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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory

1.9MiB live, 1.9MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample583.0ms (10.4%)

Memory

13.3MiB live, 773.8MiB allocated

Samples

362.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 190.0ms

ival-div: 110.0ms (57.8% of total)

ival-sub: 67.0ms (35.2% of total)

ival-true: 6.0ms (3.2% of total)

exact: 4.0ms (2.1% of total)

ival-assert: 3.0ms (1.6% of total)

Bogosity

explain47.0ms (0.8%)

Memory

-4.3MiB live, 74.0MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(/.f64 x (-.f64 #s(literal 1 binary64) x))`
-	-	`(-.f64 #s(literal 1 binary64) x)`
-	-	`#s(literal 1 binary64)`
-	-	`x`

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

22.0ms

512×

valid

Compiler

Compiled 30 to 16 computations (46.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-div: 4.0ms (54.3% of total)

ival-sub: 3.0ms (40.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess21.0ms (0.4%)

Memory

14.8MiB live, 14.8MiB allocated

Algorithm

1×	egg-herbie

Rules

44×	`associate-l`
42×	`times-frac`
36×	`lower-+.f64`
36×	`lower-+.f32`
34×	`unsub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	20	11
2	47	10
3	100	10
4	195	10
5	284	10
6	295	10
7	309	10
8	322	10
0	4	5
0	6	5
1	10	5
2	14	5
3	19	5
4	26	5
5	36	5
6	51	5
7	74	5
8	96	5
9	104	5
10	106	5
0	106	5

Stop Event

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

Calls

Call 1

Inputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))

Outputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))

Compiler

Compiled 6 to 4 computations (33.3% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify6.0ms (0.1%)

Memory

3.6MiB live, 3.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(-.f64 #s(literal 1 binary64) x)
cost-diff	0	(/.f64 x (-.f64 #s(literal 1 binary64) x))

Rules

36×	`lower-+.f64`
36×	`lower-+.f32`
26×	`sub-neg`
26×	`lower--.f32`
24×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	6	10
1	10	10
2	14	10
3	19	10
4	26	10
5	36	10
6	51	10
7	74	10
8	96	10
9	104	10
10	106	10
0	106	10

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
x
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)

Outputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
x
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)

localize87.0ms (1.6%)

Memory

-10.7MiB live, 27.8MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(-.f64 #s(literal 1 binary64) x)
accuracy	0.01171875	(/.f64 x (-.f64 #s(literal 1 binary64) x))

Samples

82.0ms

256×

valid

Compiler

Compiled 12 to 6 computations (50% saved)

Precisions

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

ival-div: 3.0ms (59.1% of total)

ival-sub: 1.0ms (19.7% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

3.2MiB live, 3.2MiB allocated

Counts

2 → 24

Calls

Call 1

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

Inputs

#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())

#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())

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

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(/ x (- 1 x))
0.0ms	x	@	inf	(- 1 x)
0.0ms	x	@	-inf	(/ x (- 1 x))
0.0ms	x	@	0	(/ x (- 1 x))
0.0ms	x	@	-inf	(- 1 x)

simplify173.0ms (3.1%)

Memory

-27.4MiB live, 130.5MiB allocated

Algorithm

1×	egg-herbie

Rules

4 624×	`lower-fma.f64`
4 624×	`lower-fma.f32`
1 550×	`unsub-neg`
1 096×	`lower-*.f64`
1 096×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	135
1	93	120
2	220	114
3	546	112
4	1048	112
5	1960	112
6	3386	112
7	4530	112
8	4646	112
9	4646	112
10	4808	112
11	4883	112
12	4883	112
0	4883	109

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 23

Calls

Call 1

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

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

rewrite245.0ms (4.4%)

Memory

-1.1MiB live, 367.2MiB allocated

Rules

3 858×	`lower-/.f32`
3 856×	`lower-/.f64`
3 778×	`lower-fma.f64`
3 778×	`lower-fma.f32`
2 920×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	29	8
2	183	8
3	1612	8
0	9347	8

Stop Event

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

Counts

2 → 425

Calls

Call 1

Inputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)

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

eval55.0ms (1%)

Memory: 35.5MiB live, 107.8MiB allocated
Compiler: Compiled 12 167 to 1 267 computations (89.6% saved)

prune77.0ms (1.4%)

Memory

-9.1MiB live, 144.5MiB allocated

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	444	4	448
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	444	5	449

Accuracy

100.0%

Counts

449 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))
▶	99.9%	(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
▶	45.7%	#s(approx (/ x (- 1 x)) (fma.f64 x (fma.f64 x x x) x))
▶	44.7%	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
▶	55.7%	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Compiler

Compiled 32 to 17 computations (46.9% saved)

simplify76.0ms (1.4%)

Memory

0.8MiB live, 39.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

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

Rules

880×	`lower-fma.f32`
876×	`lower-fma.f64`
376×	`lower-*.f64`
376×	`lower-*.f32`
232×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	66
0	20	66
1	34	66
2	53	66
3	77	66
4	98	66
5	144	66
6	174	66
7	284	66
8	501	66
9	622	66
10	794	66
11	1007	66
12	1110	66
13	1177	66
14	1195	66
15	1209	66
16	1222	66
17	1231	66
18	1240	66
19	1247	66
20	1252	66
21	1253	66
0	1253	66

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize71.0ms (1.3%)

Memory

-25.3MiB live, 72.2MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal 1 binary64) x)
accuracy	0	(+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64))
accuracy	0.0546875	(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
accuracy	0	(fma.f64 x x x)
accuracy	0.04296875	(fma.f64 x (fma.f64 x x x) x)
accuracy	34.73435747975013	#s(approx (/ x (- 1 x)) (fma.f64 x (fma.f64 x x x) x))
accuracy	0	(fma.f64 x x x)
accuracy	35.392777684387546	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
accuracy	28.326477140467784	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Samples

51.0ms

256×

valid

Compiler

Compiled 57 to 14 computations (75.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-div: 21.0ms (49.5% of total)

ival-add: 16.0ms (37.7% of total)

ival-mult: 3.0ms (7.1% of total)

ival-sub: 2.0ms (4.7% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

12.6MiB live, 12.6MiB allocated

Counts

8 → 96

Calls

Call 1

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

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

Calls

24 calls:

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

simplify313.0ms (5.6%)

Memory

0.5MiB live, 344.1MiB allocated

Algorithm

1×	egg-herbie

Rules

17 584×	`lower-fma.f64`
17 584×	`lower-fma.f32`
2 894×	`lower-*.f64`
2 894×	`lower-*.f32`
1 936×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	607
1	116	574
2	306	546
3	968	538
4	3364	538
5	7050	538
0	8588	502

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 90

Calls

Call 1

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

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

rewrite715.0ms (12.7%)

Memory

22.0MiB live, 380.4MiB allocated

Rules

7 438×	`lower-fma.f32`
7 434×	`lower-fma.f64`
4 404×	`lower-*.f64`
4 404×	`lower-*.f32`
3 940×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	56
0	20	54
1	97	54
2	680	54
3	7987	54
0	8665	53

Stop Event

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

Counts

8 → 612

Calls

Call 1

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

Outputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) (fma.f64 x x x))
(+.f64 x (*.f64 x x))
(+.f64 (*.f64 x x) x)
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) x)) (neg.f64 (.f64 x (/.f64 x (-.f64 (.f64 x x) x)))))
(-.f64 (*.f64 x x) (neg.f64 x))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) x)) (.f64 x (/.f64 x (-.f64 (.f64 x x) x))))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 x x))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 x (.f64 x x))))
(fma.f64 x x x)
(fma.f64 x #s(literal 1 binary64) (*.f64 x x))
(fma.f64 x (/.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 x x) x)) (neg.f64 (.f64 x (/.f64 x (-.f64 (*.f64 x x) x)))))
(fma.f64 #s(literal 1 binary64) x (*.f64 x x))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) x)
(fma.f64 #s(literal -1 binary64) (neg.f64 x) (*.f64 x x))
(fma.f64 #s(literal -1 binary64) (*.f64 x (neg.f64 x)) x)
(fma.f64 (*.f64 x x) #s(literal 1 binary64) x)
(fma.f64 (.f64 x x) (.f64 x (/.f64 x (-.f64 (.f64 x x) x))) (neg.f64 (.f64 x (/.f64 x (-.f64 (*.f64 x x) x)))))
(fma.f64 (neg.f64 x) #s(literal -1 binary64) (*.f64 x x))
(fma.f64 (neg.f64 x) (neg.f64 x) x)
(fma.f64 (.f64 x (.f64 x x)) (/.f64 x (-.f64 (.f64 x x) x)) (neg.f64 (.f64 x (/.f64 x (-.f64 (*.f64 x x) x)))))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) x)) (neg.f64 (.f64 x (/.f64 x (-.f64 (.f64 x x) x)))))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (*.f64 x x))
(fma.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (-.f64 (.f64 x (.f64 x x)) x))) (fma.f64 x x x) (neg.f64 (.f64 x (/.f64 x (-.f64 (.f64 x x) x)))))
(fma.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 x (.f64 x x))) x))) (.f64 x (fma.f64 x (fma.f64 x x x) x)) (neg.f64 (.f64 x (/.f64 x (-.f64 (*.f64 x x) x)))))
(neg.f64 (/.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) x)) (neg.f64 (fma.f64 x (.f64 x (-.f64 (.f64 x x) x)) (*.f64 x x)))))
(neg.f64 (/.f64 (.f64 x (-.f64 (.f64 x (*.f64 x x)) x)) (fma.f64 x (neg.f64 x) x)))
(neg.f64 (/.f64 (neg.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) x))) (fma.f64 x (.f64 x (-.f64 (.f64 x x) x)) (*.f64 x x))))
(neg.f64 (/.f64 (.f64 (fma.f64 x x x) (fma.f64 x (neg.f64 x) x)) (-.f64 (.f64 x x) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 x x)) (.f64 x (-.f64 x (.f64 x (.f64 x x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x x))))
(/.f64 (fma.f64 x x x) #s(literal 1 binary64))
(/.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) x)) (fma.f64 x (.f64 x (-.f64 (.f64 x x) x)) (*.f64 x x)))
(/.f64 (.f64 x (-.f64 (.f64 x (.f64 x x)) x)) (-.f64 (.f64 x x) x))
(/.f64 (+.f64 x #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) x))) (neg.f64 (fma.f64 x (.f64 x (-.f64 (.f64 x x) x)) (*.f64 x x))))
(/.f64 (*.f64 (fma.f64 x x x) (fma.f64 x (neg.f64 x) x)) (fma.f64 x (neg.f64 x) x))
(/.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 (fma.f64 x (.f64 x (-.f64 (.f64 x x) x)) (.f64 x x)) (fma.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))))
(/.f64 (.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) x)) (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 x (.f64 x x))) x))) (.f64 (fma.f64 x (.f64 x (-.f64 (.f64 x x) x)) (.f64 x x)) (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 x (*.f64 x x))) x))))
(/.f64 (.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) x)) (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 x (.f64 x x))) x))) (.f64 (-.f64 (.f64 x x) x) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x x) x)) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))))
(/.f64 (.f64 x (-.f64 x (.f64 x (.f64 x x)))) (-.f64 x (.f64 x x)))
(/.f64 (.f64 (.f64 x (fma.f64 x (.f64 x x) x)) (.f64 x (-.f64 (.f64 x (.f64 x x)) x))) (.f64 (-.f64 (.f64 x x) x) (.f64 x (fma.f64 x (.f64 x x) x))))
(/.f64 (*.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) x)) (.f64 (-.f64 (.f64 x x) x) (.f64 x x))) (.f64 (-.f64 (.f64 x x) x) (-.f64 (*.f64 x x) x)))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) x))) (fma.f64 x (.f64 x (-.f64 (.f64 x x) x)) (.f64 x x)))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 x (-.f64 (.f64 x (.f64 x x)) x))) (-.f64 (*.f64 x x) x))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) x)))) (neg.f64 (fma.f64 x (.f64 x (-.f64 (.f64 x x) x)) (.f64 x x))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x x) (fma.f64 x (neg.f64 x) x))) (fma.f64 x (neg.f64 x) x))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 x (-.f64 x (.f64 x (.f64 x x))))) (-.f64 x (*.f64 x x)))
(/.f64 (.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) x)) #s(literal 1 binary64)) (fma.f64 x (.f64 x (-.f64 (.f64 x x) x)) (.f64 x x)))
(/.f64 (.f64 (.f64 x (-.f64 (.f64 x (.f64 x x)) x)) #s(literal 1 binary64)) (-.f64 (*.f64 x x) x))
(/.f64 (.f64 (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (fma.f64 x (.f64 x (-.f64 (.f64 x x) x)) (*.f64 x x))))
(/.f64 (.f64 (.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) x)) (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 x (.f64 x x))) x))) #s(literal 1 binary64)) (.f64 (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 x (.f64 x x))) x)) (fma.f64 x (.f64 x (-.f64 (.f64 x x) x)) (.f64 x x))))
(/.f64 (.f64 (.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) x)) (.f64 (.f64 x x) (-.f64 (.f64 x (.f64 x (.f64 x x))) x))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x x) x)) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (-.f64 (*.f64 x x) x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (neg.f64 x)) #s(literal -1 binary64))
(/.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 x (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(/.f64 (.f64 x (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (*.f64 #s(literal 1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
(/.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (+.f64 x #s(literal -1 binary64)))
(/.f64 (.f64 x (fma.f64 x x #s(literal -1 binary64))) (.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(/.f64 (.f64 (.f64 (.f64 x (fma.f64 x (.f64 x x) x)) (.f64 x (-.f64 (.f64 x (.f64 x x)) x))) #s(literal 1 binary64)) (.f64 (.f64 x (fma.f64 x (.f64 x x) x)) (-.f64 (*.f64 x x) x)))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
(/.f64 (.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -1 binary64))) (.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64))))
(/.f64 (.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 x #s(literal -1 binary64)))
(/.f64 (.f64 (neg.f64 x) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) (*.f64 #s(literal -1 binary64) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x)))
(/.f64 (*.f64 (neg.f64 x) (fma.f64 x x #s(literal -1 binary64))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x) (-.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (neg.f64 x)) (+.f64 x #s(literal -1 binary64)))
(/.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) x) (-.f64 (fma.f64 x x #s(literal 1 binary64)) x))
(/.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) x) (*.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x) #s(literal 1 binary64)))
(/.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 (fma.f64 x (.f64 x x) #s(literal 1 binary64)) (neg.f64 x)) (*.f64 (-.f64 (fma.f64 x x #s(literal 1 binary64)) x) #s(literal -1 binary64)))
(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) x) (+.f64 x #s(literal -1 binary64)))
(/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) x) (.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))
(/.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (neg.f64 x)) (.f64 (+.f64 x #s(literal -1 binary64)) #s(literal -1 binary64)))
(/.f64 (neg.f64 (neg.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) x)))) (neg.f64 (neg.f64 (fma.f64 x (.f64 x (-.f64 (.f64 x x) x)) (*.f64 x x)))))
(/.f64 (neg.f64 (*.f64 (fma.f64 x x x) (fma.f64 x (neg.f64 x) x))) (neg.f64 (fma.f64 x (neg.f64 x) x)))
(/.f64 (neg.f64 (.f64 x (-.f64 x (.f64 x (.f64 x x))))) (neg.f64 (-.f64 x (.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (neg.f64 (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x (-.f64 (.f64 x x) x)) (.f64 x x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) x)) #s(literal 3 binary64)) (pow.f64 (.f64 x (/.f64 x (-.f64 (.f64 x x) x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) x)) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) x)) (fma.f64 (.f64 x (/.f64 x (-.f64 (.f64 x x) x))) (.f64 x (/.f64 x (-.f64 (.f64 x x) x))) (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) x)) (.f64 x (/.f64 x (-.f64 (*.f64 x x) x)))))))
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(/.f64 (*.f64 (neg.f64 x) (+.f64 x #s(literal 1 binary64))) #s(literal -1 binary64))
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(/.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 x x))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 x x)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))
(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x))))
(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) x)) (+.f64 x (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) x)) (+.f64 x #s(literal 1 binary64)))
(/.f64 (.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) x)) (neg.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64)))))
(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1 binary64) (neg.f64 x)))
(/.f64 (.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) #s(literal 1 binary64)) (neg.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x)))))
(/.f64 (.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))) #s(literal 1 binary64)) (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1 binary64)) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x)))
(/.f64 (.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x))))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
(/.f64 (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x))))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))) #s(literal 1 binary64)))
(/.f64 (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))))
(/.f64 (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 x (fma.f64 x x #s(literal 1 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (+.f64 x #s(literal 1 binary64)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) x))) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (-.f64 (.f64 x x) x)) (.f64 x x))))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (-.f64 (.f64 x (.f64 x x)) x))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) x)))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) (pow.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 x x))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))
(pow.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(pow.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)))
(*.f64 (-.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))
(*.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(*.f64 (+.f64 x #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) x))
(.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x)))))
(.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (*.f64 x x)))) #s(literal 1 binary64)))
(.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x)))) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 x #s(literal -1 binary64)))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 x (fma.f64 x x x) x)))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))) x))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) x)))
(.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
(.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) x))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) x)))
(.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x))))))
(.f64 (neg.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))
(*.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) #s(literal -1 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x)))) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))) x) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))) x))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) x))
(*.f64 (+.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) x) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) x))) (fma.f64 x (.f64 x (-.f64 (.f64 x x) x)) (*.f64 x x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (-.f64 (.f64 x (.f64 x x)) x))) (-.f64 (.f64 x x) x))
(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (neg.f64 (.f64 (.f64 x x) (fma.f64 x (.f64 x (.f64 x x)) x)))) (neg.f64 (fma.f64 x (.f64 x (-.f64 (.f64 x x) x)) (*.f64 x x))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (*.f64 (fma.f64 x x x) (fma.f64 x (neg.f64 x) x))) (fma.f64 x (neg.f64 x) x))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (-.f64 x (.f64 x (.f64 x x))))) (-.f64 x (.f64 x x)))
(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (fma.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 x x))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))))) (+.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))))
(.f64 (/.f64 (+.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64))) (fma.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) #s(literal 1 binary64)))
(exp.f64 (neg.f64 (log.f64 x)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) x))
(neg.f64 (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(/.f64 #s(literal -1 binary64) (neg.f64 x))
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(pow.f64 x #s(literal -1 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1 binary64))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1/2 binary64))) (pow.f64 x #s(literal -1/2 binary64)))

eval108.0ms (1.9%)

Memory: -1.6MiB live, 272.6MiB allocated
Compiler: Compiled 19 742 to 1 599 computations (91.9% saved)

prune146.0ms (2.6%)

Memory

12.9MiB live, 208.9MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	824	2	826
Fresh	0	0	0
Picked	0	4	4
Done	0	1	1
Total	824	7	831

Accuracy

100.0%

Counts

831 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))
✓	99.9%	(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
✓	45.7%	#s(approx (/ x (- 1 x)) (fma.f64 x (fma.f64 x x x) x))
✓	44.7%	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
▶	44.7%	#s(approx (/ x (- 1 x)) (*.f64 (+.f64 x #s(literal 1 binary64)) x))
▶	2.9%	#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
✓	55.7%	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Compiler

Compiled 45 to 23 computations (48.9% saved)

simplify35.0ms (0.6%)

Memory

-45.6MiB live, 16.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

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

Rules

224×	`lower-fma.f64`
224×	`lower-fma.f32`
152×	`lower-*.f32`
148×	`lower-*.f64`
80×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	49
0	15	49
1	23	49
2	33	49
3	38	49
4	62	49
5	81	49
6	123	49
7	224	49
8	292	49
9	312	49
10	340	49
11	366	49
12	444	49
13	512	49
14	517	49
0	517	45

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize28.0ms (0.5%)

Memory

9.4MiB live, 46.0MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 x #s(literal 1 binary64))
accuracy	0.01171875	(*.f64 (+.f64 x #s(literal 1 binary64)) x)
accuracy	35.392777684387546	#s(approx (/ x (- 1 x)) (*.f64 (+.f64 x #s(literal 1 binary64)) x))
accuracy	0	(*.f64 x x)
accuracy	27.948134439917553	#s(approx (+ (* x x) x) (*.f64 x x))
accuracy	35.392777684387546	#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))

Samples

16.0ms

256×

valid

Compiler

Compiled 31 to 10 computations (67.7% saved)

Precisions

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

ival-mult: 3.0ms (32.2% of total)

ival-sub: 2.0ms (21.5% of total)

ival-div: 2.0ms (21.5% of total)

ival-add: 2.0ms (21.5% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

5.7MiB live, 5.7MiB allocated

Counts

6 → 72

Calls

Call 1

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

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

Calls

18 calls:

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

simplify353.0ms (6.3%)

Memory

28.5MiB live, 381.3MiB allocated

Algorithm

1×	egg-herbie

Rules

18 312×	`lower-fma.f64`
18 312×	`lower-fma.f32`
5 068×	`lower-*.f64`
5 068×	`lower-*.f32`
1 770×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	358
1	89	346
2	197	334
3	621	330
4	2754	330
5	5308	330
0	8134	302

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 66

Calls

Call 1

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

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

rewrite311.0ms (5.5%)

Memory

-32.5MiB live, 369.4MiB allocated

Rules

4 618×	`lower-fma.f64`
4 618×	`lower-fma.f32`
2 884×	`lower-*.f32`
2 880×	`lower-*.f64`
2 800×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	46
0	15	46
1	61	46
2	388	46
3	4538	46
0	9672	42

Stop Event

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

Counts

6 → 330

Calls

Call 1

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

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

eval86.0ms (1.5%)

Memory: 21.3MiB live, 97.2MiB allocated
Compiler: Compiled 7 819 to 828 computations (89.4% saved)

prune51.0ms (0.9%)

Memory

-1.8MiB live, 116.9MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	395	1	396
Fresh	0	0	0
Picked	1	1	2
Done	0	5	5
Total	396	7	403

Accuracy

100.0%

Counts

403 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))
✓	99.9%	(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
✓	45.7%	#s(approx (/ x (- 1 x)) (fma.f64 x (fma.f64 x x x) x))
✓	44.7%	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
✓	44.7%	#s(approx (/ x (- 1 x)) (*.f64 (+.f64 x #s(literal 1 binary64)) x))
▶	45.4%	#s(approx (/ x (- 1 x)) (*.f64 #s(approx (+ x 1) #s(literal 1 binary64)) x))
✓	55.7%	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Compiler

Compiled 45 to 24 computations (46.7% saved)

simplify7.0ms (0.1%)

Memory

12.5MiB live, 12.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Rules

48×	`lower-+.f64`
48×	`lower-+.f32`
30×	`lower--.f64`
30×	`lower--.f32`
26×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	27
0	9	27
1	15	27
2	19	27
3	24	27
4	31	27
5	41	27
6	56	27
7	86	27
8	111	27
9	119	27
10	121	27
0	121	27

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize22.0ms (0.4%)

Memory

1.4MiB live, 38.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(*.f64 #s(approx (+ x 1) #s(literal 1 binary64)) x)
accuracy	34.91141271905422	#s(approx (+ x 1) #s(literal 1 binary64))
accuracy	35.392777684387546	#s(approx (/ x (- 1 x)) (*.f64 #s(approx (+ x 1) #s(literal 1 binary64)) x))

Samples

15.0ms

256×

valid

Compiler

Compiled 17 to 8 computations (52.9% saved)

Precisions

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

ival-div: 4.0ms (43.9% of total)

ival-mult: 2.0ms (21.9% of total)

ival-sub: 1.0ms (11% of total)

ival-add: 1.0ms (11% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

2.4MiB live, 2.4MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs

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

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

#s(alt #s(approx (+ x 1) #s(literal 1 binary64)) (patch #s(approx (+ x 1) #s(literal 1 binary64)) #<representation binary64>) () ())

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

Calls

9 calls:

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

simplify294.0ms (5.2%)

Memory

-6.0MiB live, 352.1MiB allocated

Algorithm

1×	egg-herbie

Rules

18 312×	`lower-fma.f64`
18 312×	`lower-fma.f32`
5 068×	`lower-*.f64`
5 068×	`lower-*.f32`
1 770×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	176
1	89	170
2	197	164
3	621	162
4	2754	162
5	5308	162
0	8134	148

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 32

Calls

Call 1

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

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

rewrite267.0ms (4.7%)

Memory

-19.5MiB live, 337.9MiB allocated

Rules

6 482×	`lower-fma.f64`
6 482×	`lower-fma.f32`
4 894×	`lower-*.f32`
4 892×	`lower-*.f64`
3 184×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	25
0	9	25
1	42	25
2	268	25
3	2942	25
0	10331	25

Stop Event

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

Counts

3 → 8

Calls

Call 1

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

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

eval4.0ms (0.1%)

Memory: 9.2MiB live, 9.2MiB allocated
Compiler: Compiled 270 to 26 computations (90.4% saved)

prune6.0ms (0.1%)

Memory

12.6MiB live, 12.6MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	40	7	47

Accuracy

100.0%

Counts

47 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))
✓	99.9%	(/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
✓	45.7%	#s(approx (/ x (- 1 x)) (fma.f64 x (fma.f64 x x x) x))
✓	44.7%	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
✓	44.7%	#s(approx (/ x (- 1 x)) (*.f64 (+.f64 x #s(literal 1 binary64)) x))
✓	45.4%	#s(approx (/ x (- 1 x)) (*.f64 #s(approx (+ x 1) #s(literal 1 binary64)) x))
✓	55.7%	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Compiler

Compiled 89 to 38 computations (57.3% saved)

regimes6.0ms (0.1%)

Memory

12.3MiB live, 12.3MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))

Calls

2 calls:

3.0ms	x
3.0ms	(/.f64 x (-.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(/.f64 x (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 8 to 5 computations (37.5% saved)

regimes13.0ms (0.2%)

Memory

-30.2MiB live, 9.0MiB allocated

Counts

6 → 2

Calls

Call 1

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

Outputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) (fma.f64 x (fma.f64 x x x) x))

Calls

2 calls:

10.0ms	(/.f64 x (-.f64 #s(literal 1 binary64) x))
3.0ms	x

Results

Accuracy	Segments	Branch
98.4%	3	`x`
98.4%	2	`(/.f64 x (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 8 to 5 computations (37.5% saved)

regimes2.0ms (0%)

Memory

6.1MiB live, 6.1MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

(/.f64 x (-.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
98.2%	2	`(/.f64 x (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes2.0ms (0%)

Memory

5.0MiB live, 5.0MiB allocated

Counts

4 → 2

Calls

Call 1

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

Outputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) (fma.f64 x x x))

Calls

1 calls:

2.0ms

(/.f64 x (-.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
98.2%	2	`(/.f64 x (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes2.0ms (0%)

Memory

3.7MiB live, 3.7MiB allocated

Counts

3 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

(/.f64 x (-.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
97.6%	2	`(/.f64 x (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0.1%)

Memory

6.2MiB live, 6.2MiB allocated

Accuracy

Total -34.6b remaining (-122%)

Threshold costs -34.6b (-122%)

Counts

2 → 1

Calls

Call 1

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

Outputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Calls

2 calls:

2.0ms	x
1.0ms	(/.f64 x (-.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
55.7%	1	`x`
55.7%	1	`(/.f64 x (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 8 to 5 computations (37.5% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9992394211666616	-1.2242432935997335e-5

Compiler

Compiled 9 to 8 computations (11.1% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9992394211666616	-1.2242432935997335e-5

Compiler

Compiled 9 to 8 computations (11.1% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9992394211666616	-1.2242432935997335e-5

Compiler

Compiled 9 to 8 computations (11.1% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9992394211666616	-1.2242432935997335e-5

Compiler

Compiled 9 to 8 computations (11.1% saved)

simplify7.0ms (0.1%)

Memory

11.6MiB live, 11.6MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
6×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	119
1	33	119
2	36	119
3	38	119
4	39	119

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (fma.f64 x (fma.f64 x x x) x)))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (*.f64 (+.f64 x #s(literal 1 binary64)) x)))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (fma.f64 x x x)))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (*.f64 #s(approx (+ x 1) #s(literal 1 binary64)) x)))
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Outputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (fma.f64 x (fma.f64 x x x) x)))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (*.f64 (+.f64 x #s(literal 1 binary64)) x)))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (*.f64 x (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (fma.f64 x x x)))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (*.f64 #s(approx (+ x 1) #s(literal 1 binary64)) x)))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (*.f64 x #s(approx (+ x 1) #s(literal 1 binary64)))))
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

soundness1.3s (22.4%)

Memory

-23.0MiB live, 491.1MiB allocated

Rules

18 312×	`lower-fma.f64`
18 312×	`lower-fma.f32`
7 438×	`lower-fma.f32`
7 434×	`lower-fma.f64`
5 068×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	358
1	89	346
2	197	334
3	621	330
4	2754	330
5	5308	330
0	8134	302
0	33	135
1	93	120
2	220	114
3	546	112
4	1048	112
5	1960	112
6	3386	112
7	4530	112
8	4646	112
9	4646	112
10	4808	112
11	4883	112
12	4883	112
0	4883	109
0	13	56
0	20	54
1	97	54
2	680	54
3	7987	54
0	8665	53

Stop Event

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

Compiler

Compiled 122 to 42 computations (65.6% saved)

preprocess126.0ms (2.2%)

Memory: 0.2MiB live, 114.0MiB allocated
Compiler: Compiled 156 to 40 computations (74.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	6	15
1	20	11
2	47	10
3	100	10
4	195	10
5	284	10
6	295	10
7	309	10
8	322	10
0	4	5
0	6	5
1	10	5
2	14	5
3	19	5
4	26	5
5	36	5
6	51	5
7	74	5
8	96	5
9	104	5
10	106	5
0	106	5

Iter	Nodes	Cost
0	4	10
0	6	10
1	10	10
2	14	10
3	19	10
4	26	10
5	36	10
6	51	10
7	74	10
8	96	10
9	104	10
10	106	10
0	106	10

Iter	Nodes	Cost
0	12	49
0	15	49
1	23	49
2	33	49
3	38	49
4	62	49
5	81	49
6	123	49
7	224	49
8	292	49
9	312	49
10	340	49
11	366	49
12	444	49
13	512	49
14	517	49
0	517	45

Iter	Nodes	Cost
0	8	27
0	9	27
1	15	27
2	19	27
3	24	27
4	31	27
5	41	27
6	56	27
7	86	27
8	111	27
9	119	27
10	121	27
0	121	27

Iter	Nodes	Cost
0	6	15
1	20	11
2	47	10
3	100	10
4	195	10
5	284	10
6	295	10
7	309	10
8	322	10
0	4	5
0	6	5
1	10	5
2	14	5
3	19	5
4	26	5
5	36	5
6	51	5
7	74	5
8	96	5
9	104	5
10	106	5
0	106	5

Iter	Nodes	Cost
0	4	10
0	6	10
1	10	10
2	14	10
3	19	10
4	26	10
5	36	10
6	51	10
7	74	10
8	96	10
9	104	10
10	106	10
0	106	10

Iter	Nodes	Cost
0	12	49
0	15	49
1	23	49
2	33	49
3	38	49
4	62	49
5	81	49
6	123	49
7	224	49
8	292	49
9	312	49
10	340	49
11	366	49
12	444	49
13	512	49
14	517	49
0	517	45

Iter	Nodes	Cost
0	8	27
0	9	27
1	15	27
2	19	27
3	24	27
4	31	27
5	41	27
6	56	27
7	86	27
8	111	27
9	119	27
10	121	27
0	121	27

start0.0ms (0%)

analyze1.0ms (0%)

sample583.0ms (10.4%)

explain47.0ms (0.8%)

preprocess21.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify6.0ms (0.1%)

localize87.0ms (1.6%)

series1.0ms (0%)

simplify173.0ms (3.1%)

rewrite245.0ms (4.4%)

eval55.0ms (1%)

prune77.0ms (1.4%)

simplify76.0ms (1.4%)

localize71.0ms (1.3%)

series4.0ms (0.1%)

simplify313.0ms (5.6%)

rewrite715.0ms (12.7%)

eval108.0ms (1.9%)

prune146.0ms (2.6%)

simplify35.0ms (0.6%)

localize28.0ms (0.5%)

series3.0ms (0.1%)

simplify353.0ms (6.3%)

rewrite311.0ms (5.5%)

eval86.0ms (1.5%)

prune51.0ms (0.9%)

simplify7.0ms (0.1%)

localize22.0ms (0.4%)

series1.0ms (0%)

simplify294.0ms (5.2%)

rewrite267.0ms (4.7%)

eval4.0ms (0.1%)

prune6.0ms (0.1%)

regimes6.0ms (0.1%)

regimes13.0ms (0.2%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes3.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify7.0ms (0.1%)

soundness1.3s (22.4%)

preprocess126.0ms (2.2%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	6	15
1	20	11
2	47	10
3	100	10
4	195	10
5	284	10
6	295	10
7	309	10
8	322	10
0	4	5
0	6	5
1	10	5
2	14	5
3	19	5
4	26	5
5	36	5
6	51	5
7	74	5
8	96	5
9	104	5
10	106	5
0	106	5

Iter	Nodes	Cost
0	4	10
0	6	10
1	10	10
2	14	10
3	19	10
4	26	10
5	36	10
6	51	10
7	74	10
8	96	10
9	104	10
10	106	10
0	106	10

Iter	Nodes	Cost
0	12	49
0	15	49
1	23	49
2	33	49
3	38	49
4	62	49
5	81	49
6	123	49
7	224	49
8	292	49
9	312	49
10	340	49
11	366	49
12	444	49
13	512	49
14	517	49
0	517	45

Iter	Nodes	Cost
0	8	27
0	9	27
1	15	27
2	19	27
3	24	27
4	31	27
5	41	27
6	56	27
7	86	27
8	111	27
9	119	27
10	121	27
0	121	27