y x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(*.f64 (-.f64 x y) (+.f64 y x))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(*.f64 (-.f64 x y) (+.f64 y x))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(*.f64 (-.f64 x y) (+.f64 y x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite214.0ms (5.3%)

Memory

-27.6MiB live, 208.0MiB allocated

Rules

8 026×	`lower-fma.f64`
8 026×	`lower-fma.f32`
4 450×	`lower-/.f64`
4 450×	`lower-/.f32`
3 184×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	32	13
2	216	13
3	1967	13
0	8778	13

Stop Event

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

Counts

3 → 252

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (.f64 y y))
(*.f64 x x)
(*.f64 y y)

Outputs
#<batchref>
#<batchref>
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eval54.0ms (1.3%)

Memory: 15.5MiB live, 52.1MiB allocated
Compiler: Compiled 8 583 to 756 computations (91.2% saved)

prune5.0ms (0.1%)

Memory

15.0MiB live, 15.0MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	297	3	300
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	298	3	301

Accuracy

100.0%

Counts

301 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 (-.f64 x y) (+.f64 y x))
▶	48.2%	#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))
▶	57.4%	#s(approx (- (* x x) (* y y)) (*.f64 x x))

Compiler

Compiled 16 to 14 computations (12.5% saved)

simplify283.0ms (7%)

Memory

-10.2MiB live, 242.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(+.f64 y x)
cost-diff	0	(-.f64 x y)
cost-diff	0	(*.f64 (-.f64 x y) (+.f64 y x))
cost-diff	0	(neg.f64 y)
cost-diff	0	(*.f64 (neg.f64 y) y)
cost-diff	0	#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (- (* x x) (* y y)) (*.f64 x x))

Rules

31 184×	`lower-fma.f64`
31 184×	`lower-fma.f32`
7 084×	`lower-+.f32`
7 082×	`lower-+.f64`
3 784×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	49
0	19	49
1	37	49
2	64	49
3	144	49
4	285	49
5	590	49
6	1490	49
7	2883	49
8	3991	49
9	4558	49
10	4797	49
11	4927	49
12	4949	49
13	4949	49
14	4949	49
0	8683	49

Stop Event

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

Calls

Call 1

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

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

localize30.0ms (0.7%)

Memory

1.2MiB live, 40.1MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x y)
accuracy	0	(+.f64 y x)
accuracy	0	(*.f64 (-.f64 x y) (+.f64 y x))
accuracy	0	(*.f64 (neg.f64 y) y)
accuracy	0	(neg.f64 y)
accuracy	33.1363227721594	#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))
accuracy	0	(*.f64 x x)
accuracy	27.295026130899345	#s(approx (- (* x x) (* y y)) (*.f64 x x))

Samples

23.0ms

256×

valid

Compiler

Compiled 42 to 12 computations (71.4% saved)

Precisions

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

ival-mult: 6.0ms (53.4% of total)

ival-sub: 2.0ms (17.8% of total)

ival-add: 1.0ms (8.9% of total)

ival-neg: 1.0ms (8.9% of total)

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

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

series33.0ms (0.8%)

Memory

-21.9MiB live, 16.6MiB allocated

Counts

8 → 156

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
26.0ms	y	@	inf	((- (* x x) (* y y)) (* x x) (- (* x x) (* y y)) (* (neg y) y) (neg y) (* (- x y) (+ y x)) (- x y) (+ y x))
1.0ms	x	@	-inf	((- (* x x) (* y y)) (* x x) (- (* x x) (* y y)) (* (neg y) y) (neg y) (* (- x y) (+ y x)) (- x y) (+ y x))
1.0ms	y	@	0	((- (* x x) (* y y)) (* x x) (- (* x x) (* y y)) (* (neg y) y) (neg y) (* (- x y) (+ y x)) (- x y) (+ y x))
1.0ms	y	@	-inf	((- (* x x) (* y y)) (* x x) (- (* x x) (* y y)) (* (neg y) y) (neg y) (* (- x y) (+ y x)) (- x y) (+ y x))
1.0ms	x	@	inf	((- (* x x) (* y y)) (* x x) (- (* x x) (* y y)) (* (neg y) y) (neg y) (* (- x y) (+ y x)) (- x y) (+ y x))

simplify161.0ms (4%)

Memory

23.0MiB live, 216.0MiB allocated

Algorithm

1×	egg-herbie

Rules

15 540×	`lower-fma.f64`
15 540×	`lower-fma.f32`
2 570×	`lower--.f64`
2 570×	`lower--.f32`
2 510×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	651
1	281	651
2	829	651
3	3560	651
0	8744	651

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 147

Calls

Call 1

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

Outputs
(pow x 2)
(*.f64 x x)
(+ (* -1 (pow y 2)) (pow x 2))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(+ (* -1 (pow y 2)) (pow x 2))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(+ (* -1 (pow y 2)) (pow x 2))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(pow x 2)
(*.f64 x x)
(+ (* -1 (pow y 2)) (pow x 2))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(+ (* -1 (pow y 2)) (pow x 2))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(+ (* -1 (pow y 2)) (pow x 2))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(pow x 2)
(*.f64 x x)
(+ (* y (+ x (* -1 x))) (pow x 2))
(*.f64 x x)
(+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2))
(fma.f64 (neg.f64 y) y (*.f64 x x))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
x
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (+ (* -1 (/ x y)) (/ x y)) 1))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* -1 y)
(neg.f64 y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* y (- (/ x y) 1))
(-.f64 x y)
(* y (- (/ x y) 1))
(-.f64 x y)
y
(* y (+ 1 (/ x y)))
(+.f64 y x)
(* y (+ 1 (/ x y)))
(+.f64 y x)
(* y (+ 1 (/ x y)))
(+.f64 y x)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 y)
(neg.f64 y)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (* -1 (/ (+ x (* -1 x)) y)) 1))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 x y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 x y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(-.f64 x y)
y
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 y x)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 y x)
(* -1 (* y (- (* -1 (/ x y)) 1)))
(+.f64 y x)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(- (pow x 2) (pow y 2))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(- (pow x 2) (pow y 2))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(- (pow x 2) (pow y 2))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(- (pow x 2) (pow y 2))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(- (pow x 2) (pow y 2))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(- (pow x 2) (pow y 2))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* -1 (pow y 2))
(*.f64 (neg.f64 y) y)
(+ (* -1 (pow y 2)) (* x (+ y (* -1 y))))
(*.f64 (neg.f64 y) y)
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* -1 y)
(neg.f64 y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
y
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(+ x y)
(+.f64 y x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x))))
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
x
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
(* x (+ 1 (* -1 (/ y x))))
(-.f64 x y)
x
(* x (+ 1 (/ y x)))
(+.f64 y x)
(* x (+ 1 (/ y x)))
(+.f64 y x)
(* x (+ 1 (/ y x)))
(+.f64 y x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x))))
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
(fma.f64 (neg.f64 y) y (*.f64 x x))
x
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
(* -1 (* x (- (/ y x) 1)))
(-.f64 x y)
x
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 y x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 y x)
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+.f64 y x)

rewrite575.0ms (14.1%)

Memory

-6.7MiB live, 197.3MiB allocated

Rules

4 964×	`lower-fma.f64`
4 964×	`lower-fma.f32`
3 312×	`lower-*.f32`
3 306×	`lower-*.f64`
2 364×	`lower-/.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	45
0	19	45
1	70	45
2	511	45
3	6763	36
0	9290	36

Stop Event

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

Counts

8 → 733

Calls

Call 1

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

Outputs
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eval188.0ms (4.6%)

Memory: 14.1MiB live, 228.4MiB allocated
Compiler: Compiled 17 707 to 1 561 computations (91.2% saved)

prune18.0ms (0.4%)

Memory

25.7MiB live, 64.0MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	880	0	880
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	880	3	883

Accuracy

100.0%

Counts

883 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (-.f64 x y) (+.f64 y x))
✓	48.2%	#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))
✓	57.4%	#s(approx (- (* x x) (* y y)) (*.f64 x x))

Compiler

Compiled 39 to 26 computations (33.3% saved)

regimes15.0ms (0.4%)

Memory

-18.8MiB live, 32.5MiB allocated

Counts

4 → 1

Calls

Call 1

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

Outputs
(*.f64 (-.f64 x y) (+.f64 y x))

Calls

5 calls:

7.0ms	(*.f64 y y)
2.0ms	x
2.0ms	y
2.0ms	(-.f64 (.f64 x x) (.f64 y y))
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(-.f64 (.f64 x x) (.f64 y y))`
100.0%	1	`(*.f64 x x)`
100.0%	1	`(*.f64 y y)`

Compiler

Compiled 15 to 15 computations (0% saved)

regimes9.0ms (0.2%)

Memory

-14.6MiB live, 24.2MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (- (* x x) (* y y)) (*.f64 x x))
#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))

Outputs
#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))
#s(approx (- (* x x) (* y y)) (*.f64 x x))

Calls

5 calls:

1.0ms	y
1.0ms	x
1.0ms	(-.f64 (.f64 x x) (.f64 y y))
1.0ms	(*.f64 y y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
82.3%	2	`x`
76.9%	2	`y`
98.3%	2	`(-.f64 (.f64 x x) (.f64 y y))`
82.3%	2	`(*.f64 x x)`
76.9%	2	`(*.f64 y y)`

Compiler

Compiled 15 to 15 computations (0% saved)

regimes6.0ms (0.2%)

Memory

23.2MiB live, 23.2MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (* x x) (* y y)) (*.f64 x x))

Outputs
#s(approx (- (* x x) (* y y)) (*.f64 x x))

Calls

5 calls:

1.0ms	y
1.0ms	x
1.0ms	(-.f64 (.f64 x x) (.f64 y y))
1.0ms	(*.f64 x x)
1.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
57.4%	1	`y`
57.4%	1	`(*.f64 y y)`
57.4%	1	`x`
57.4%	1	`(*.f64 x x)`
57.4%	1	`(-.f64 (.f64 x x) (.f64 y y))`

Compiler

Compiled 15 to 15 computations (0% saved)

bsearch0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.5360569610804272e-302	0.0

Compiler

Compiled 10 to 10 computations (0% saved)

simplify25.0ms (0.6%)

Memory

-20.0MiB live, 57.0MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	51
1	29	51
2	35	51
3	38	51
4	39	51

Stop Event

1×

saturated

Calls

Call 1

Inputs

(*.f64 (-.f64 x y) (+.f64 y x))

(if (<=.f64 (-.f64 (*.f64 x x) (*.f64 y y)) #s(literal -1930258305619341/193025830561934107162947985381047541665608072055952185017491682078771915023799273387871154500424503798663213600460826789274033295999330021731389427128542432710187362934652673115221889249890533772697227171395058697282798274445240687006095271729621464100656563293799180557568945517759802372156455525060659659679134121984 binary64)) #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #s(approx (- (* x x) (* y y)) (*.f64 x x)))

#s(approx (- (* x x) (* y y)) (*.f64 x x))

Outputs
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 (+.f64 y x) (-.f64 x y))
(if (<=.f64 (-.f64 (.f64 x x) (.f64 y y)) #s(literal -1930258305619341/193025830561934107162947985381047541665608072055952185017491682078771915023799273387871154500424503798663213600460826789274033295999330021731389427128542432710187362934652673115221889249890533772697227171395058697282798274445240687006095271729621464100656563293799180557568945517759802372156455525060659659679134121984 binary64)) #s(approx (- (* x x) (* y y)) (.f64 (neg.f64 y) y)) #s(approx (- ( x x) (* y y)) (*.f64 x x)))
#s(approx (- (* x x) (* y y)) (*.f64 x x))

soundness428.0ms (10.5%)

Memory

1.2MiB live, 197.1MiB allocated

Rules

12 540×	`lower-fma.f64`
12 540×	`lower-fma.f32`
8 026×	`lower-fma.f64`
8 026×	`lower-fma.f32`
4 450×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	219
1	39	219
2	113	219
3	469	219
4	1679	219
5	2846	219
6	5006	219
0	8448	219
0	5	13
0	8	13
1	32	13
2	216	13
3	1967	13
0	8778	13

Stop Event

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

Compiler

Compiled 54 to 33 computations (38.9% saved)

preprocess29.0ms (0.7%)

Memory

-2.9MiB live, 70.1MiB allocated

Remove

(abs x)

(abs y)

Compiler

Compiled 130 to 80 computations (38.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample528.0ms (13%)

explain72.0ms (1.8%)

preprocess714.0ms (17.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify332.0ms (8.2%)

localize87.0ms (2.1%)

series4.0ms (0.1%)

simplify257.0ms (6.3%)

rewrite214.0ms (5.3%)

eval54.0ms (1.3%)

prune5.0ms (0.1%)

simplify283.0ms (7%)

localize30.0ms (0.7%)

series33.0ms (0.8%)

simplify161.0ms (4%)

rewrite575.0ms (14.1%)

eval188.0ms (4.6%)

prune18.0ms (0.4%)

regimes15.0ms (0.4%)

regimes9.0ms (0.2%)

regimes6.0ms (0.2%)

bsearch0.0ms (0%)

simplify25.0ms (0.6%)

soundness428.0ms (10.5%)

preprocess29.0ms (0.7%)

end0.0ms (0%)

Profiling