Metrics for Expression 4, p15

start0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated

analyze19.0ms (0.5%)

Memory

-12.0MiB live, 26.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	0%	100%	0%	0%	0%	0
0%	0%	0%	100%	0%	0%	0%	1
0%	0%	0%	100%	0%	0%	0%	2
50%	0%	0%	100%	0%	0%	0%	3
50%	0%	0%	100%	0%	0%	0%	4
75%	0%	0%	100%	0%	0%	0%	5
75%	0%	0%	100%	0%	0%	0%	6
87.5%	0%	0%	100%	0%	0%	0%	7
87.5%	0%	0%	100%	0%	0%	0%	8
93.8%	0%	0%	100%	0%	0%	0%	9
93.8%	0%	0%	100%	0%	0%	0%	10
96.9%	0%	0%	100%	0%	0%	0%	11
96.9%	0%	0%	100%	0%	0%	0%	12

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample1.1s (31.1%)

Memory

41.9MiB live, 1 442.0MiB allocated

Samples

649.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 435.0ms

const: 158.0ms (36.4% of total)

ival-<=: 136.0ms (31.3% of total)

ival-mult: 51.0ms (11.7% of total)

ival-add: 49.0ms (11.3% of total)

ival-and: 24.0ms (5.5% of total)

exact: 14.0ms (3.2% of total)

ival-assert: 3.0ms (0.7% of total)

Bogosity

explain130.0ms (3.5%)

Memory

-24.5MiB live, 61.6MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(+.f64 a b)`
-	-	`(*.f64 (+.f64 a b) (+.f64 a b))`
-	-	`a`
-	-	`b`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

17.0ms

512×

valid

Compiler

Compiled 35 to 16 computations (54.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-add: 3.0ms (47.3% of total)

ival-mult: 3.0ms (47.3% of total)

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

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

preprocess81.0ms (2.2%)

Memory

22.3MiB live, 60.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	50	35
2	210	35
3	533	35
4	1075	35
5	1970	35
6	2756	35
7	2900	35
8	2900	35
9	2900	35
10	2942	35
11	2958	35
0	4	7
0	6	7
1	13	7
2	29	7
3	57	7
4	80	7
5	96	7
6	105	7
7	111	7
0	111	7

Stop Event

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

Calls

Call 1

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

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

Symmetry

(sort a b)

Compiler

Compiled 7 to 4 computations (42.9% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 (+.f64 a b) (+.f64 a b))

Compiler

Compiled 7 to 4 computations (42.9% saved)

simplify4.0ms (0.1%)

Memory

11.2MiB live, 11.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	12
0	6	12
1	13	12
2	29	12
3	57	12
4	80	12
5	96	12
6	105	12
7	111	12
0	111	12

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize15.0ms (0.4%)

Memory

-3.5MiB live, 34.2MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 a b)
accuracy	0.0234375	(*.f64 (+.f64 a b) (+.f64 a b))

Samples

11.0ms

256×

valid

Compiler

Compiled 14 to 6 computations (57.1% saved)

Precisions

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

ival-mult: 3.0ms (63.8% of total)

ival-add: 1.0ms (21.3% of total)

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

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

series3.0ms (0.1%)

Memory

8.1MiB live, 8.1MiB allocated

Counts

2 → 48

Calls

Call 1

Inputs
#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>) () ())

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

Calls

6 calls:

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

simplify105.0ms (2.8%)

Memory

-3.9MiB live, 158.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	270
1	193	264
2	488	264
3	1576	252
4	3881	252
5	6929	252
0	8083	222

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 42

Calls

Call 1

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

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

rewrite430.0ms (11.7%)

Memory

2.0MiB live, 315.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	6	8
1	28	8
2	220	8
3	2817	8
0	9151	8

Stop Event

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

Counts

2 → 989

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval325.0ms (8.8%)

Memory: -21.5MiB live, 334.9MiB allocated
Compiler: Compiled 43 687 to 2 966 computations (93.2% saved)

prune20.0ms (0.5%)

Memory

22.9MiB live, 72.2MiB allocated

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	1 138	3	1 141
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	1 138	4	1 142

Accuracy

100.0%

Counts

1 142 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 (+.f64 b a) a (*.f64 (+.f64 b a) b))
✓	100.0%	(*.f64 (+.f64 a b) (+.f64 a b))
▶	99.7%	#s(approx (* (+ a b) (+ a b)) (*.f64 (fma.f64 #s(literal 2 binary64) a b) b))
▶	98.8%	#s(approx (* (+ a b) (+ a b)) (*.f64 b b))

Compiler

Compiled 28 to 19 computations (32.1% saved)

simplify8.0ms (0.2%)

Memory

-27.7MiB live, 11.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (+.f64 b a) b)
cost-diff	0	(+.f64 b a)
cost-diff	384	(fma.f64 (+.f64 b a) a (*.f64 (+.f64 b a) b))
cost-diff	0	(fma.f64 #s(literal 2 binary64) a b)
cost-diff	0	(*.f64 (fma.f64 #s(literal 2 binary64) a b) b)
cost-diff	0	#s(approx (* (+ a b) (+ a b)) (*.f64 (fma.f64 #s(literal 2 binary64) a b) b))
cost-diff	0	(*.f64 b b)
cost-diff	0	#s(approx (* (+ a b) (+ a b)) (*.f64 b b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	62
0	21	59
1	36	59
2	53	59
3	88	59
4	113	59
5	128	59
6	139	59
0	139	59

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (* (+ a b) (+ a b)) (*.f64 b b))
(*.f64 b b)
b
#s(approx (* (+ a b) (+ a b)) (*.f64 (fma.f64 #s(literal 2 binary64) a b) b))
(*.f64 (fma.f64 #s(literal 2 binary64) a b) b)
(fma.f64 #s(literal 2 binary64) a b)
#s(literal 2 binary64)
a
b
(fma.f64 (+.f64 b a) a (*.f64 (+.f64 b a) b))
(+.f64 b a)
b
a
(*.f64 (+.f64 b a) b)

Outputs
#s(approx (* (+ a b) (+ a b)) (*.f64 b b))
(*.f64 b b)
b
#s(approx (* (+ a b) (+ a b)) (*.f64 (fma.f64 #s(literal 2 binary64) a b) b))
(*.f64 (fma.f64 #s(literal 2 binary64) a b) b)
(fma.f64 #s(literal 2 binary64) a b)
#s(literal 2 binary64)
a
b
(fma.f64 (+.f64 b a) a (*.f64 (+.f64 b a) b))
(*.f64 (+.f64 b a) (+.f64 b a))
(+.f64 b a)
b
a
(*.f64 (+.f64 b a) b)

localize37.0ms (1%)

Memory

-2.3MiB live, 74.6MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 b a)
accuracy	0.015625	(fma.f64 (+.f64 b a) a (*.f64 (+.f64 b a) b))
accuracy	0.015625	(*.f64 (+.f64 b a) b)
accuracy	0	(fma.f64 #s(literal 2 binary64) a b)
accuracy	0.0078125	(*.f64 (fma.f64 #s(literal 2 binary64) a b) b)
accuracy	0.21146014436971716	#s(approx (* (+ a b) (+ a b)) (*.f64 (fma.f64 #s(literal 2 binary64) a b) b))
accuracy	0	(*.f64 b b)
accuracy	0.7820666924352742	#s(approx (* (+ a b) (+ a b)) (*.f64 b b))

Samples

27.0ms

256×

valid

Compiler

Compiled 56 to 15 computations (73.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-mult: 12.0ms (67.2% of total)

ival-add: 5.0ms (28% of total)

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

exact: 0.0ms (0% of total)

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

series10.0ms (0.3%)

Memory

24.6MiB live, 24.6MiB allocated

Counts

8 → 180

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	b	@	inf	((* (+ a b) (+ a b)) (* b b) (* (+ a b) (+ a b)) (* (+ (* 2 a) b) b) (+ (* 2 a) b) (+ (* (+ b a) a) (* (+ b a) b)) (+ b a) (* (+ b a) b))
1.0ms	b	@	-inf	((* (+ a b) (+ a b)) (* b b) (* (+ a b) (+ a b)) (* (+ (* 2 a) b) b) (+ (* 2 a) b) (+ (* (+ b a) a) (* (+ b a) b)) (+ b a) (* (+ b a) b))
1.0ms	b	@	0	((* (+ a b) (+ a b)) (* b b) (* (+ a b) (+ a b)) (* (+ (* 2 a) b) b) (+ (* 2 a) b) (+ (* (+ b a) a) (* (+ b a) b)) (+ b a) (* (+ b a) b))
1.0ms	a	@	inf	((* (+ a b) (+ a b)) (* b b) (* (+ a b) (+ a b)) (* (+ (* 2 a) b) b) (+ (* 2 a) b) (+ (* (+ b a) a) (* (+ b a) b)) (+ b a) (* (+ b a) b))
1.0ms	a	@	-inf	((* (+ a b) (+ a b)) (* b b) (* (+ a b) (+ a b)) (* (+ (* 2 a) b) b) (+ (* 2 a) b) (+ (* (+ b a) a) (* (+ b a) b)) (+ b a) (* (+ b a) b))

simplify197.0ms (5.3%)

Memory

7.4MiB live, 125.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	88	1050
1	279	1032
2	741	1032
3	2150	1032
4	4783	1032
0	8093	906

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 171

Calls

Call 1

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

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

rewrite260.0ms (7%)

Memory

-18.5MiB live, 268.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	56
0	21	47
1	79	47
2	658	47
0	8350	47

Stop Event

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

Counts

8 → 754

Calls

Call 1

Inputs
#s(approx (* (+ a b) (+ a b)) (*.f64 b b))
(*.f64 b b)
#s(approx (* (+ a b) (+ a b)) (*.f64 (fma.f64 #s(literal 2 binary64) a b) b))
(*.f64 (fma.f64 #s(literal 2 binary64) a b) b)
(fma.f64 #s(literal 2 binary64) a b)
(fma.f64 (+.f64 b a) a (*.f64 (+.f64 b a) b))
(+.f64 b a)
(*.f64 (+.f64 b a) b)

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval143.0ms (3.9%)

Memory: 2.5MiB live, 305.2MiB allocated
Compiler: Compiled 26 146 to 2 295 computations (91.2% saved)

prune17.0ms (0.5%)

Memory

21.0MiB live, 59.8MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	1 053	1	1 054
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	1 053	5	1 058

Accuracy

100.0%

Counts

1 058 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (+.f64 b a) a (*.f64 (+.f64 b a) b))
✓	100.0%	(*.f64 (+.f64 a b) (+.f64 a b))
▶	99.7%	#s(approx (* (+ a b) (+ a b)) (fma.f64 (.f64 b a) #s(literal 2 binary64) (.f64 b b)))
✓	99.7%	#s(approx (* (+ a b) (+ a b)) (*.f64 (fma.f64 #s(literal 2 binary64) a b) b))
✓	98.8%	#s(approx (* (+ a b) (+ a b)) (*.f64 b b))

Compiler

Compiled 37 to 26 computations (29.7% saved)

simplify5.0ms (0.1%)

Memory

6.5MiB live, 6.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
0	13	33
1	25	31
2	43	31
3	62	31
4	85	31
5	100	31
6	110	31
0	110	29

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (* (+ a b) (+ a b)) (fma.f64 (.f64 b a) #s(literal 2 binary64) (.f64 b b)))
(fma.f64 (.f64 b a) #s(literal 2 binary64) (.f64 b b))
(*.f64 b a)
b
a
#s(literal 2 binary64)
(*.f64 b b)

Outputs
#s(approx (* (+ a b) (+ a b)) (fma.f64 (.f64 b a) #s(literal 2 binary64) (.f64 b b)))
#s(approx (* (+ a b) (+ a b)) (*.f64 (fma.f64 #s(literal 2 binary64) a b) b))
(fma.f64 (.f64 b a) #s(literal 2 binary64) (.f64 b b))
(*.f64 (fma.f64 #s(literal 2 binary64) a b) b)
(*.f64 b a)
b
a
#s(literal 2 binary64)
(*.f64 b b)

localize22.0ms (0.6%)

Memory

-2.8MiB live, 35.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 b b)
accuracy	0	(*.f64 b a)
accuracy	0.0078125	(fma.f64 (.f64 b a) #s(literal 2 binary64) (.f64 b b))
accuracy	0.21146014436971716	#s(approx (* (+ a b) (+ a b)) (fma.f64 (.f64 b a) #s(literal 2 binary64) (.f64 b b)))

Samples

16.0ms

256×

valid

Compiler

Compiled 27 to 11 computations (59.3% saved)

Precisions

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

ival-mult: 6.0ms (65.4% of total)

ival-add: 3.0ms (32.7% of total)

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

exact: 0.0ms (0% of total)

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

series10.0ms (0.3%)

Memory

-33.2MiB live, 11.3MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	a	@	0	((+ (* (* b a) 2) (* b b)) (* (+ a b) (+ a b)) (* b a) (* b b))
1.0ms	b	@	-inf	((+ (* (* b a) 2) (* b b)) (* (+ a b) (+ a b)) (* b a) (* b b))
1.0ms	b	@	inf	((+ (* (* b a) 2) (* b b)) (* (+ a b) (+ a b)) (* b a) (* b b))
1.0ms	b	@	0	((+ (* (* b a) 2) (* b b)) (* (+ a b) (+ a b)) (* b a) (* b b))
1.0ms	a	@	-inf	((+ (* (* b a) 2) (* b b)) (* (+ a b) (+ a b)) (* b a) (* b b))

simplify106.0ms (2.9%)

Memory

32.9MiB live, 106.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

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

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

rewrite157.0ms (4.2%)

Memory

-2.9MiB live, 155.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	30
0	13	28
1	51	26
2	397	26
3	4767	26
0	8344	24

Stop Event

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

Counts

4 → 108

Calls

Call 1

Inputs
(fma.f64 (.f64 b a) #s(literal 2 binary64) (.f64 b b))
#s(approx (* (+ a b) (+ a b)) (fma.f64 (.f64 b a) #s(literal 2 binary64) (.f64 b b)))
(*.f64 b a)
(*.f64 b b)

Outputs
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eval22.0ms (0.6%)

Memory: 6.7MiB live, 43.6MiB allocated
Compiler: Compiled 3 425 to 433 computations (87.4% saved)

prune19.0ms (0.5%)

Memory

-12.8MiB live, 34.9MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	192	5	197

Accuracy

100.0%

Counts

197 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 (+.f64 b a) a (*.f64 (+.f64 b a) b))
✓	100.0%	(*.f64 (+.f64 a b) (+.f64 a b))
✓	99.7%	#s(approx (* (+ a b) (+ a b)) (fma.f64 (.f64 b a) #s(literal 2 binary64) (.f64 b b)))
✓	99.7%	#s(approx (* (+ a b) (+ a b)) (*.f64 (fma.f64 #s(literal 2 binary64) a b) b))
✓	98.8%	#s(approx (* (+ a b) (+ a b)) (*.f64 b b))

Compiler

Compiled 74 to 42 computations (43.2% saved)

regimes11.0ms (0.3%)

Memory

-14.7MiB live, 23.8MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (* (+ a b) (+ a b)) (*.f64 b b))
#s(approx (* (+ a b) (+ a b)) (*.f64 (fma.f64 #s(literal 2 binary64) a b) b))
(*.f64 (+.f64 a b) (+.f64 a b))
#s(approx (* (+ a b) (+ a b)) (fma.f64 (.f64 b a) #s(literal 2 binary64) (.f64 b b)))
(fma.f64 (+.f64 b a) a (*.f64 (+.f64 b a) b))

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

Calls

4 calls:

3.0ms	a
2.0ms	(+.f64 a b)
2.0ms	(*.f64 (+.f64 a b) (+.f64 a b))
2.0ms	b

Results

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

Compiler

Compiled 12 to 11 computations (8.3% saved)

regimes6.0ms (0.2%)

Memory

15.6MiB live, 15.6MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (* (+ a b) (+ a b)) (*.f64 b b))
#s(approx (* (+ a b) (+ a b)) (*.f64 (fma.f64 #s(literal 2 binary64) a b) b))

Outputs
#s(approx (* (+ a b) (+ a b)) (*.f64 (fma.f64 #s(literal 2 binary64) a b) b))

Calls

4 calls:

2.0ms	(+.f64 a b)
2.0ms	(*.f64 (+.f64 a b) (+.f64 a b))
2.0ms	b
1.0ms	a

Results

Accuracy	Segments	Branch
99.7%	1	`a`
99.7%	1	`b`
99.7%	1	`(*.f64 (+.f64 a b) (+.f64 a b))`
99.7%	1	`(+.f64 a b)`

Compiler

Compiled 12 to 11 computations (8.3% saved)

regimes5.0ms (0.1%)

Memory

13.9MiB live, 13.9MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
98.8%	1	`a`
98.8%	1	`b`
98.8%	1	`(*.f64 (+.f64 a b) (+.f64 a b))`
98.8%	1	`(+.f64 a b)`

Compiler

Compiled 12 to 11 computations (8.3% saved)

simplify27.0ms (0.7%)

Memory

-11.2MiB live, 62.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	32
1	14	32

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 (+.f64 a b) (+.f64 a b))
#s(approx (* (+ a b) (+ a b)) (*.f64 (fma.f64 #s(literal 2 binary64) a b) b))
#s(approx (* (+ a b) (+ a b)) (*.f64 b b))

Outputs
(*.f64 (+.f64 a b) (+.f64 a b))
(*.f64 (+.f64 b a) (+.f64 b a))
#s(approx (* (+ a b) (+ a b)) (*.f64 (fma.f64 #s(literal 2 binary64) a b) b))
#s(approx (* (+ a b) (+ a b)) (*.f64 b b))

soundness289.0ms (7.8%)

Memory

-9.1MiB live, 145.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	270
1	193	264
2	488	264
3	1576	252
4	3881	252
5	6929	252
0	8083	222

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 27 to 18 computations (33.3% saved)

preprocess60.0ms (1.6%)

Memory: 7.1MiB live, 92.5MiB allocated
Remove: (sort a b)
Compiler: Compiled 108 to 60 computations (44.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze19.0ms (0.5%)

sample1.1s (31.1%)

explain130.0ms (3.5%)

preprocess81.0ms (2.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize15.0ms (0.4%)

series3.0ms (0.1%)

simplify105.0ms (2.8%)

rewrite430.0ms (11.7%)

eval325.0ms (8.8%)

prune20.0ms (0.5%)

simplify8.0ms (0.2%)

localize37.0ms (1%)

series10.0ms (0.3%)

simplify197.0ms (5.3%)

rewrite260.0ms (7%)

eval143.0ms (3.9%)

prune17.0ms (0.5%)

simplify5.0ms (0.1%)

localize22.0ms (0.6%)

series10.0ms (0.3%)

simplify106.0ms (2.9%)

rewrite157.0ms (4.2%)

eval22.0ms (0.6%)

prune19.0ms (0.5%)

regimes11.0ms (0.3%)

regimes6.0ms (0.2%)

regimes5.0ms (0.1%)

simplify27.0ms (0.7%)

soundness289.0ms (7.8%)

preprocess60.0ms (1.6%)

end0.0ms (0%)

Profiling