Metrics for Difference of squares

analyze0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample654.0ms (8.9%)

Memory

-14.5MiB live, 1 105.0MiB allocated

Samples

398.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 176.0ms

ival-mult: 130.0ms (73.7% of total)

ival-sub: 38.0ms (21.6% of total)

ival-true: 6.0ms (3.4% of total)

ival-assert: 3.0ms (1.7% of total)

Bogosity

preprocess755.0ms (10.3%)

Memory

-6.0MiB live, 748.9MiB 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 a a) (.f64 b b))

Outputs
(-.f64 (.f64 a a) (.f64 b b))
(*.f64 (+.f64 a b) (-.f64 a b))

Symmetry

(abs b)

(abs a)

explain61.0ms (0.8%)

Memory

27.7MiB live, 106.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
7	-	-	`(-.f64 (.f64 a a) (.f64 b b))`
0	-	-	`(*.f64 a a)`
0	-	-	`a`
0	-	-	`b`
0	-	-	`(*.f64 b b)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (.f64 a a) (.f64 b b))`	nan-rescue	7	0
↳	`(*.f64 a a)`	overflow	70
↳	`(*.f64 b b)`	overflow	47

Confusion

	Predicted +	Predicted -
+	7	0
-	0	249

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	7	0	0
-	0	0	249

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	249
1	7

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

21.0ms

512×

valid

Compiler

Compiled 52 to 24 computations (53.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 7.0ms (74% of total)

ival-sub: 2.0ms (21.1% of total)

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

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

2.4MiB live, 2.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.3%	(-.f64 (.f64 a a) (.f64 b b))

Compiler

Compiled 9 to 5 computations (44.4% saved)

simplify831.0ms (11.3%)

Memory

-21.3MiB live, 535.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 b b)
✓	cost-diff	0	(*.f64 a a)
✓	cost-diff	128	(-.f64 (.f64 a a) (.f64 b b))

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 a a) (.f64 b b))
(*.f64 a a)
a
(*.f64 b b)
b

Outputs
(-.f64 (.f64 a a) (.f64 b b))
(*.f64 (+.f64 a b) (-.f64 a b))
(*.f64 a a)
a
(*.f64 b b)
b

localize16.0ms (0.2%)

Memory

6.9MiB live, 6.9MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 b b)
✓	accuracy	100.0%	(*.f64 a a)
✓	accuracy	97.6%	(-.f64 (.f64 a a) (.f64 b b))

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 (66.3% of total)

ival-sub: 1.0ms (22.1% of total)

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

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

series3.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Counts

3 → 48

Calls

Call 1

Inputs
#s(alt (-.f64 (.f64 a a) (.f64 b b)) (patch (-.f64 (.f64 a a) (.f64 b b)) #<representation binary64>) () ())
#s(alt (.f64 a a) (patch (.f64 a a) #<representation binary64>) () ())
#s(alt (.f64 b b) (patch (.f64 b b) #<representation binary64>) () ())

Inputs

#s(alt (-.f64 (*.f64 a a) (*.f64 b b)) (patch (-.f64 (*.f64 a a) (*.f64 b b)) #<representation binary64>) () ())

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

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

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

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	a	@	0	(- (* a a) (* b b))
0.0ms	a	@	inf	(- (* a a) (* b b))
0.0ms	b	@	0	(- (* a a) (* b b))
0.0ms	b	@	inf	(- (* a a) (* b b))
0.0ms	a	@	-inf	(- (* a a) (* b b))

simplify425.0ms (5.8%)

Memory

18.0MiB live, 372.3MiB 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	468	219
4	1684	219
5	2832	219
6	4991	219
0	8406	219

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(- (pow a 2) (pow b 2))
(- (pow a 2) (pow b 2))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(pow a 2)
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(* -1 (pow b 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* -1 (pow b 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)

Outputs
(* -1 (pow b 2))
(neg.f64 (*.f64 b b))
(- (pow a 2) (pow b 2))
(*.f64 (+.f64 b a) (-.f64 a b))
(- (pow a 2) (pow b 2))
(*.f64 (+.f64 b a) (-.f64 a b))
(- (pow a 2) (pow b 2))
(*.f64 (+.f64 b a) (-.f64 a b))
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (+.f64 b a) (-.f64 a b))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (+.f64 b a) (-.f64 a b))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (+.f64 b a) (-.f64 a b))
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (+.f64 b a) (-.f64 a b))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (+.f64 b a) (-.f64 a b))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (+.f64 b a) (-.f64 a b))
(pow a 2)
(*.f64 a a)
(+ (* -1 (pow b 2)) (pow a 2))
(*.f64 (+.f64 b a) (-.f64 a b))
(+ (* -1 (pow b 2)) (pow a 2))
(*.f64 (+.f64 b a) (-.f64 a b))
(+ (* -1 (pow b 2)) (pow a 2))
(*.f64 (+.f64 b a) (-.f64 a b))
(* -1 (pow b 2))
(neg.f64 (*.f64 b b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (+.f64 b a) (-.f64 a b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (+.f64 b a) (-.f64 a b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (+.f64 b a) (-.f64 a b))
(* -1 (pow b 2))
(neg.f64 (*.f64 b b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (+.f64 b a) (-.f64 a b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (+.f64 b a) (-.f64 a b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (+.f64 b a) (-.f64 a b))
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)

rewrite460.0ms (6.2%)

Memory

1.3MiB live, 598.1MiB allocated

Algorithm

1×	batch-egg-rewrite

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 a a) (.f64 b b))
(*.f64 a a)
(*.f64 b b)

Outputs
(+.f64 (.f64 a a) (.f64 b (neg.f64 b)))
(+.f64 (.f64 b (neg.f64 b)) (.f64 a a))
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(.f64 (/.f64 (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (.f64 (fma.f64 b (+.f64 a b) (.f64 a a)) (-.f64 a b))) (.f64 (fma.f64 a (.f64 a (.f64 a a)) (.f64 b (.f64 b (fma.f64 a a (.f64 b b))))) (-.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 b (.f64 b (fma.f64 a a (.f64 b b))))))) (-.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 b (.f64 b (fma.f64 a a (*.f64 b b))))))
(.f64 (pow.f64 (/.f64 (fma.f64 a (.f64 a (.f64 a a)) (.f64 b (.f64 b (fma.f64 a a (.f64 b b))))) (fma.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a))))) (.f64 (.f64 (.f64 b b) (.f64 b (.f64 b (.f64 b b)))) (.f64 (.f64 (.f64 b b) (.f64 b (.f64 b (.f64 b b)))) (.f64 (.f64 b b) (.f64 b (.f64 b (.f64 b b)))))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 b b) (.f64 b (.f64 b (.f64 b b)))) (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (.f64 (fma.f64 b (+.f64 a b) (.f64 a a)) (-.f64 a b))) (.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (.f64 a a) (.f64 a (.f64 a (*.f64 a a))))))))
(.f64 (pow.f64 (/.f64 (fma.f64 a (.f64 a (.f64 a a)) (.f64 b (.f64 b (fma.f64 a a (.f64 b b))))) (.f64 (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (.f64 (fma.f64 b (+.f64 a b) (.f64 a a)) (-.f64 a b))) (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (.f64 (fma.f64 b (+.f64 a b) (.f64 a a)) (-.f64 a b))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (.f64 (fma.f64 b (+.f64 a b) (*.f64 a a)) (-.f64 a b)))))
(.f64 (pow.f64 (/.f64 (fma.f64 a a (.f64 b b)) (.f64 (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (.f64 (fma.f64 b (+.f64 a b) (.f64 a a)) (-.f64 a b))) (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (.f64 (fma.f64 b (+.f64 a b) (.f64 a a)) (-.f64 a b))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 b (.f64 b (.f64 b b))) (fma.f64 a (.f64 a (.f64 a a)) (.f64 b (.f64 b (.f64 b b)))) (.f64 (.f64 a a) (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a))))))))
(.f64 (pow.f64 (/.f64 (fma.f64 a a (.f64 b b)) (.f64 (fma.f64 a (.f64 a (.f64 a a)) (.f64 b (.f64 b (.f64 b b)))) (.f64 (.f64 (+.f64 a b) (-.f64 a b)) (fma.f64 a a (.f64 b b))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 a (.f64 a (.f64 a a)) (.f64 b (.f64 b (.f64 b b))))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 a)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 a)) #s(literal 1 binary64)))
(pow.f64 a #s(literal 2 binary64))
(pow.f64 (*.f64 a a) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 a))
(*.f64 a a)
(exp.f64 (log.f64 (*.f64 b b)))
(exp.f64 (.f64 (log.f64 (.f64 b b)) #s(literal 1 binary64)))
(pow.f64 b #s(literal 2 binary64))
(pow.f64 (*.f64 b b) #s(literal 1 binary64))
(pow.f64 (neg.f64 b) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 b))
(*.f64 b b)
(*.f64 (neg.f64 b) (neg.f64 b))

eval42.0ms (0.6%)

Memory: -6.4MiB live, 68.0MiB allocated
Compiler: Compiled 16 205 to 750 computations (95.4% saved)

prune40.0ms (0.5%)

Memory

33.5MiB live, 111.3MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	296	4	300
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	297	4	301

Accuracy

100.0%

Counts

301 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.4%	(fma.f64 a a (*.f64 b (neg.f64 b)))
▶	100.0%	(*.f64 (-.f64 a b) (+.f64 a b))
▶	57.7%	#s(approx (- (* a a) (* b b)) (*.f64 a a))
▶	50.2%	#s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b)))

Compiler

Compiled 31 to 17 computations (45.2% saved)

simplify1.1s (14.8%)

Memory

-23.3MiB live, 1 579.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(neg.f64 b)
✓	cost-diff	0	(*.f64 b (neg.f64 b))
✓	cost-diff	128	(fma.f64 a a (*.f64 b (neg.f64 b)))
✓	cost-diff	0	(+.f64 a b)
✓	cost-diff	0	(-.f64 a b)
✓	cost-diff	0	(*.f64 (-.f64 a b) (+.f64 a b))
✓	cost-diff	0	(*.f64 a a)
✓	cost-diff	0	#s(approx (- (* a a) (* b b)) (*.f64 a a))
✓	cost-diff	0	(*.f64 b b)
✓	cost-diff	0	(neg.f64 (*.f64 b b))
✓	cost-diff	0	#s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b)))

Rules

58 480×	`lower-fma.f32`
58 478×	`lower-fma.f64`
7 684×	`lower-+.f32`
7 682×	`lower-+.f64`
6 192×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	65
0	24	65
1	44	65
2	72	65
3	160	65
4	319	65
5	646	65
6	1669	65
7	2830	65
8	3824	65
9	4311	65
10	4526	65
11	4652	65
12	4662	65
13	5814	65
14	6006	65
15	6198	65
16	6294	65
17	6294	65
18	6678	65
19	6774	65
20	6870	65
21	6870	65
22	6870	65
23	6870	65
0	11017	65

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b)))
(neg.f64 (*.f64 b b))
(*.f64 b b)
b
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(*.f64 a a)
a
(*.f64 (-.f64 a b) (+.f64 a b))
(-.f64 a b)
a
b
(+.f64 a b)
(fma.f64 a a (*.f64 b (neg.f64 b)))
a
(*.f64 b (neg.f64 b))
b
(neg.f64 b)

Outputs
#s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b)))
#s(approx (- (* a a) (* b b)) (*.f64 b (neg.f64 b)))
(neg.f64 (*.f64 b b))
(*.f64 b (neg.f64 b))
(*.f64 b b)
b
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(*.f64 a a)
a
(*.f64 (-.f64 a b) (+.f64 a b))
(-.f64 a b)
a
b
(+.f64 a b)
(fma.f64 a a (*.f64 b (neg.f64 b)))
(*.f64 (-.f64 a b) (+.f64 a b))
a
(*.f64 b (neg.f64 b))
b
(neg.f64 b)

localize62.0ms (0.8%)

Memory

-14.7MiB live, 65.3MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 b (neg.f64 b))
✓	accuracy	100.0%	(neg.f64 b)
✓	accuracy	98.4%	(fma.f64 a a (*.f64 b (neg.f64 b)))
✓	accuracy	100.0%	(-.f64 a b)
✓	accuracy	100.0%	(+.f64 a b)
✓	accuracy	100.0%	(*.f64 (-.f64 a b) (+.f64 a b))
✓	accuracy	100.0%	(*.f64 a a)
✓	accuracy	57.7%	#s(approx (- (* a a) (* b b)) (*.f64 a a))
✓	accuracy	100.0%	(*.f64 b b)
✓	accuracy	100.0%	(neg.f64 (*.f64 b b))
✓	accuracy	50.2%	#s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b)))

Samples

24.0ms

256×

valid

Compiler

Compiled 59 to 14 computations (76.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-mult: 6.0ms (46% of total)

ival-sub: 2.0ms (15.3% of total)

ival-add: 2.0ms (15.3% of total)

ival-neg: 2.0ms (15.3% of total)

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

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

series8.0ms (0.1%)

Memory

11.6MiB live, 11.6MiB allocated

Counts

11 → 204

Calls

Call 1

Inputs
#s(alt #s(approx (- (* a a) (* b b)) (neg.f64 (.f64 b b))) (patch #s(approx (- ( a a) (* b b)) (neg.f64 (*.f64 b b))) #<representation binary64>) () ())
#s(alt (neg.f64 (.f64 b b)) (patch (neg.f64 (.f64 b b)) #<representation binary64>) () ())
#s(alt (.f64 b b) (patch (.f64 b b) #<representation binary64>) () ())
#s(alt #s(approx (- (* a a) (* b b)) (.f64 a a)) (patch #s(approx (- ( a a) (* b b)) (*.f64 a a)) #<representation binary64>) () ())
#s(alt (.f64 a a) (patch (.f64 a a) #<representation binary64>) () ())
#s(alt (.f64 (-.f64 a b) (+.f64 a b)) (patch (.f64 (-.f64 a b) (+.f64 a b)) #<representation binary64>) () ())
#s(alt (-.f64 a b) (patch (-.f64 a b) #<representation binary64>) () ())
#s(alt (+.f64 a b) (patch (+.f64 a b) #<representation binary64>) () ())
#s(alt (fma.f64 a a (.f64 b (neg.f64 b))) (patch (fma.f64 a a (.f64 b (neg.f64 b))) #<representation binary64>) () ())
#s(alt (.f64 b (neg.f64 b)) (patch (.f64 b (neg.f64 b)) #<representation binary64>) () ())
#s(alt (neg.f64 b) (patch (neg.f64 b) #<representation binary64>) () ())

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

Calls

51 calls:

Time	Variable		Point	Expression
0.0ms	a	@	inf	(* (- a b) (+ a b))
0.0ms	b	@	inf	(+ (* a a) (* b (neg b)))
0.0ms	b	@	inf	(* (- a b) (+ a b))
0.0ms	b	@	inf	(* b (neg b))
0.0ms	a	@	-inf	(* (- a b) (+ a b))

simplify453.0ms (6.2%)

Memory

7.1MiB live, 366.7MiB 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	882
1	281	882
2	829	882
3	3572	882
0	8751	882

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 195

Calls

Call 1

Inputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(- (pow a 2) (pow b 2))
(- (pow a 2) (pow b 2))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(pow a 2)
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(* -1 (pow b 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* -1 (pow b 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(pow b 2)
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(- (pow a 2) (pow b 2))
(- (pow a 2) (pow b 2))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(pow a 2)
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(* -1 (pow b 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* -1 (pow b 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(pow a 2)
(* -1 (pow b 2))
(+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(pow a 2)
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(pow a 2)
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(pow a 2)
(+ (* b (+ a (* -1 a))) (pow a 2))
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(* -1 (pow b 2))
(* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(* -1 (pow b 2))
(* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(* -1 b)
(- a b)
(- a b)
(- a b)
a
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (* -1 (/ b a))))
a
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (/ b a) 1)))
a
(+ a (* -1 b))
(+ a (* -1 b))
(+ a (* -1 b))
(* -1 b)
(* b (- (/ a b) 1))
(* b (- (/ a b) 1))
(* b (- (/ a b) 1))
(* -1 b)
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
b
(+ a b)
(+ a b)
(+ a b)
a
(* a (+ 1 (/ b a)))
(* a (+ 1 (/ b a)))
(* a (+ 1 (/ b a)))
a
(* -1 (* a (- (* -1 (/ b a)) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
a
(+ a b)
(+ a b)
(+ a b)
b
(* b (+ 1 (/ a b)))
(* b (+ 1 (/ a b)))
(* b (+ 1 (/ a b)))
b
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(* -1 (pow b 2))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(pow a 2)
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* -1 (pow b 2)) (pow a 2))
(* -1 (pow b 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* -1 (pow b 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 (pow b 2))
(* -1 b)
(* -1 b)
(* -1 b)
(* -1 b)
(* -1 b)
(* -1 b)
(* -1 b)
(* -1 b)
(* -1 b)
(* -1 b)
(* -1 b)
(* -1 b)

Outputs
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(- (pow a 2) (pow b 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(- (pow a 2) (pow b 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(- (pow a 2) (pow b 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(pow a 2)
(*.f64 a a)
(+ (* -1 (pow b 2)) (pow a 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(+ (* -1 (pow b 2)) (pow a 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(+ (* -1 (pow b 2)) (pow a 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(pow b 2)
(*.f64 b b)
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(- (pow a 2) (pow b 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(- (pow a 2) (pow b 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(- (pow a 2) (pow b 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(pow a 2)
(*.f64 a a)
(+ (* -1 (pow b 2)) (pow a 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(+ (* -1 (pow b 2)) (pow a 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(+ (* -1 (pow b 2)) (pow a 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(pow a 2)
(*.f64 a a)
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))
(*.f64 b (neg.f64 b))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(*.f64 a a)
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(*.f64 (-.f64 a b) (+.f64 b a))
(pow a 2)
(*.f64 a a)
(+ (* b (+ a (* -1 a))) (pow a 2))
(*.f64 a a)
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))
(*.f64 b (neg.f64 b))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))
(*.f64 b (neg.f64 b))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* -1 b)
(neg.f64 b)
(- a b)
(-.f64 a b)
(- a b)
(-.f64 a b)
(- a b)
(-.f64 a b)
a
(* a (+ 1 (* -1 (/ b a))))
(-.f64 a b)
(* a (+ 1 (* -1 (/ b a))))
(-.f64 a b)
(* a (+ 1 (* -1 (/ b a))))
(-.f64 a b)
a
(* -1 (* a (- (/ b a) 1)))
(-.f64 a b)
(* -1 (* a (- (/ b a) 1)))
(-.f64 a b)
(* -1 (* a (- (/ b a) 1)))
(-.f64 a b)
a
(+ a (* -1 b))
(-.f64 a b)
(+ a (* -1 b))
(-.f64 a b)
(+ a (* -1 b))
(-.f64 a b)
(* -1 b)
(neg.f64 b)
(* b (- (/ a b) 1))
(-.f64 a b)
(* b (- (/ a b) 1))
(-.f64 a b)
(* b (- (/ a b) 1))
(-.f64 a b)
(* -1 b)
(neg.f64 b)
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(-.f64 a b)
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(-.f64 a b)
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(-.f64 a b)
b
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
a
(* a (+ 1 (/ b a)))
(+.f64 b a)
(* a (+ 1 (/ b a)))
(+.f64 b a)
(* a (+ 1 (/ b a)))
(+.f64 b a)
a
(* -1 (* a (- (* -1 (/ b a)) 1)))
(+.f64 b a)
(* -1 (* a (- (* -1 (/ b a)) 1)))
(+.f64 b a)
(* -1 (* a (- (* -1 (/ b a)) 1)))
(+.f64 b a)
a
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
(+ a b)
(+.f64 b a)
b
(* b (+ 1 (/ a b)))
(+.f64 b a)
(* b (+ 1 (/ a b)))
(+.f64 b a)
(* b (+ 1 (/ a b)))
(+.f64 b a)
b
(* -1 (* b (- (* -1 (/ a b)) 1)))
(+.f64 b a)
(* -1 (* b (- (* -1 (/ a b)) 1)))
(+.f64 b a)
(* -1 (* b (- (* -1 (/ a b)) 1)))
(+.f64 b a)
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(+ (* -1 (pow b 2)) (pow a 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(+ (* -1 (pow b 2)) (pow a 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(+ (* -1 (pow b 2)) (pow a 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(pow a 2)
(*.f64 a a)
(+ (* -1 (pow b 2)) (pow a 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(+ (* -1 (pow b 2)) (pow a 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(+ (* -1 (pow b 2)) (pow a 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 (pow b 2))
(*.f64 b (neg.f64 b))
(* -1 b)
(neg.f64 b)
(* -1 b)
(neg.f64 b)
(* -1 b)
(neg.f64 b)
(* -1 b)
(neg.f64 b)
(* -1 b)
(neg.f64 b)
(* -1 b)
(neg.f64 b)
(* -1 b)
(neg.f64 b)
(* -1 b)
(neg.f64 b)
(* -1 b)
(neg.f64 b)
(* -1 b)
(neg.f64 b)
(* -1 b)
(neg.f64 b)
(* -1 b)
(neg.f64 b)

rewrite1.1s (15.1%)

Memory

-4.1MiB live, 307.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 706×	`lower-fma.f32`
4 704×	`lower-fma.f64`
2 602×	`lower-*.f32`
2 596×	`lower-*.f64`
2 172×	`lower-/.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	59
0	24	60
1	83	60
2	643	51
0	10235	51

Stop Event

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

Counts

11 → 985

Calls

Call 1

Inputs
#s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b)))
(neg.f64 (*.f64 b b))
(*.f64 b b)
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(*.f64 a a)
(*.f64 (-.f64 a b) (+.f64 a b))
(-.f64 a b)
(+.f64 a b)
(fma.f64 a a (*.f64 b (neg.f64 b)))
(*.f64 b (neg.f64 b))
(neg.f64 b)

Outputs
#s(approx (- (* a a) (* b b)) (*.f64 b b))
(+.f64 #s(literal 0 binary64) (*.f64 b b))
(+.f64 (.f64 b #s(literal 0 binary64)) (.f64 b b))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 b)))
(-.f64 #s(literal 0 binary64) (*.f64 b b))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 (.f64 b b) (.f64 b b) #s(literal 0 binary64))) (*.f64 b b))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 b b))
(fma.f64 b #s(literal 0 binary64) (*.f64 b b))
(neg.f64 (*.f64 b b))
(/.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 b b))
(/.f64 (.f64 (.f64 b b) (*.f64 b b)) (fma.f64 b b #s(literal 0 binary64)))
(/.f64 (.f64 b (.f64 b b)) b)
(/.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (fma.f64 (.f64 b b) (*.f64 b b) #s(literal 0 binary64)))
(/.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (neg.f64 (fma.f64 (.f64 b b) (*.f64 b b) #s(literal 0 binary64))))
(/.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 b b) (.f64 b b)) #s(literal 0 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 b b) (.f64 b b) #s(literal 0 binary64)) (.f64 (.f64 b b) (.f64 (.f64 b b) (*.f64 b b)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))))
(pow.f64 b #s(literal 2 binary64))
(pow.f64 (*.f64 b b) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 b)) #s(literal 2 binary64))
(*.f64 b b)
(.f64 (.f64 b b) #s(literal -1 binary64))
(.f64 (.f64 b b) #s(literal 1 binary64))
(.f64 (.f64 (.f64 b b) (.f64 b b)) (/.f64 #s(literal 1 binary64) (*.f64 b b)))
(.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 b b) (.f64 b b) #s(literal 0 binary64))))
(.f64 #s(literal -1 binary64) (.f64 b b))
(.f64 #s(literal 1 binary64) (.f64 b b))
(*.f64 (exp.f64 (log.f64 b)) (exp.f64 (log.f64 b)))
(+.f64 #s(literal 0 binary64) (*.f64 b b))
(+.f64 (.f64 b #s(literal 0 binary64)) (.f64 b b))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 b)))
(-.f64 #s(literal 0 binary64) (*.f64 b b))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 (.f64 b b) (.f64 b b) #s(literal 0 binary64))) (*.f64 b b))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 b b))
(fma.f64 b #s(literal 0 binary64) (*.f64 b b))
(neg.f64 (*.f64 b b))
(/.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 b b))
(/.f64 (.f64 (.f64 b b) (*.f64 b b)) (fma.f64 b b #s(literal 0 binary64)))
(/.f64 (.f64 b (.f64 b b)) b)
(/.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (fma.f64 (.f64 b b) (*.f64 b b) #s(literal 0 binary64)))
(/.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (neg.f64 (fma.f64 (.f64 b b) (*.f64 b b) #s(literal 0 binary64))))
(/.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 b b) (.f64 b b)) #s(literal 0 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 b b) (.f64 b b) #s(literal 0 binary64)) (.f64 (.f64 b b) (.f64 (.f64 b b) (*.f64 b b)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))))
(pow.f64 b #s(literal 2 binary64))
(pow.f64 (*.f64 b b) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 b)) #s(literal 2 binary64))
(*.f64 b b)
(.f64 (.f64 b b) #s(literal -1 binary64))
(.f64 (.f64 b b) #s(literal 1 binary64))
(.f64 (.f64 (.f64 b b) (.f64 b b)) (/.f64 #s(literal 1 binary64) (*.f64 b b)))
(.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 b b) (.f64 b b) #s(literal 0 binary64))))
(.f64 #s(literal -1 binary64) (.f64 b b))
(.f64 #s(literal 1 binary64) (.f64 b b))
(*.f64 (exp.f64 (log.f64 b)) (exp.f64 (log.f64 b)))
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(+.f64 (*.f64 a a) #s(literal 0 binary64))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 a)))
(-.f64 (*.f64 a a) #s(literal 0 binary64))
(fma.f64 a a #s(literal 0 binary64))
(fma.f64 (exp.f64 (log.f64 a)) (exp.f64 (log.f64 a)) #s(literal 0 binary64))
(/.f64 (fma.f64 (.f64 a (.f64 a a)) (.f64 a (.f64 a a)) #s(literal 0 binary64)) (fma.f64 a (.f64 a (.f64 a a)) (-.f64 #s(literal 0 binary64) (.f64 (.f64 a a) #s(literal 0 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) #s(literal 0 binary64)) (fma.f64 a (.f64 a (.f64 a a)) (+.f64 #s(literal 0 binary64) (.f64 (*.f64 a a) #s(literal 0 binary64)))))
(/.f64 (-.f64 (.f64 a (.f64 a (.f64 a a))) #s(literal 0 binary64)) (.f64 a a))
(pow.f64 a #s(literal 2 binary64))
(pow.f64 (*.f64 a a) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 a)) #s(literal 2 binary64))
(*.f64 a a)
(*.f64 (exp.f64 (log.f64 a)) (exp.f64 (log.f64 a)))
(+.f64 (.f64 b b) (.f64 a a))
(+.f64 (.f64 a a) (.f64 b b))
(+.f64 (.f64 a a) (fma.f64 a b (.f64 b (+.f64 a b))))
(+.f64 (.f64 a a) (-.f64 (.f64 a b) (*.f64 b (+.f64 a b))))
(+.f64 (.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b))))
(+.f64 (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))
(+.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (.f64 a b))
(+.f64 #s(literal 0 binary64) (fma.f64 a a (*.f64 b b)))
(+.f64 (.f64 a (+.f64 a b)) (.f64 b (+.f64 a b)))
(+.f64 (/.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (fma.f64 a a (.f64 b (+.f64 a b))))) (neg.f64 (/.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (fma.f64 a a (.f64 b (+.f64 a b)))))))
(+.f64 (/.f64 (.f64 a (.f64 a (.f64 a a))) (fma.f64 a a (.f64 b b))) (/.f64 (.f64 (.f64 b b) (.f64 b b)) (fma.f64 a a (.f64 b b))))
(+.f64 (fma.f64 a (+.f64 a b) (.f64 a b)) (.f64 b b))
(-.f64 (.f64 a a) (.f64 b b))
(-.f64 #s(literal 0 binary64) (*.f64 (+.f64 a b) (-.f64 b a)))
(-.f64 (.f64 a (+.f64 a b)) (.f64 b (+.f64 a b)))
(-.f64 (/.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (fma.f64 a a (.f64 b (+.f64 a b))))) (/.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (fma.f64 a a (.f64 b (+.f64 a b))))))
(-.f64 (/.f64 (.f64 a (.f64 a (.f64 a a))) (fma.f64 a a (.f64 b b))) (/.f64 (.f64 (.f64 b b) (.f64 b b)) (fma.f64 a a (.f64 b b))))
(-.f64 (/.f64 (.f64 (.f64 b b) (.f64 b b)) (fma.f64 a a (.f64 b b))) (/.f64 (.f64 a (.f64 a (.f64 a a))) (.f64 (+.f64 a b) (-.f64 b a))))
(-.f64 (/.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (fma.f64 b (.f64 b (.f64 b b)) (.f64 a (.f64 (fma.f64 a a (.f64 b b)) a)))) (/.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (fma.f64 b (.f64 b (.f64 b b)) (.f64 a (.f64 (fma.f64 a a (.f64 b b)) a)))))
(-.f64 (/.f64 (.f64 a (.f64 (fma.f64 a a (.f64 b b)) a)) (fma.f64 a a (.f64 b b))) (/.f64 (.f64 b (.f64 b (fma.f64 a a (.f64 b b)))) (fma.f64 a a (.f64 b b))))
(-.f64 (-.f64 (.f64 a (+.f64 a b)) (.f64 a b)) (*.f64 b b))
(fma.f64 a a (*.f64 b b))
(fma.f64 a a (fma.f64 a b (*.f64 b (+.f64 a b))))
(fma.f64 a a (-.f64 (.f64 a b) (.f64 b (+.f64 a b))))
(fma.f64 a b (fma.f64 a a (*.f64 b (+.f64 a b))))
(fma.f64 a (+.f64 a b) (*.f64 b (+.f64 a b)))
(fma.f64 b a (fma.f64 a a (*.f64 b (+.f64 a b))))
(fma.f64 b b (*.f64 a a))
(fma.f64 b (+.f64 a b) (*.f64 a (+.f64 a b)))
(fma.f64 b (-.f64 b a) (*.f64 a (+.f64 a b)))
(fma.f64 b (neg.f64 a) (fma.f64 a a (*.f64 b (+.f64 a b))))
(fma.f64 (fma.f64 a a (.f64 b b)) (/.f64 a (+.f64 a b)) (.f64 b (+.f64 a b)))
(fma.f64 (fma.f64 a a (.f64 b b)) (/.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))
(fma.f64 (fma.f64 a a (.f64 b b)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 a b)) b) (*.f64 a (+.f64 a b)))
(fma.f64 (fma.f64 a a (.f64 b b)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 a b)) a) (*.f64 b (+.f64 a b)))
(fma.f64 (.f64 b b) #s(literal -1 binary64) (.f64 a a))
(fma.f64 (.f64 b b) #s(literal 1 binary64) (.f64 a a))
(fma.f64 (+.f64 a b) a (*.f64 b (+.f64 a b)))
(fma.f64 (+.f64 a b) b (*.f64 a (+.f64 a b)))
(fma.f64 (+.f64 a b) (/.f64 a #s(literal 1 binary64)) (*.f64 b (+.f64 a b)))
(fma.f64 (+.f64 a b) (/.f64 b #s(literal 1 binary64)) (*.f64 a (+.f64 a b)))
(fma.f64 (+.f64 a b) (.f64 #s(literal 1 binary64) a) (.f64 b (+.f64 a b)))
(fma.f64 (.f64 (.f64 a a) (.f64 a (.f64 a (.f64 a a)))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (fma.f64 a a (.f64 b (+.f64 a b))))) (neg.f64 (/.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (fma.f64 a a (.f64 b (+.f64 a b)))))))
(fma.f64 (.f64 a (.f64 a (.f64 a a))) (/.f64 #s(literal 1 binary64) (fma.f64 a a (.f64 b b))) (/.f64 (.f64 (.f64 b b) (.f64 b b)) (fma.f64 a a (.f64 b b))))
(fma.f64 (.f64 (.f64 b b) (.f64 b b)) (/.f64 #s(literal 1 binary64) (.f64 b b)) (*.f64 a a))
(fma.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a a (.f64 b (+.f64 a b)))) b) (.f64 a (+.f64 a b)))
(fma.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (.f64 (/.f64 #s(literal 1 binary64) (fma.f64 a a (.f64 b (+.f64 a b)))) a) (.f64 b (+.f64 a b)))
(fma.f64 (.f64 a b) #s(literal -1 binary64) (fma.f64 a a (.f64 b (+.f64 a b))))
(fma.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 b b) (.f64 b b) #s(literal 0 binary64))) (.f64 a a))
(fma.f64 (.f64 b (.f64 b (fma.f64 a a (.f64 b b)))) (/.f64 #s(literal 1 binary64) (.f64 b (+.f64 a b))) (*.f64 a (+.f64 a b)))
(fma.f64 (.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (fma.f64 a a (.f64 b (+.f64 a b)))) (/.f64 #s(literal 1 binary64) (fma.f64 a a (.f64 b (+.f64 a b)))) (*.f64 a b))
(fma.f64 (.f64 b (+.f64 a b)) #s(literal -1 binary64) (.f64 a (+.f64 a b)))
(fma.f64 (.f64 b (+.f64 a b)) #s(literal 1 binary64) (.f64 a (+.f64 a b)))
(fma.f64 #s(literal -1 binary64) (.f64 b b) (.f64 a a))
(fma.f64 #s(literal -1 binary64) (.f64 a b) (fma.f64 a a (.f64 b (+.f64 a b))))
(fma.f64 #s(literal -1 binary64) (.f64 b (+.f64 a b)) (.f64 a (+.f64 a b)))
(fma.f64 (.f64 a (+.f64 a b)) #s(literal 1 binary64) (.f64 b (+.f64 a b)))
(fma.f64 (-.f64 b a) b (*.f64 a (+.f64 a b)))
(fma.f64 (.f64 (.f64 b (.f64 b b)) (fma.f64 a (.f64 a a) (.f64 b (.f64 b b)))) (/.f64 #s(literal 1 binary64) (fma.f64 b (.f64 b (.f64 b b)) (.f64 (.f64 b b) (.f64 a (+.f64 a b))))) (.f64 a (+.f64 a b)))
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(.f64 (/.f64 (.f64 (fma.f64 a a (.f64 b b)) (+.f64 a b)) (.f64 (fma.f64 a a (.f64 b b)) (fma.f64 a a (.f64 b b)))) (.f64 (fma.f64 a a (.f64 b b)) (+.f64 a b)))
(.f64 (/.f64 (.f64 (fma.f64 a a (.f64 b b)) (+.f64 a b)) (.f64 (+.f64 a b) (-.f64 b a))) (-.f64 b a))
(.f64 (/.f64 (.f64 (fma.f64 a a (.f64 b b)) (+.f64 a b)) (.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (-.f64 b a))) (fma.f64 a (neg.f64 a) (.f64 b (+.f64 a b))))
(.f64 (/.f64 (.f64 (+.f64 a b) (fma.f64 a (.f64 a a) (.f64 b (.f64 b b)))) (fma.f64 a (.f64 (.f64 a a) (.f64 a (.f64 a a))) (.f64 (.f64 b (.f64 b (fma.f64 a a (.f64 b b)))) (.f64 b (+.f64 a b))))) (fma.f64 a (.f64 a (.f64 a a)) (.f64 (.f64 b (+.f64 a b)) (-.f64 (.f64 b (+.f64 a b)) (.f64 a a)))))
(.f64 (/.f64 (.f64 (+.f64 a b) (fma.f64 a (.f64 a a) (.f64 b (.f64 b b)))) (.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (fma.f64 a a (.f64 b (+.f64 a b))))) (fma.f64 a a (*.f64 b (+.f64 a b))))
(.f64 (/.f64 (.f64 (fma.f64 a a (.f64 b b)) (fma.f64 a a (.f64 b b))) (.f64 (fma.f64 a a (.f64 b b)) (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))))) (.f64 (+.f64 a b) (fma.f64 a a (*.f64 b (+.f64 a b)))))
(.f64 (/.f64 (.f64 (fma.f64 a a (.f64 b b)) (fma.f64 a a (.f64 b b))) (.f64 (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))) (fma.f64 a a (.f64 b b)))) (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))))
(.f64 (/.f64 (.f64 (fma.f64 a a (.f64 b b)) (fma.f64 a a (.f64 b b))) (.f64 (.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (fma.f64 a a (.f64 b (+.f64 a b)))) (.f64 (+.f64 a b) (-.f64 b a)))) (neg.f64 (.f64 (fma.f64 a a (.f64 b (+.f64 a b))) (fma.f64 a a (.f64 b (+.f64 a b))))))
(.f64 (/.f64 (.f64 (fma.f64 a a (.f64 b b)) (fma.f64 a a (.f64 b b))) (.f64 (fma.f64 a a (.f64 b b)) (.f64 (+.f64 a b) (-.f64 b a)))) (.f64 (+.f64 a b) (-.f64 b a)))
(.f64 (/.f64 (.f64 (fma.f64 a a (.f64 b b)) (fma.f64 a a (.f64 b b))) (.f64 (-.f64 (.f64 (fma.f64 a a (.f64 b b)) (fma.f64 a a (.f64 b b))) (.f64 a (.f64 b (fma.f64 a a (.f64 b b))))) (fma.f64 a a (.f64 b b)))) (-.f64 (.f64 (fma.f64 a a (.f64 b b)) (fma.f64 a a (.f64 b b))) (.f64 a (.f64 b (fma.f64 a a (.f64 b b))))))
(.f64 (/.f64 (.f64 (fma.f64 a a (.f64 b b)) (fma.f64 a a (.f64 b b))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 a a (*.f64 b b))))
(.f64 (/.f64 (.f64 (fma.f64 a a (.f64 b b)) (fma.f64 a a (.f64 b b))) (.f64 (+.f64 a b) (fma.f64 a (.f64 a a) (.f64 b (.f64 b b))))) (fma.f64 a a (*.f64 b (+.f64 a b))))
(+.f64 #s(literal 0 binary64) (*.f64 b b))
(+.f64 (.f64 b #s(literal 0 binary64)) (.f64 b b))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 b)))
(-.f64 #s(literal 0 binary64) (*.f64 b b))
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 (.f64 b b) (.f64 b b) #s(literal 0 binary64))) (*.f64 b b))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 b b)) (.f64 b b))
(fma.f64 b #s(literal 0 binary64) (*.f64 b b))
(neg.f64 (*.f64 b b))
(/.f64 (.f64 (.f64 b b) (.f64 b b)) (.f64 b b))
(/.f64 (.f64 (.f64 b b) (*.f64 b b)) (fma.f64 b b #s(literal 0 binary64)))
(/.f64 (.f64 b (.f64 b b)) b)
(/.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (fma.f64 (.f64 b b) (*.f64 b b) #s(literal 0 binary64)))
(/.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (neg.f64 (fma.f64 (.f64 b b) (*.f64 b b) #s(literal 0 binary64))))
(/.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 b b) (.f64 b b)) #s(literal 0 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 b b) (.f64 b b) #s(literal 0 binary64)) (.f64 (.f64 b b) (.f64 (.f64 b b) (*.f64 b b)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))))
(pow.f64 b #s(literal 2 binary64))
(pow.f64 (*.f64 b b) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 b)) #s(literal 2 binary64))
(*.f64 b b)
(.f64 (.f64 b b) #s(literal -1 binary64))
(.f64 (.f64 b b) #s(literal 1 binary64))
(.f64 (.f64 (.f64 b b) (.f64 b b)) (/.f64 #s(literal 1 binary64) (*.f64 b b)))
(.f64 (.f64 (.f64 b b) (.f64 (.f64 b b) (.f64 b b))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 b b) (.f64 b b) #s(literal 0 binary64))))
(.f64 #s(literal -1 binary64) (.f64 b b))
(.f64 #s(literal 1 binary64) (.f64 b b))
(*.f64 (exp.f64 (log.f64 b)) (exp.f64 (log.f64 b)))
b
(+.f64 #s(literal 0 binary64) b)
(exp.f64 (*.f64 (log.f64 b) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) b)
(-.f64 (/.f64 #s(literal 0 binary64) b) b)
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 b b #s(literal 0 binary64))) b)
(neg.f64 b)
(/.f64 (*.f64 b b) b)
(/.f64 (.f64 b (.f64 b b)) (fma.f64 b b #s(literal 0 binary64)))
(/.f64 (.f64 b (.f64 b b)) (neg.f64 (fma.f64 b b #s(literal 0 binary64))))
(/.f64 (.f64 b (.f64 b b)) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 b b) #s(literal 0 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 b (*.f64 b b)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 b b #s(literal 0 binary64)) (.f64 b (.f64 b b))))
(pow.f64 b #s(literal 1 binary64))
(*.f64 b #s(literal -1 binary64))
(*.f64 b #s(literal 1 binary64))
(.f64 (.f64 b b) (/.f64 #s(literal 1 binary64) b))
(.f64 (.f64 b (*.f64 b b)) (/.f64 #s(literal 1 binary64) (fma.f64 b b #s(literal 0 binary64))))
(*.f64 #s(literal -1 binary64) b)
(*.f64 #s(literal 1 binary64) b)
(*.f64 (pow.f64 b #s(literal 1/2 binary64)) (pow.f64 b #s(literal 1/2 binary64)))

eval427.0ms (5.8%)

Memory: 22.0MiB live, 173.0MiB allocated
Compiler: Compiled 31 992 to 1 380 computations (95.7% saved)

prune272.0ms (3.7%)

Memory

-22.9MiB live, 201.3MiB allocated

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	1 180	0	1 180
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	1 180	4	1 184

Accuracy

100.0%

Counts

1 184 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.4%	(fma.f64 a a (*.f64 b (neg.f64 b)))
✓	100.0%	(*.f64 (-.f64 a b) (+.f64 a b))
✓	57.7%	#s(approx (- (* a a) (* b b)) (*.f64 a a))
✓	50.2%	#s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b)))

Compiler

Compiled 63 to 29 computations (54% saved)

regimes11.0ms (0.2%)

Memory

13.2MiB live, 13.2MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
#s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b)))
(*.f64 (-.f64 a b) (+.f64 a b))
(-.f64 (.f64 a a) (.f64 b b))
(fma.f64 a a (*.f64 b (neg.f64 b)))

Outputs
(*.f64 (-.f64 a b) (+.f64 a b))

Calls

5 calls:

2.0ms	a
2.0ms	b
2.0ms	(-.f64 (.f64 a a) (.f64 b b))
2.0ms	(*.f64 b b)
2.0ms	(*.f64 a a)

Results

Accuracy	Segments	Branch
100.0%	1	`a`
100.0%	1	`b`
100.0%	1	`(-.f64 (.f64 a a) (.f64 b b))`
100.0%	1	`(*.f64 a a)`
100.0%	1	`(*.f64 b b)`

Compiler

Compiled 25 to 15 computations (40% saved)

regimes10.0ms (0.1%)

Memory

-32.4MiB live, 10.0MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
#s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b)))

Outputs
#s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b)))
#s(approx (- (* a a) (* b b)) (*.f64 a a))

Calls

5 calls:

4.0ms	b
2.0ms	a
1.0ms	(-.f64 (.f64 a a) (.f64 b b))
1.0ms	(*.f64 b b)
1.0ms	(*.f64 a a)

Results

Accuracy	Segments	Branch
82.6%	2	`a`
79.0%	2	`b`
97.9%	2	`(-.f64 (.f64 a a) (.f64 b b))`
82.6%	2	`(*.f64 a a)`
79.0%	2	`(*.f64 b b)`

Compiler

Compiled 25 to 15 computations (40% saved)

regimes6.0ms (0.1%)

Memory

9.8MiB live, 9.8MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))

Outputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))

Calls

5 calls:

1.0ms	a
1.0ms	b
1.0ms	(-.f64 (.f64 a a) (.f64 b b))
1.0ms	(*.f64 b b)
1.0ms	(*.f64 a a)

Results

Accuracy	Segments	Branch
57.7%	1	`b`
57.7%	1	`(*.f64 b b)`
57.7%	1	`a`
57.7%	1	`(*.f64 a a)`
57.7%	1	`(-.f64 (.f64 a a) (.f64 b b))`

Compiler

Compiled 25 to 15 computations (40% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-4.419245205073925e-280	0.0

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify6.0ms (0.1%)

Memory

6.5MiB live, 6.5MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	51
1	29	51
2	35	51
3	38	51
4	39	51

Stop Event

1×

saturated

Calls

Call 1

Inputs

(*.f64 (-.f64 a b) (+.f64 a b))

(if (<=.f64 (-.f64 (*.f64 a a) (*.f64 b b)) #s(literal -2043740476963553/5109351192408882717840314145374306729132675226714771306246520940639262443184548008409492391661147394788716663921132787824569441250287599771492279803609168436019214522754779331884896566897569247187592593266032445422926874765109428195555469487226993043218229521601935466604437747789680665415385088 binary64)) #s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b))) #s(approx (- (* a a) (* b b)) (*.f64 a a)))

#s(approx (- (* a a) (* b b)) (*.f64 a a))

Outputs

(*.f64 (-.f64 a b) (+.f64 a b))

(if (<=.f64 (-.f64 (*.f64 a a) (*.f64 b b)) #s(literal -2043740476963553/5109351192408882717840314145374306729132675226714771306246520940639262443184548008409492391661147394788716663921132787824569441250287599771492279803609168436019214522754779331884896566897569247187592593266032445422926874765109428195555469487226993043218229521601935466604437747789680665415385088 binary64)) #s(approx (- (* a a) (* b b)) (neg.f64 (*.f64 b b))) #s(approx (- (* a a) (* b b)) (*.f64 a a)))

#s(approx (- (* a a) (* b b)) (*.f64 a a))

soundness585.0ms (8%)

Memory

11.1MiB live, 166.1MiB 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	5	13
0	8	13
1	32	13
2	216	13
3	1967	13
0	8778	13
0	17	219
1	39	219
2	113	219
3	468	219
4	1684	219
5	2832	219
6	4991	219
0	8406	219

Stop Event

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

Compiler

Compiled 64 to 30 computations (53.1% saved)

preprocess34.0ms (0.5%)

Memory

4.2MiB live, 80.3MiB allocated

Remove

(abs a)

(abs b)

Compiler

Compiled 136 to 64 computations (52.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

sample654.0ms (8.9%)

preprocess755.0ms (10.3%)

explain61.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify831.0ms (11.3%)

localize16.0ms (0.2%)

series3.0ms (0%)

simplify425.0ms (5.8%)

rewrite460.0ms (6.2%)

eval42.0ms (0.6%)

prune40.0ms (0.5%)

simplify1.1s (14.8%)

localize62.0ms (0.8%)

series8.0ms (0.1%)

simplify453.0ms (6.2%)

rewrite1.1s (15.1%)

eval427.0ms (5.8%)

prune272.0ms (3.7%)

regimes11.0ms (0.2%)

regimes10.0ms (0.1%)

regimes6.0ms (0.1%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

soundness585.0ms (8%)

preprocess34.0ms (0.5%)

end0.0ms (0%)

Profiling