Metrics for Hyperbolic arc-(co)tangent

analyze3.0ms (0%)

Memory

3.9MiB live, 3.9MiB 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
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	50%	0%	0%	50%	0%	3
50%	25%	25%	0%	0%	50%	0%	4
75%	37.5%	12.5%	0%	0%	50%	0%	5
87.5%	43.7%	6.2%	0%	0%	50%	0%	6
93.8%	46.9%	3.1%	0%	0%	50%	0%	7
96.9%	48.4%	1.6%	0%	0%	50%	0%	8
98.4%	49.2%	0.8%	0%	0%	50%	0%	9
99.2%	49.6%	0.4%	0%	0%	50%	0%	10
99.6%	49.8%	0.2%	0%	0%	50%	0%	11
99.8%	49.9%	0.1%	0%	0%	50%	0%	12

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample3.4s (27.5%)

Memory

-121.3MiB live, 3 695.9MiB allocated

Samples

2.0s	3 073×	2	valid
966.0ms	4 857×	1	valid
22.0ms	317×	0	valid
5.0ms	9×	4	valid
0.0ms	5×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 2.6s

ival-log: 1.2s (47.8% of total)

ival-div: 602.0ms (23.2% of total)

ival-sub: 211.0ms (8.1% of total)

ival-mult: 209.0ms (8% of total)

adjust: 201.0ms (7.7% of total)

ival-add: 107.0ms (4.1% of total)

exact: 16.0ms (0.6% of total)

ival-true: 7.0ms (0.3% of total)

ival-assert: 4.0ms (0.2% of total)

Bogosity

preprocess51.0ms (0.4%)

Memory

11.7MiB live, 92.9MiB allocated

Algorithm

1×	egg-herbie

Rules

208×	`lower-fma.f64`
208×	`lower-fma.f32`
132×	`lower-*.f32`
130×	`lower-*.f64`
112×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	29	20
2	53	20
3	94	20
4	155	20
5	276	20
6	514	20
7	596	20
8	604	20
0	9	10
0	16	10
1	22	10
2	26	10
3	31	10
4	38	10
5	48	10
6	64	10
7	85	10
8	115	10
9	165	10
10	208	10
11	301	10
12	476	10
13	654	10
0	654	10

Stop Event

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

Calls

Call 1

Inputs
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))

Outputs

(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))

(*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))

explain233.0ms (1.9%)

Memory

1.3MiB live, 560.3MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
256	-	-	`(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))`
0	-	-	`(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(-.f64 #s(literal 1 binary64) x)`
0	-	-	`(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))`
0	-	-	`(+.f64 #s(literal 1 binary64) x)`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`(/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`log.f64`	`(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))`	sensitivity	256	0

Confusion

	Predicted +	Predicted -
+	256	0
-	0	0

Precision

1.0

Recall

1.0

Confusion?

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

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
1	256

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

82.0ms	178×	2	valid
66.0ms	324×	1	valid
5.0ms	2×	4	valid
1.0ms	8×	0	valid

Compiler

Compiled 108 to 40 computations (63% saved)

Precisions

Click to see histograms. Total time spent on operations: 128.0ms

ival-log: 74.0ms (57.9% of total)

ival-div: 16.0ms (12.5% of total)

adjust: 13.0ms (10.2% of total)

ival-add: 9.0ms (7% of total)

ival-mult: 7.0ms (5.5% of total)

ival-sub: 6.0ms (4.7% of total)

exact: 1.0ms (0.8% of total)

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

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

eval0.0ms (0%)

Memory: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

2.2MiB live, 2.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.6%	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify20.0ms (0.2%)

Memory

-3.9MiB live, 43.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))
✓	cost-diff	704	(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))

Rules

208×	`lower-fma.f64`
208×	`lower-fma.f32`
132×	`lower-*.f32`
130×	`lower-*.f64`
104×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	35
0	16	35
1	22	35
2	26	35
3	31	35
4	38	35
5	48	35
6	64	35
7	85	35
8	115	35
9	165	35
10	208	35
11	301	35
12	476	35
13	654	35
0	654	35

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
#s(literal 1 binary64)
#s(literal 2 binary64)
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
x
(-.f64 #s(literal 1 binary64) x)

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

localize101.0ms (0.8%)

Memory

9.6MiB live, 48.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))
✓	accuracy	100.0%	(/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))
✓	accuracy	6.6%	(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))

Samples

55.0ms	89×	2	valid
30.0ms	162×	1	valid
1.0ms	1×	4	valid
0.0ms	4×	0	valid

Compiler

Compiled 41 to 11 computations (73.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 73.0ms

ival-log: 29.0ms (39.7% of total)

ival-div: 28.0ms (38.3% of total)

adjust: 5.0ms (6.8% of total)

ival-mult: 4.0ms (5.5% of total)

ival-add: 4.0ms (5.5% of total)

ival-sub: 3.0ms (4.1% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0%)

Memory

4.1MiB live, 4.1MiB allocated

Counts

5 → 48

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 1 binary64) #s(literal 2 binary64))>
#<alt (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))>
#<alt (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))>
#<alt (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))>
#<alt (+.f64 #s(literal 1 binary64) x)>

Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/3 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* 1/5 (pow x 2))))))>
#<alt (* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/5 (* 1/7 (pow x 2))))))))>
#<alt (* 1/2 (log -1))>
#<alt (+ (* 1/2 (log -1)) (/ 1 x))>
#<alt (+ (* 1/2 (log -1)) (+ (/ 1/3 (pow x 3)) (/ 1 x)))>
#<alt (+ (* 1/2 (log -1)) (+ (/ 1/3 (pow x 3)) (+ (/ 1 x) (* 1/5 (/ 1 (pow x 5))))))>
#<alt (* 1/2 (log -1))>
#<alt (+ (* 1/2 (log -1)) (/ 1 x))>
#<alt (+ (* 1/2 (log -1)) (+ (/ 1/3 (pow x 3)) (/ 1 x)))>
#<alt (+ (* -1 (/ (- (* -1 (/ (+ 1/3 (* 1/5 (/ 1 (pow x 2)))) (pow x 2))) 1) x)) (* 1/2 (log -1)))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* 2/3 (pow x 2))))>
#<alt (* x (+ 2 (* (pow x 2) (+ 2/3 (* 2/5 (pow x 2))))))>
#<alt (* x (+ 2 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 2/5 (* 2/7 (pow x 2))))))))>
#<alt (log -1)>
#<alt (+ (log -1) (* 2 (/ 1 x)))>
#<alt (+ (log -1) (+ (/ 2/3 (pow x 3)) (* 2 (/ 1 x))))>
#<alt (+ (log -1) (+ (/ 2/3 (pow x 3)) (+ (* 2 (/ 1 x)) (* 2/5 (/ 1 (pow x 5))))))>
#<alt (log -1)>
#<alt (+ (log -1) (* 2 (/ 1 x)))>
#<alt (+ (log -1) (+ (/ 2/3 (pow x 3)) (* 2 (/ 1 x))))>
#<alt (+ (log -1) (* -1 (/ (- (* -1 (/ (+ 2/3 (* 2/5 (/ 1 (pow x 2)))) (pow x 2))) 2) x)))>
#<alt 1>
#<alt (+ 1 (* 2 x))>
#<alt (+ 1 (* x (+ 2 (* 2 x))))>
#<alt (+ 1 (* x (+ 2 (* x (+ 2 (* 2 x))))))>
#<alt -1>
#<alt (* -1 (+ 1 (* 2 (/ 1 x))))>
#<alt (- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 1)>
#<alt (- (* -1 (/ (+ 2 (* 2 (/ 1 x))) (pow x 2))) (+ 1 (* 2 (/ 1 x))))>
#<alt -1>
#<alt (* -1 (+ 1 (* 2 (/ 1 x))))>
#<alt (- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 1)>
#<alt (- (* -1 (/ (+ 2 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))) x)) 1)>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(* (/ 1 2) (log (/ (+ 1 x) (- 1 x))))
1.0ms	x	@	-inf	(* (/ 1 2) (log (/ (+ 1 x) (- 1 x))))
1.0ms	x	@	inf	(* (/ 1 2) (log (/ (+ 1 x) (- 1 x))))
0.0ms	x	@	inf	(/ (+ 1 x) (- 1 x))
0.0ms	x	@	inf	(log (/ (+ 1 x) (- 1 x)))

rewrite220.0ms (1.8%)

Memory

-5.9MiB live, 435.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 620×	`lower-fma.f64`
2 620×	`lower-fma.f32`
2 338×	`lower-*.f32`
2 336×	`lower-*.f64`
1 694×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
0	16	29
1	49	29
2	308	29
3	4075	29
0	9498	22

Stop Event

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

Counts

5 → 799

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) #s(literal 2 binary64))
(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))
(/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)

Outputs
#s(literal 1/2 binary64)
(+.f64 (.f64 #s(literal 1/2 binary64) (log1p.f64 x)) (.f64 #s(literal 1/2 binary64) (neg.f64 (log1p.f64 x))))
(+.f64 (.f64 (log1p.f64 x) #s(literal 1/2 binary64)) (.f64 (neg.f64 (log1p.f64 x)) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (log1p.f64 x) (*.f64 #s(literal 1/2 binary64) (neg.f64 (log1p.f64 x))))
(fma.f64 (log1p.f64 x) #s(literal 1/2 binary64) (*.f64 (neg.f64 (log1p.f64 x)) #s(literal 1/2 binary64)))
(neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (pow.f64 (log1p.f64 x) #s(literal 3 binary64)) (pow.f64 (log1p.f64 x) #s(literal 3 binary64)))) (fma.f64 (log1p.f64 x) (.f64 #s(literal 2 binary64) (log1p.f64 x)) (pow.f64 (log1p.f64 x) #s(literal 2 binary64))))
(/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 #s(literal 2 binary64) (log1p.f64 x)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))) (.f64 #s(literal 2 binary64) (log1p.f64 x)))
(/.f64 (.f64 (-.f64 (pow.f64 (log1p.f64 x) #s(literal 3 binary64)) (pow.f64 (log1p.f64 x) #s(literal 3 binary64))) #s(literal 1/2 binary64)) (fma.f64 (log1p.f64 x) (.f64 #s(literal 2 binary64) (log1p.f64 x)) (pow.f64 (log1p.f64 x) #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 (.f64 #s(literal 2 binary64) (log1p.f64 x)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))) #s(literal 1/2 binary64)) (.f64 #s(literal 2 binary64) (log1p.f64 x)))
(*.f64 #s(literal 1/2 binary64) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(*.f64 (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64))
(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)))
(+.f64 (log1p.f64 x) (neg.f64 (log1p.f64 x)))
(+.f64 (log1p.f64 x) (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))))
(+.f64 #s(literal 0 binary64) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))))
(+.f64 (log1p.f64 (.f64 x (.f64 x x))) (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 x (fma.f64 x x #s(literal 1 binary64))))))
(+.f64 (log1p.f64 (.f64 x (.f64 x x))) (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) x))))
(+.f64 (log1p.f64 (.f64 x (.f64 x x))) (log.f64 (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))))))
(+.f64 (log1p.f64 (.f64 x (neg.f64 x))) (neg.f64 (.f64 #s(literal 2 binary64) (log1p.f64 x))))
(+.f64 (log1p.f64 (*.f64 x (neg.f64 x))) (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))))
(+.f64 (log1p.f64 (fma.f64 x x x)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))))
(+.f64 (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal 0 binary64))
(+.f64 (log.f64 (+.f64 x #s(literal -1 binary64))) (neg.f64 (log.f64 (+.f64 x #s(literal -1 binary64)))))
(+.f64 (neg.f64 (log1p.f64 x)) (log1p.f64 x))
(+.f64 (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (log1p.f64 (fma.f64 x x x)))
(+.f64 (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))))))
(+.f64 (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (log.f64 (/.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(literal 1 binary64))))
(+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x #s(literal -1 binary64)))))
(+.f64 (neg.f64 (log1p.f64 (.f64 x (.f64 x x)))) (log.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 x (fma.f64 x x #s(literal 1 binary64))))))
(+.f64 (neg.f64 (log1p.f64 (.f64 x (.f64 x x)))) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))))))
(+.f64 (neg.f64 (log1p.f64 (.f64 x (neg.f64 x)))) (.f64 #s(literal 2 binary64) (log1p.f64 x)))
(+.f64 (log.f64 (/.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x))) (neg.f64 (log1p.f64 (fma.f64 x x x))))
(+.f64 (neg.f64 (log.f64 (+.f64 x #s(literal -1 binary64)))) (log.f64 (+.f64 x #s(literal -1 binary64))))
(+.f64 (log.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (log.f64 (/.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x))))
(+.f64 (log.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (log.f64 (*.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))))
(+.f64 (log.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x (.f64 x x) #s(literal 1 binary64)))) (log.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64)))))))
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(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64))))) #s(literal -1 binary64)))
(.f64 (pow.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 (pow.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 x (fma.f64 x x #s(literal 1 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1 binary64))) #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 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.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 #s(literal 1 binary64) x) (+.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 #s(literal 1 binary64) x) (-.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 #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 (+.f64 x (fma.f64 x x #s(literal 1 binary64))))))
(.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal -1 binary64))))
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (fma.f64 x (.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #s(literal 1 binary64))))))
(.f64 (pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x (fma.f64 x x #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 (+.f64 x (fma.f64 x x #s(literal 1 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 x (fma.f64 x 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 (+.f64 x (fma.f64 x 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))))

simplify363.0ms (2.9%)

Memory

-18.8MiB live, 461.3MiB allocated

Algorithm

1×	egg-herbie

Rules

11 698×	`lower-fma.f64`
11 698×	`lower-fma.f32`
3 498×	`lower-*.f64`
3 498×	`lower-*.f32`
2 550×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	110	390
1	322	376
2	811	374
3	2110	370
4	3888	370
5	6111	370
0	8213	346

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 45

Calls

Call 1

Inputs
x
(* x (+ 1 (* 1/3 (pow x 2))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 1/5 (pow x 2))))))
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/5 (* 1/7 (pow x 2))))))))
(* 1/2 (log -1))
(+ (* 1/2 (log -1)) (/ 1 x))
(+ (* 1/2 (log -1)) (+ (/ 1/3 (pow x 3)) (/ 1 x)))
(+ (* 1/2 (log -1)) (+ (/ 1/3 (pow x 3)) (+ (/ 1 x) (* 1/5 (/ 1 (pow x 5))))))
(* 1/2 (log -1))
(+ (* 1/2 (log -1)) (/ 1 x))
(+ (* 1/2 (log -1)) (+ (/ 1/3 (pow x 3)) (/ 1 x)))
(+ (* -1 (/ (- (* -1 (/ (+ 1/3 (* 1/5 (/ 1 (pow x 2)))) (pow x 2))) 1) x)) (* 1/2 (log -1)))
(* 2 x)
(* x (+ 2 (* 2/3 (pow x 2))))
(* x (+ 2 (* (pow x 2) (+ 2/3 (* 2/5 (pow x 2))))))
(* x (+ 2 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 2/5 (* 2/7 (pow x 2))))))))
(log -1)
(+ (log -1) (* 2 (/ 1 x)))
(+ (log -1) (+ (/ 2/3 (pow x 3)) (* 2 (/ 1 x))))
(+ (log -1) (+ (/ 2/3 (pow x 3)) (+ (* 2 (/ 1 x)) (* 2/5 (/ 1 (pow x 5))))))
(log -1)
(+ (log -1) (* 2 (/ 1 x)))
(+ (log -1) (+ (/ 2/3 (pow x 3)) (* 2 (/ 1 x))))
(+ (log -1) (* -1 (/ (- (* -1 (/ (+ 2/3 (* 2/5 (/ 1 (pow x 2)))) (pow x 2))) 2) x)))
1
(+ 1 (* 2 x))
(+ 1 (* x (+ 2 (* 2 x))))
(+ 1 (* x (+ 2 (* x (+ 2 (* 2 x))))))
-1
(* -1 (+ 1 (* 2 (/ 1 x))))
(- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 1)
(- (* -1 (/ (+ 2 (* 2 (/ 1 x))) (pow x 2))) (+ 1 (* 2 (/ 1 x))))
-1
(* -1 (+ 1 (* 2 (/ 1 x))))
(- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 1)
(- (* -1 (/ (+ 2 (+ (* 2 (/ 1 x)) (/ 2 (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 (* 1/3 (pow x 2))))
(fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* 1/5 (pow x 2))))))
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/5 binary64)) #s(literal 1/3 binary64)) (.f64 x (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (+ 1/3 (* (pow x 2) (+ 1/5 (* 1/7 (pow x 2))))))))
(fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/7 binary64)) #s(literal 1/5 binary64))) #s(literal 1/3 binary64)) (.f64 x (.f64 x x)) x)
(* 1/2 (log -1))
(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64)))
(+ (* 1/2 (log -1)) (/ 1 x))
(fma.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(+ (* 1/2 (log -1)) (+ (/ 1/3 (pow x 3)) (/ 1 x)))
(+.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)))))
(+ (* 1/2 (log -1)) (+ (/ 1/3 (pow x 3)) (+ (/ 1 x) (* 1/5 (/ 1 (pow x 5))))))
(+.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1/5 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x)))))))
(* 1/2 (log -1))
(*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64)))
(+ (* 1/2 (log -1)) (/ 1 x))
(fma.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) x))
(+ (* 1/2 (log -1)) (+ (/ 1/3 (pow x 3)) (/ 1 x)))
(+.f64 (/.f64 #s(literal 1 binary64) x) (fma.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)))))
(+ (* -1 (/ (- (* -1 (/ (+ 1/3 (* 1/5 (/ 1 (pow x 2)))) (pow x 2))) 1) x)) (* 1/2 (log -1)))
(fma.f64 #s(literal 1/2 binary64) (log.f64 #s(literal -1 binary64)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1/5 binary64) (.f64 x x))) (.f64 x x))) x))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* 2/3 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 2/3 binary64)) #s(literal 2 binary64)))
(* x (+ 2 (* (pow x 2) (+ 2/3 (* 2/5 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 2/5 binary64)) #s(literal 2/3 binary64)) #s(literal 2 binary64)))
(* x (+ 2 (* (pow x 2) (+ 2/3 (* (pow x 2) (+ 2/5 (* 2/7 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 2/7 binary64) #s(literal 2/5 binary64)) #s(literal 2/3 binary64)) #s(literal 2 binary64)))
(log -1)
(log.f64 #s(literal -1 binary64))
(+ (log -1) (* 2 (/ 1 x)))
(+.f64 (log.f64 #s(literal -1 binary64)) (/.f64 #s(literal 2 binary64) x))
(+ (log -1) (+ (/ 2/3 (pow x 3)) (* 2 (/ 1 x))))
(+.f64 (log.f64 #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x x)))))
(+ (log -1) (+ (/ 2/3 (pow x 3)) (+ (* 2 (/ 1 x)) (* 2/5 (/ 1 (pow x 5))))))
(+.f64 (/.f64 #s(literal 2 binary64) x) (+.f64 (/.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x x))) (+.f64 (log.f64 #s(literal -1 binary64)) (/.f64 #s(literal 2/5 binary64) (.f64 x (.f64 x (.f64 x (.f64 x x))))))))
(log -1)
(log.f64 #s(literal -1 binary64))
(+ (log -1) (* 2 (/ 1 x)))
(+.f64 (log.f64 #s(literal -1 binary64)) (/.f64 #s(literal 2 binary64) x))
(+ (log -1) (+ (/ 2/3 (pow x 3)) (* 2 (/ 1 x))))
(+.f64 (log.f64 #s(literal -1 binary64)) (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 #s(literal 2/3 binary64) (.f64 x (.f64 x x)))))
(+ (log -1) (* -1 (/ (- (* -1 (/ (+ 2/3 (* 2/5 (/ 1 (pow x 2)))) (pow x 2))) 2) x)))
(+.f64 (log.f64 #s(literal -1 binary64)) (/.f64 (-.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal -2/3 binary64) (/.f64 #s(literal -2/5 binary64) (.f64 x x))) (.f64 x x))) x))
1
#s(literal 1 binary64)
(+ 1 (* 2 x))
(fma.f64 x #s(literal 2 binary64) #s(literal 1 binary64))
(+ 1 (* x (+ 2 (* 2 x))))
(fma.f64 x (fma.f64 x #s(literal 2 binary64) #s(literal 2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 2 (* x (+ 2 (* 2 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 2 binary64) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(* -1 (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x))
(- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal -2 binary64) x)) x))
(- (* -1 (/ (+ 2 (* 2 (/ 1 x))) (pow x 2))) (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal -2 binary64) x)) x) #s(literal -2 binary64)) x))
-1
#s(literal -1 binary64)
(* -1 (+ 1 (* 2 (/ 1 x))))
(+.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) x))
(- (* -1 (/ (+ 2 (* 2 (/ 1 x))) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal -2 binary64) x)) x))
(- (* -1 (/ (+ 2 (+ (* 2 (/ 1 x)) (/ 2 (pow x 2)))) x)) 1)
(+.f64 #s(literal -1 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 #s(literal -2 binary64) x)) x) #s(literal -2 binary64)) 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))

eval154.0ms (1.2%)

Memory: 42.6MiB live, 265.3MiB allocated
Compiler: Compiled 23 068 to 3 090 computations (86.6% saved)

prune179.0ms (1.4%)

Memory

-23.6MiB live, 272.3MiB allocated

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	843	1	844
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	844	1	845

Accuracy

100.0%

Counts

845 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) x)

Compiler

Compiled 9 to 5 computations (44.4% saved)

simplify8.0ms (0.1%)

Memory

-19.7MiB live, 18.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 x (.f64 x x))
✓	cost-diff	(fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) x)

Rules

66×	`lower-*.f32`
62×	`lower-*.f64`
32×	`lower-fma.f32`
30×	`lower-fma.f64`
26×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	18
0	9	14
1	16	14
2	25	14
3	33	14
4	37	14
5	43	14
6	43	14
7	67	14
8	67	14
0	67	14

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) x)
#s(literal 1/3 binary64)
(.f64 x (.f64 x x))
x
(*.f64 x x)

Outputs
(fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) x)
#s(literal 1/3 binary64)
(.f64 x (.f64 x x))
x
(*.f64 x x)

localize23.0ms (0.2%)

Memory

23.7MiB live, 62.5MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) x)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(.f64 x (.f64 x x))

Samples

16.0ms

256×

valid

Compiler

Compiled 21 to 8 computations (61.9% saved)

Precisions

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

ival-mult: 6.0ms (56.8% of total)

const: 3.0ms (28.4% of total)

ival-add: 1.0ms (9.5% of total)

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

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

series2.0ms (0%)

Memory

6.6MiB live, 6.6MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) x)>
#<alt (.f64 x (.f64 x x))>
#<alt (*.f64 x x)>

Outputs
#<alt x>
#<alt (* x (+ 1 (* 1/3 (pow x 2))))>
#<alt (* x (+ 1 (* 1/3 (pow x 2))))>
#<alt (* x (+ 1 (* 1/3 (pow x 2))))>
#<alt (* 1/3 (pow x 3))>
#<alt (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))>
#<alt (* 1/3 (pow x 3))>
#<alt (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/3 (/ 1 (pow x 2))))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(+ (* 1/3 (* x (* x x))) x)
0.0ms	x	@	0	(+ (* 1/3 (* x (* x x))) x)
0.0ms	x	@	-inf	(* x (* x x))
0.0ms	x	@	inf	(* x x)
0.0ms	x	@	0	(* x (* x x))

rewrite515.0ms (4.1%)

Memory

11.2MiB live, 720.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

12 978×	`lower-fma.f32`
12 976×	`lower-fma.f64`
4 024×	`lower-*.f32`
4 020×	`lower-*.f64`
3 990×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	9	12
1	28	12
2	177	12
3	1798	12
0	8292	12

Stop Event

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

Counts

3 → 193

Calls

Call 1

Inputs
(fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) x)
(.f64 x (.f64 x x))
(*.f64 x x)

Outputs
(+.f64 x (.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x x))))
(+.f64 (.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x x))) x)
(+.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 #s(literal -1/9 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/3 binary64) x))) (neg.f64 (/.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x x)) (neg.f64 x)))))
(+.f64 (/.f64 (.f64 x x) (+.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/3 binary64)))) (neg.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/9 binary64)))) (+.f64 x (.f64 (.f64 x (*.f64 x x)) #s(literal -1/3 binary64))))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x x)) x))) #s(literal -1 binary64)))
(-.f64 (.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x x))) (neg.f64 x))
(-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (/.f64 #s(literal -1/9 binary64) (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/3 binary64) x))) (/.f64 (.f64 x x) (fma.f64 #s(literal 1/3 binary64) (.f64 x (*.f64 x x)) (neg.f64 x))))
(-.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) x)))
(-.f64 (/.f64 (.f64 x x) (+.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/3 binary64)))) (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/9 binary64)))) (+.f64 x (.f64 (.f64 x (*.f64 x x)) #s(literal -1/3 binary64)))))
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(.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x x) #s(literal 1 binary64)) x)
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(.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/729 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (fma.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/9 binary64)) (.f64 #s(literal 1/3 binary64) x)) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (*.f64 x x)))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/729 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) (neg.f64 x))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/81 binary64) (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/9 binary64)) #s(literal 1 binary64)) (*.f64 x x))))))
(.f64 (/.f64 (.f64 (.f64 (fma.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/9 binary64)) #s(literal 1 binary64)) (.f64 x x)) (fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/9 binary64))) (.f64 x (neg.f64 x)))) (fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) (neg.f64 x))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/9 binary64)) #s(literal 1 binary64)) (.f64 x x))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (fma.f64 (.f64 x (+.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/3 binary64)))) (.f64 (.f64 x (+.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/3 binary64)))) (.f64 x (+.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/3 binary64))))) (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/729 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))) (fma.f64 (.f64 x (+.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/3 binary64)))) (fma.f64 x (+.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/3 binary64))) (neg.f64 (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/9 binary64)))))) (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))) #s(literal 1/81 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (.f64 (fma.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/9 binary64)) (.f64 #s(literal 1/3 binary64) x)) (.f64 x x)) (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/9 binary64)))) (.f64 x (+.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal -1/3 binary64))))))) (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/9 binary64)))) (.f64 x (+.f64 x (.f64 (.f64 x (*.f64 x x)) #s(literal -1/3 binary64))))))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/9 binary64))) (.f64 x (neg.f64 x))) (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (.f64 x x)))) (fma.f64 x (fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) x) (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/9 binary64))))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/9 binary64)) (.f64 #s(literal 1/3 binary64) x)) (.f64 x x)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 #s(literal 1/19683 binary64) (pow.f64 x #s(literal 27 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/729 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/9 binary64)) (.f64 #s(literal 1/3 binary64) x)) (.f64 x x)) (fma.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/729 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/27 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (.f64 x (*.f64 x x)))))
(.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) (neg.f64 x)) (fma.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/729 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) (neg.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/81 binary64) (.f64 (.f64 x x) (.f64 (fma.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/9 binary64)) #s(literal 1 binary64)) (*.f64 x x))))))
(.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) (neg.f64 x)) (.f64 (.f64 (fma.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/9 binary64)) #s(literal 1 binary64)) (.f64 x x)) (fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/9 binary64))) (.f64 x (neg.f64 x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/9 binary64)) #s(literal 1 binary64)) (.f64 x x))))
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 3/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 3/2 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 3/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 3/2 binary64) (*.f64 (log.f64 x) #s(literal 3/2 binary64))))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 3 binary64)) (log.f64 x))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 x) #s(literal 3 binary64)))
(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)))
(-.f64 #s(literal 0 binary64) (*.f64 x (neg.f64 x)))
(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 (neg.f64 x) (neg.f64 x))
(.f64 #s(literal -1 binary64) (.f64 x (neg.f64 x)))

simplify545.0ms (4.4%)

Memory

-12.0MiB live, 379.9MiB allocated

Algorithm

1×	egg-herbie

Rules

7 328×	`lower-*.f64`
7 328×	`lower-*.f32`
4 574×	`lower-fma.f64`
4 574×	`lower-fma.f32`
2 604×	`cube-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	164
1	36	146
2	75	146
3	166	146
4	603	146
5	2438	146
6	3302	146
7	4415	146
8	4846	146
9	5052	146
10	5246	146
11	5449	146
12	5656	146
13	7402	146
0	8123	137

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 35

Calls

Call 1

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

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

eval47.0ms (0.4%)

Memory: -5.6MiB live, 53.8MiB allocated
Compiler: Compiled 11 421 to 538 computations (95.3% saved)

prune38.0ms (0.3%)

Memory

-13.7MiB live, 58.4MiB allocated

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	227	1	228
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	227	2	229

Accuracy

100.0%

Counts

229 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) x)
▶	6.2%	(.f64 x (.f64 #s(literal 1/3 binary64) (*.f64 x x)))

Compiler

Compiled 17 to 10 computations (41.2% saved)

simplify5.0ms (0%)

Memory

9.3MiB live, 9.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 #s(literal 1/3 binary64) (.f64 x x))
✓	cost-diff	(.f64 x (.f64 #s(literal 1/3 binary64) (*.f64 x x)))

Rules

30×	`lower-*.f32`
24×	`lower-*.f64`
14×	`associate-r`
10×	`*-commutative`
8×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	5	17
0	8	17
1	14	17
2	26	15
3	29	15
0	29	15

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 x (.f64 #s(literal 1/3 binary64) (*.f64 x x)))
x
(.f64 #s(literal 1/3 binary64) (.f64 x x))
#s(literal 1/3 binary64)
(*.f64 x x)

Outputs
(.f64 x (.f64 #s(literal 1/3 binary64) (*.f64 x x)))
x
(.f64 #s(literal 1/3 binary64) (.f64 x x))
#s(literal 1/3 binary64)
(*.f64 x x)

localize42.0ms (0.3%)

Memory

1.4MiB live, 37.0MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(.f64 x (.f64 #s(literal 1/3 binary64) (*.f64 x x)))
✓	accuracy	99.7%	(.f64 #s(literal 1/3 binary64) (.f64 x x))

Samples

35.0ms

256×

valid

Compiler

Compiled 19 to 7 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-mult: 27.0ms (90% of total)

const: 3.0ms (10% of total)

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

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

series1.0ms (0%)

Memory

2.9MiB live, 2.9MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs
#<alt (.f64 x (.f64 #s(literal 1/3 binary64) (*.f64 x x)))>
#<alt (.f64 #s(literal 1/3 binary64) (.f64 x x))>
#<alt (*.f64 x x)>

Outputs
#<alt (* 1/3 (pow x 3))>
#<alt (* 1/3 (pow x 3))>
#<alt (* 1/3 (pow x 3))>
#<alt (* 1/3 (pow x 3))>
#<alt (* 1/3 (pow x 3))>
#<alt (* 1/3 (pow x 3))>
#<alt (* 1/3 (pow x 3))>
#<alt (* 1/3 (pow x 3))>
#<alt (* 1/3 (pow x 3))>
#<alt (* 1/3 (pow x 3))>
#<alt (* 1/3 (pow x 3))>
#<alt (* 1/3 (pow x 3))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (* 1/3 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	x	@	-inf	(* x (* 1/3 (* x x)))
0.0ms	x	@	inf	(* x (* 1/3 (* x x)))
0.0ms	x	@	inf	(* 1/3 (* x x))
0.0ms	x	@	0	(* x (* 1/3 (* x x)))
0.0ms	x	@	0	(* 1/3 (* x x))

rewrite150.0ms (1.2%)

Memory

1.8MiB live, 153.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

2 096×	`lower-pow.f64`
2 096×	`lower-pow.f32`
1 556×	`prod-exp`
1 252×	`lower-*.f64`
1 252×	`lower-*.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	17
1	16	17
2	35	13
3	55	13
4	140	13
5	479	3
6	3038	3
7	3062	3
8	3184	3
9	4391	3
0	9325	3

Stop Event

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

Counts

3 → 4

Calls

Call 1

Inputs
(.f64 x (.f64 #s(literal 1/3 binary64) (*.f64 x x)))
(.f64 #s(literal 1/3 binary64) (.f64 x x))
(*.f64 x x)

Outputs
#s(literal 1/3 binary64)
#s(literal 1/3 binary64)
#s(literal 1 binary64)
x

simplify5.0ms (0%)

Memory

9.6MiB live, 9.6MiB allocated

Algorithm

1×	egg-herbie

Rules

30×	`lower-*.f64`
30×	`lower-*.f32`
10×	`associate-r`
10×	`associate-l`
8×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	156
1	13	156
2	23	156
3	31	156
0	31	156

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

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

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

eval4.0ms (0%)

Memory: 8.7MiB live, 8.7MiB allocated
Compiler: Compiled 267 to 12 computations (95.5% saved)

prune2.0ms (0%)

Memory

4.9MiB live, 4.9MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	38	2	40
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	39	3	42

Accuracy

100.0%

Counts

42 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) x)
▶	17.7%	(*.f64 x #s(literal 1/3 binary64))
▶	3.5%	#s(literal 1/3 binary64)

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify4.0ms (0%)

Memory

6.5MiB live, 6.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x #s(literal 1/3 binary64))

Rules

4×	`lower-*.f32`
2×	`*-commutative`
2×	`lower-*.f64`
2×	`lift-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	6
0	4	6
1	5	6
0	5	6

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(literal 1/3 binary64)
(*.f64 x #s(literal 1/3 binary64))
x
#s(literal 1/3 binary64)

Outputs
#s(literal 1/3 binary64)
(*.f64 x #s(literal 1/3 binary64))
(*.f64 #s(literal 1/3 binary64) x)
x
#s(literal 1/3 binary64)

localize55.0ms (0.4%)

Memory

-8.5MiB live, 35.7MiB allocated

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.4%	(*.f64 x #s(literal 1/3 binary64))

Samples

46.0ms

256×

valid

Compiler

Compiled 8 to 5 computations (37.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-mult: 38.0ms (92.2% of total)

const: 3.0ms (7.3% of total)

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

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

series1.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Counts

1 → 12

Calls

Call 1

Inputs
#<alt (*.f64 x #s(literal 1/3 binary64))>

Outputs
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>
#<alt (* 1/3 x)>

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(* x 1/3)
0.0ms	x	@	inf	(* x 1/3)
0.0ms	x	@	-inf	(* x 1/3)

rewrite44.0ms (0.4%)

Memory

-29.2MiB live, 9.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4×	`lower-*.f32`
2×	`lower-*.f64`
2×	`*-commutative`
2×	`lift-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
0	4	3
1	5	3
0	5	3

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Counts

1 → 2

Calls

Call 1

Inputs
(*.f64 x #s(literal 1/3 binary64))

Outputs
(*.f64 x #s(literal 1/3 binary64))
(*.f64 #s(literal 1/3 binary64) x)

simplify3.0ms (0%)

Memory

5.3MiB live, 5.3MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`lower-*.f64`
4×	`lower-*.f32`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	36
1	4	36
0	4	36

Stop Event

1×	iter limit
1×	saturated

Counts

12 → 12

Calls

Call 1

Inputs
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)
(* 1/3 x)

Outputs
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)
(* 1/3 x)
(*.f64 #s(literal 1/3 binary64) x)

eval1.0ms (0%)

Memory: 3.1MiB live, 3.1MiB allocated
Compiler: Compiled 43 to 4 computations (90.7% saved)

prune2.0ms (0%)

Memory

5.9MiB live, 5.9MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	14	3	17

Accuracy

100.0%

Counts

17 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) x)
✓	17.7%	(*.f64 x #s(literal 1/3 binary64))
✓	3.5%	#s(literal 1/3 binary64)

Compiler

Compiled 47 to 26 computations (44.7% saved)

regimes8.0ms (0.1%)

Memory

17.2MiB live, 17.2MiB allocated

Counts

5 → 1

Calls

Call 1

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

Outputs
(fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) x)

Calls

4 calls:

2.0ms	x
2.0ms	(/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))
2.0ms	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))
2.0ms	(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))`
100.0%	1	`(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))`
100.0%	1	`(/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 32 to 21 computations (34.4% saved)

regimes41.0ms (0.3%)

Memory

-25.9MiB live, 13.3MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs
#s(literal 1/3 binary64)
(*.f64 x #s(literal 1/3 binary64))
(.f64 x (.f64 #s(literal 1/3 binary64) (*.f64 x x)))

Outputs
(*.f64 x #s(literal 1/3 binary64))

Calls

4 calls:

36.0ms	(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))
2.0ms	x
1.0ms	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))
1.0ms	(/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
17.7%	1	`x`
17.7%	1	`(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))`
17.7%	1	`(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))`
17.7%	1	`(/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 32 to 21 computations (34.4% saved)

regimes5.0ms (0%)

Memory

9.5MiB live, 9.5MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1/3 binary64)

Outputs
#s(literal 1/3 binary64)

Calls

4 calls:

1.0ms	x
1.0ms	(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))
1.0ms	(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))
1.0ms	(/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
3.5%	1	`(*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))))`
3.5%	1	`(log.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))`
3.5%	1	`(/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))`
3.5%	1	`x`

Compiler

Compiled 32 to 21 computations (34.4% saved)

simplify5.0ms (0%)

Memory

9.4MiB live, 9.4MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	12
1	8	12

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) x)
(*.f64 x #s(literal 1/3 binary64))
#s(literal 1/3 binary64)

Outputs
(fma.f64 #s(literal 1/3 binary64) (.f64 x (.f64 x x)) x)
(*.f64 x #s(literal 1/3 binary64))
(*.f64 #s(literal 1/3 binary64) x)
#s(literal 1/3 binary64)

soundness6.1s (48.9%)

Memory

-25.1MiB live, 342.0MiB allocated

Rules

11 698×	`lower-fma.f64`
11 698×	`lower-fma.f32`
7 328×	`lower-*.f64`
7 328×	`lower-*.f32`
4 574×	`lower-fma.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	14	164
1	36	146
2	75	146
3	166	146
4	603	146
5	2438	146
6	3302	146
7	4415	146
8	4846	146
9	5052	146
10	5246	146
11	5449	146
12	5656	146
13	7402	146
0	8123	137
0	110	390
1	322	376
2	811	374
3	2110	370
4	3888	370
5	6111	370
0	8213	346
0	5	15
0	8	17
1	16	17
2	35	13
3	55	13
4	140	13
5	479	3
6	3038	3
7	3062	3
8	3184	3
9	4391	3
0	9325	3

Stop Event

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

Compiler

Compiled 57 to 32 computations (43.9% saved)

preprocess63.0ms (0.5%)

Memory: -12.3MiB live, 71.8MiB allocated
Compiler: Compiled 52 to 30 computations (42.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	12	22
1	29	20
2	53	20
3	94	20
4	155	20
5	276	20
6	514	20
7	596	20
8	604	20
0	9	10
0	16	10
1	22	10
2	26	10
3	31	10
4	38	10
5	48	10
6	64	10
7	85	10
8	115	10
9	165	10
10	208	10
11	301	10
12	476	10
13	654	10
0	654	10

Iter	Nodes	Cost
0	9	35
0	16	35
1	22	35
2	26	35
3	31	35
4	38	35
5	48	35
6	64	35
7	85	35
8	115	35
9	165	35
10	208	35
11	301	35
12	476	35
13	654	35
0	654	35

Iter	Nodes	Cost
0	12	22
1	29	20
2	53	20
3	94	20
4	155	20
5	276	20
6	514	20
7	596	20
8	604	20
0	9	10
0	16	10
1	22	10
2	26	10
3	31	10
4	38	10
5	48	10
6	64	10
7	85	10
8	115	10
9	165	10
10	208	10
11	301	10
12	476	10
13	654	10
0	654	10

Iter	Nodes	Cost
0	9	35
0	16	35
1	22	35
2	26	35
3	31	35
4	38	35
5	48	35
6	64	35
7	85	35
8	115	35
9	165	35
10	208	35
11	301	35
12	476	35
13	654	35
0	654	35

analyze3.0ms (0%)

sample3.4s (27.5%)

preprocess51.0ms (0.4%)

explain233.0ms (1.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify20.0ms (0.2%)

localize101.0ms (0.8%)

series4.0ms (0%)

rewrite220.0ms (1.8%)

simplify363.0ms (2.9%)

eval154.0ms (1.2%)

prune179.0ms (1.4%)

simplify8.0ms (0.1%)

localize23.0ms (0.2%)

series2.0ms (0%)

rewrite515.0ms (4.1%)

simplify545.0ms (4.4%)

eval47.0ms (0.4%)

prune38.0ms (0.3%)

simplify5.0ms (0%)

localize42.0ms (0.3%)

series1.0ms (0%)

rewrite150.0ms (1.2%)

simplify5.0ms (0%)

eval4.0ms (0%)

prune2.0ms (0%)

simplify4.0ms (0%)

localize55.0ms (0.4%)

series1.0ms (0%)

rewrite44.0ms (0.4%)

simplify3.0ms (0%)

eval1.0ms (0%)

prune2.0ms (0%)

regimes8.0ms (0.1%)

regimes41.0ms (0.3%)

regimes5.0ms (0%)

simplify5.0ms (0%)

soundness6.1s (48.9%)

preprocess63.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	12	22
1	29	20
2	53	20
3	94	20
4	155	20
5	276	20
6	514	20
7	596	20
8	604	20
0	9	10
0	16	10
1	22	10
2	26	10
3	31	10
4	38	10
5	48	10
6	64	10
7	85	10
8	115	10
9	165	10
10	208	10
11	301	10
12	476	10
13	654	10
0	654	10

Iter	Nodes	Cost
0	9	35
0	16	35
1	22	35
2	26	35
3	31	35
4	38	35
5	48	35
6	64	35
7	85	35
8	115	35
9	165	35
10	208	35
11	301	35
12	476	35
13	654	35
0	654	35