Metrics for sqrt C (should all be same)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB 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
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample792.0ms (6.7%)

Memory

12.5MiB live, 861.7MiB allocated

Samples

435.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 202.0ms

ival-mult: 131.0ms (65% of total)

ival-sqrt: 58.0ms (28.8% of total)

ival-true: 6.0ms (3% of total)

exact: 4.0ms (2% of total)

ival-assert: 3.0ms (1.5% of total)

Bogosity

explain60.0ms (0.5%)

Memory

-2.7MiB live, 116.1MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
120	-	2	(4.864449213424914e-160)	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`(.f64 #s(literal 2 binary64) (.f64 x x))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`	oflow-rescue	68	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	overflow	68
↳	`(*.f64 x x)`	overflow	68
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`	uflow-rescue	50	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	underflow	50
↳	`(*.f64 x x)`	underflow	50

Confusion

	Predicted +	Predicted -
+	118	2
-	0	136

Precision

1.0

Recall

0.9833333333333333

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	118	0	2
-	0	0	136

Precision?

1.0

Recall?

0.9833333333333333

Freqs

test

number	freq
0	138
1	118

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

28.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

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

ival-sqrt: 9.0ms (49.6% of total)

ival-mult: 8.0ms (44.1% of total)

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

exact: 0.0ms (0% of total)

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

preprocess15.0ms (0.1%)

Memory

21.4MiB live, 21.4MiB allocated

Algorithm

1×	egg-herbie

Rules

34×	`associate-l`
32×	`associate-r`
26×	`distribute-lft-neg-in`
24×	`distribute-lft-in`
24×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	21	13
2	63	13
3	141	13
4	204	13
5	221	13
6	223	13
0	5	6
0	8	6
1	11	6
2	14	6
0	14	6

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Outputs
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))

Symmetry

(abs x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0%)

Memory

3.9MiB live, 3.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(.f64 #s(literal 2 binary64) (.f64 x x))
cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Rules

14×	`lower-*.f32`
10×	`lower-*.f64`
6×	`*-commutative`
4×	`lift-*.f64`
2×	`lift-sqrt.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	11	16
2	14	16
0	14	16

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(.f64 #s(literal 2 binary64) (.f64 x x))
#s(literal 2 binary64)
(*.f64 x x)
x

Outputs
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(sqrt.f64 (.f64 (.f64 x x) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 x x)
x

localize27.0ms (0.2%)

Memory

-13.5MiB live, 22.6MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0	(.f64 #s(literal 2 binary64) (.f64 x x))
accuracy	27.77118890026165	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Samples

22.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

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

ival-mult: 4.0ms (64.9% of total)

ival-sqrt: 2.0ms (32.5% 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%)

Memory

6.0MiB live, 6.0MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs
#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) (.f64 x x)) (patch (.f64 #s(literal 2 binary64) (.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())

Inputs

#s(alt (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x))) (patch (sqrt.f64 (*.f64 #s(literal 2 binary64) (*.f64 x x))) #<representation binary64>) () ())

#s(alt (*.f64 #s(literal 2 binary64) (*.f64 x x)) (patch (*.f64 #s(literal 2 binary64) (*.f64 x x)) #<representation binary64>) () ())

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

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

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((sqrt (* 2 (* x x))) (* 2 (* x x)) (* x x))
1.0ms	x	@	0	((sqrt (* 2 (* x x))) (* 2 (* x x)) (* x x))
1.0ms	x	@	-inf	((sqrt (* 2 (* x x))) (* 2 (* x x)) (* x x))

simplify5.0ms (0%)

Memory

6.6MiB live, 6.6MiB allocated

Algorithm

1×	egg-herbie

Rules

38×	`lower-*.f64`
38×	`lower-fma.f64`
38×	`lower-fma.f32`
38×	`lower-*.f32`
36×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

Inputs
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* -1 (* x (sqrt 2)))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

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

rewrite212.0ms (1.8%)

Memory

-37.2MiB live, 248.3MiB allocated

Rules

6 020×	`lower-fma.f64`
6 020×	`lower-fma.f32`
3 692×	`lower-*.f32`
3 688×	`lower-*.f64`
1 894×	`lower-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	17	13
2	46	12
3	123	12
4	580	12
5	3914	12
0	8179	12

Stop Event

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

Counts

3 → 226

Calls

Call 1

Inputs
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(.f64 #s(literal 2 binary64) (.f64 x x))
(*.f64 x x)

Outputs
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eval33.0ms (0.3%)

Memory: 31.7MiB live, 69.4MiB allocated
Compiler: Compiled 3 146 to 747 computations (76.3% saved)

prune13.0ms (0.1%)

Memory

-17.1MiB live, 27.2MiB allocated

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	255	7	262
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	255	8	263

Accuracy

100.0%

Counts

263 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	30.0%	(pow.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64))
▶	99.5%	(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
	99.5%	(.f64 (pow.f64 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))))
	99.2%	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
▶	99.5%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
▶	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
▶	56.3%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
✓	56.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 112 to 97 computations (13.4% saved)

simplify5.0ms (0%)

Memory

7.5MiB live, 7.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(pow.f64 x #s(literal 4 binary64))
cost-diff	0	(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
cost-diff	0	(pow.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
cost-diff	0	(*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))
cost-diff	0	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(*.f64 x #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
cost-diff	0	(pow.f64 x #s(literal 3/4 binary64))
cost-diff	0	(*.f64 #s(literal 4 binary64) x)
cost-diff	0	(pow.f64 (*.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64))
cost-diff	0	(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))

Rules

28×	`lower-*.f32`
14×	`*-commutative`
14×	`lower-*.f64`
14×	`lift-*.f64`
10×	`lift-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	90
0	37	90
1	44	90
0	44	90

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(pow.f64 (*.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64))
(*.f64 #s(literal 4 binary64) x)
#s(literal 4 binary64)
x
#s(literal 1/4 binary64)
(pow.f64 x #s(literal 3/4 binary64))
#s(literal 3/4 binary64)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(sqrt.f64 x)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))
#s(literal 2 binary64)
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
(sqrt.f64 x)
x
#s(literal 4 binary64)
(pow.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
#s(literal 4 binary64)
(pow.f64 x #s(literal 4 binary64))
x
#s(literal 1/4 binary64)

Outputs
(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 (.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (*.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64))
(pow.f64 (*.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
(*.f64 #s(literal 4 binary64) x)
(*.f64 x #s(literal 4 binary64))
#s(literal 4 binary64)
x
#s(literal 1/4 binary64)
(pow.f64 x #s(literal 3/4 binary64))
#s(literal 3/4 binary64)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) x))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
x
#s(literal 2 binary64)
(sqrt.f64 x)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
(sqrt.f64 (*.f64 (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)) #s(literal 2 binary64)))
(*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)) #s(literal 2 binary64))
#s(literal 2 binary64)
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
(sqrt.f64 x)
x
#s(literal 4 binary64)
(pow.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64))
(pow.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 4 binary64))
#s(literal 4 binary64)
(pow.f64 x #s(literal 4 binary64))
x
#s(literal 1/4 binary64)

localize71.0ms (0.6%)

Memory

11.5MiB live, 122.4MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 x #s(literal 4 binary64))
accuracy	0.00390625	(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
accuracy	44.79658170266059	(pow.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64))
accuracy	0	(*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))
accuracy	0	(sqrt.f64 x)
accuracy	0.48357026374793477	(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
accuracy	27.77118890026165	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
accuracy	0	(*.f64 x #s(literal 2 binary64))
accuracy	0	(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
accuracy	0	(sqrt.f64 x)
accuracy	0.30859375	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.39453125	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
accuracy	0	(pow.f64 (*.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64))
accuracy	0	(pow.f64 x #s(literal 3/4 binary64))
accuracy	0	(*.f64 #s(literal 4 binary64) x)
accuracy	0.296875	(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))

Samples

58.0ms

256×

valid

Compiler

Compiled 92 to 23 computations (75% saved)

Precisions

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

ival-pow: 22.0ms (53.1% of total)

ival-mult: 12.0ms (29% of total)

ival-sqrt: 7.0ms (16.9% of total)

exact: 1.0ms (2.4% of total)

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

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

series239.0ms (2%)

Memory

-29.5MiB live, 416.9MiB allocated

Counts

16 → 180

Calls

Call 1

Inputs
#s(alt (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) (patch (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (patch (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 4 binary64) x) (patch (.f64 #s(literal 4 binary64) x) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal 3/4 binary64)) (patch (pow.f64 x #s(literal 3/4 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) x) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 x #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)) (patch (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (patch (pow.f64 (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) (patch (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal 4 binary64)) (patch (pow.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) (patch (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) (patch (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) (patch (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) (patch (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log 4) (log x)))) (taylor 0 x) (#s(alt (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (patch (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log 4) (log x)))) (taylor 0 x) (#s(alt (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (patch (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log 4) (log x)))) (taylor 0 x) (#s(alt (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (patch (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log 4) (log x)))) (taylor 0 x) (#s(alt (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (patch (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 x) (taylor 0 x) (#s(alt (.f64 #s(literal 4 binary64) x) (patch (.f64 #s(literal 4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 4 x) (taylor 0 x) (#s(alt (.f64 #s(literal 4 binary64) x) (patch (.f64 #s(literal 4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 4 x) (taylor 0 x) (#s(alt (.f64 #s(literal 4 binary64) x) (patch (.f64 #s(literal 4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 4 x) (taylor 0 x) (#s(alt (.f64 #s(literal 4 binary64) x) (patch (.f64 #s(literal 4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (pow (* 1 (pow x 3)) 1/4) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3/4 binary64)) (patch (pow.f64 x #s(literal 3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (* 1 (pow x 3)) 1/4) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3/4 binary64)) (patch (pow.f64 x #s(literal 3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (* 1 (pow x 3)) 1/4) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3/4 binary64)) (patch (pow.f64 x #s(literal 3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (* 1 (pow x 3)) 1/4) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3/4 binary64)) (patch (pow.f64 x #s(literal 3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 x #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 x #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 x #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 x #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))) #<representation binary64>) () ())) ())
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#s(alt (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 3/4 binary64)) (patch (pow.f64 x #s(literal 3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 3/4 binary64)) (patch (pow.f64 x #s(literal 3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 x #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 x #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 x #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 x #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))) (patch (sqrt.f64 (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (pow x 2) (pow (sqrt -1) 4))) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (pow x 2) (pow (sqrt -1) 4))) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (pow x 2) (pow (sqrt -1) 4))) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (pow x 2) (pow (sqrt -1) 4))) (taylor -inf x) (#s(alt (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))) (patch (.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (pow (sqrt -1) 4)) (taylor -inf x) (#s(alt (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)) (patch (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (pow (sqrt -1) 4)) (taylor -inf x) (#s(alt (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)) (patch (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (pow (sqrt -1) 4)) (taylor -inf x) (#s(alt (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)) (patch (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (pow (sqrt -1) 4)) (taylor -inf x) (#s(alt (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)) (patch (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow 4 1/4) x)) (taylor -inf x) (#s(alt (pow.f64 (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (patch (pow.f64 (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow 4 1/4) x)) (taylor -inf x) (#s(alt (pow.f64 (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (patch (pow.f64 (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow 4 1/4) x)) (taylor -inf x) (#s(alt (pow.f64 (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (patch (pow.f64 (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow 4 1/4) x)) (taylor -inf x) (#s(alt (pow.f64 (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) (patch (pow.f64 (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 (pow x 4)) (taylor -inf x) (#s(alt (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) (patch (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 4 (pow x 4)) (taylor -inf x) (#s(alt (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) (patch (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 4 (pow x 4)) (taylor -inf x) (#s(alt (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) (patch (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 4 (pow x 4)) (taylor -inf x) (#s(alt (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) (patch (.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 4 binary64)) (patch (pow.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 4 binary64)) (patch (pow.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 4 binary64)) (patch (pow.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 4) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 4 binary64)) (patch (pow.f64 x #s(literal 4 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

101.0ms

((* (pow (* 4 x) 1/4) (pow x 3/4)) (pow (* 4 x) 1/4) (* 4 x) (pow x 3/4) (* (sqrt 2) x) (sqrt 2) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x) (sqrt (* 2 (pow (sqrt x) 4))) (* 2 (pow (sqrt x) 4)) (pow (sqrt x) 4) (pow (* 4 (pow x 4)) 1/4) (* 4 (pow x 4)) (pow x 4))

68.0ms

-inf

((* (pow (* 4 x) 1/4) (pow x 3/4)) (pow (* 4 x) 1/4) (* 4 x) (pow x 3/4) (* (sqrt 2) x) (sqrt 2) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x) (sqrt (* 2 (pow (sqrt x) 4))) (* 2 (pow (sqrt x) 4)) (pow (sqrt x) 4) (pow (* 4 (pow x 4)) 1/4) (* 4 (pow x 4)) (pow x 4))

64.0ms

inf

((* (pow (* 4 x) 1/4) (pow x 3/4)) (pow (* 4 x) 1/4) (* 4 x) (pow x 3/4) (* (sqrt 2) x) (sqrt 2) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x) (sqrt (* 2 (pow (sqrt x) 4))) (* 2 (pow (sqrt x) 4)) (pow (sqrt x) 4) (pow (* 4 (pow x 4)) 1/4) (* 4 (pow x 4)) (pow x 4))

simplify150.0ms (1.3%)

Memory

39.1MiB live, 146.4MiB allocated

Algorithm

1×	egg-herbie

Rules

3 070×	`lower-*.f64`
3 070×	`lower-*.f32`
2 554×	`lower-fma.f64`
2 554×	`lower-fma.f32`
1 676×	`lower--.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	65	836
1	154	836
2	377	812
3	695	788
4	1553	784
5	3074	784
6	5342	784
7	6972	784
0	8120	784

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

Inputs
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(exp (* 1/4 (+ (log 4) (log x))))
(exp (* 1/4 (+ (log 4) (log x))))
(exp (* 1/4 (+ (log 4) (log x))))
(exp (* 1/4 (+ (log 4) (log x))))
(* 4 x)
(* 4 x)
(* 4 x)
(* 4 x)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(exp (* 1/4 (+ (log 4) (* -1 (log (/ 1 x))))))
(exp (* 1/4 (+ (log 4) (* -1 (log (/ 1 x))))))
(exp (* 1/4 (+ (log 4) (* -1 (log (/ 1 x))))))
(exp (* 1/4 (+ (log 4) (* -1 (log (/ 1 x))))))
(* 4 x)
(* 4 x)
(* 4 x)
(* 4 x)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* (sqrt x) (sqrt 2))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(* 2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(* -1 (* (pow 4 1/4) x))
(* -1 (* (pow 4 1/4) x))
(* -1 (* (pow 4 1/4) x))
(* -1 (* (pow 4 1/4) x))
(exp (* 1/4 (+ (log -4) (* -1 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -4) (* -1 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -4) (* -1 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -4) (* -1 (log (/ -1 x))))))
(* 4 x)
(* 4 x)
(* 4 x)
(* 4 x)
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(* 2 (* (pow x 2) (pow (sqrt -1) 4)))
(* 2 (* (pow x 2) (pow (sqrt -1) 4)))
(* 2 (* (pow x 2) (pow (sqrt -1) 4)))
(* 2 (* (pow x 2) (pow (sqrt -1) 4)))
(* (pow x 2) (pow (sqrt -1) 4))
(* (pow x 2) (pow (sqrt -1) 4))
(* (pow x 2) (pow (sqrt -1) 4))
(* (pow x 2) (pow (sqrt -1) 4))
(* -1 (* (pow 4 1/4) x))
(* -1 (* (pow 4 1/4) x))
(* -1 (* (pow 4 1/4) x))
(* -1 (* (pow 4 1/4) x))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(* 4 (pow x 4))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)

Outputs
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(exp (* 1/4 (+ (log 4) (log x))))
(pow.f64 (*.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log 4) (log x))))
(pow.f64 (*.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log 4) (log x))))
(pow.f64 (*.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log 4) (log x))))
(pow.f64 (*.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
(* 4 x)
(*.f64 x #s(literal 4 binary64))
(* 4 x)
(*.f64 x #s(literal 4 binary64))
(* 4 x)
(*.f64 x #s(literal 4 binary64))
(* 4 x)
(*.f64 x #s(literal 4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64))
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* 2 (pow x 2))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* 2 (pow x 2))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* 2 (pow x 2))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* 2 (pow x 2))
(.f64 (.f64 x x) #s(literal 2 binary64))
(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 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* 4 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 4 binary64))
(* 4 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 4 binary64))
(* 4 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 4 binary64))
(* 4 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(exp (* 1/4 (+ (log 4) (* -1 (log (/ 1 x))))))
(pow.f64 (*.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log 4) (* -1 (log (/ 1 x))))))
(pow.f64 (*.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log 4) (* -1 (log (/ 1 x))))))
(pow.f64 (*.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log 4) (* -1 (log (/ 1 x))))))
(pow.f64 (*.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
(* 4 x)
(*.f64 x #s(literal 4 binary64))
(* 4 x)
(*.f64 x #s(literal 4 binary64))
(* 4 x)
(*.f64 x #s(literal 4 binary64))
(* 4 x)
(*.f64 x #s(literal 4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64))
(pow (* 1 (pow x 3)) 1/4)
(pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64))
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* (sqrt x) (sqrt 2))
(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* 2 (pow x 2))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* 2 (pow x 2))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* 2 (pow x 2))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* 2 (pow x 2))
(.f64 (.f64 x x) #s(literal 2 binary64))
(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 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* 4 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 4 binary64))
(* 4 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 4 binary64))
(* 4 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 4 binary64))
(* 4 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* -1 (* (pow 4 1/4) x))
(*.f64 (neg.f64 x) (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* -1 (* (pow 4 1/4) x))
(*.f64 (neg.f64 x) (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* -1 (* (pow 4 1/4) x))
(*.f64 (neg.f64 x) (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* -1 (* (pow 4 1/4) x))
(*.f64 (neg.f64 x) (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(exp (* 1/4 (+ (log -4) (* -1 (log (/ -1 x))))))
(pow.f64 (*.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log -4) (* -1 (log (/ -1 x))))))
(pow.f64 (*.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log -4) (* -1 (log (/ -1 x))))))
(pow.f64 (*.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log -4) (* -1 (log (/ -1 x))))))
(pow.f64 (*.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
(* 4 x)
(*.f64 x #s(literal 4 binary64))
(* 4 x)
(*.f64 x #s(literal 4 binary64))
(* 4 x)
(*.f64 x #s(literal 4 binary64))
(* 4 x)
(*.f64 x #s(literal 4 binary64))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(/.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 (neg.f64 x) #s(literal -3/4 binary64)))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(/.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 (neg.f64 x) #s(literal -3/4 binary64)))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(/.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 (neg.f64 x) #s(literal -3/4 binary64)))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(/.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/4 binary64)) (pow.f64 (neg.f64 x) #s(literal -3/4 binary64)))
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* x (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 x) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 x) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 x) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (neg.f64 x) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(neg.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 x)))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(neg.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 x)))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(neg.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 x)))
(* -1 (* (sqrt x) (* (sqrt -2) (sqrt -1))))
(neg.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -2 binary64))) (sqrt.f64 x)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* -1 (* x (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(* 2 (* (pow x 2) (pow (sqrt -1) 4)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* 2 (* (pow x 2) (pow (sqrt -1) 4)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* 2 (* (pow x 2) (pow (sqrt -1) 4)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* 2 (* (pow x 2) (pow (sqrt -1) 4)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* (pow x 2) (pow (sqrt -1) 4))
(*.f64 x x)
(* (pow x 2) (pow (sqrt -1) 4))
(*.f64 x x)
(* (pow x 2) (pow (sqrt -1) 4))
(*.f64 x x)
(* (pow x 2) (pow (sqrt -1) 4))
(*.f64 x x)
(* -1 (* (pow 4 1/4) x))
(*.f64 (neg.f64 x) (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* -1 (* (pow 4 1/4) x))
(*.f64 (neg.f64 x) (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* -1 (* (pow 4 1/4) x))
(*.f64 (neg.f64 x) (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* -1 (* (pow 4 1/4) x))
(*.f64 (neg.f64 x) (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* 4 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 4 binary64))
(* 4 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 4 binary64))
(* 4 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 4 binary64))
(* 4 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))

rewrite103.0ms (0.9%)

Memory

-21.7MiB live, 133.8MiB allocated

Rules

1 640×	`lower-/.f64`
1 640×	`lower-/.f32`
1 624×	`lower-*.f32`
1 622×	`lower-*.f64`
954×	`lower-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	74
0	37	96
1	88	96
2	253	56
3	1125	24
4	5525	24
0	8095	24

Stop Event

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

Counts

16 → 380

Calls

Call 1

Inputs
(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(pow.f64 (*.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64))
(*.f64 #s(literal 4 binary64) x)
(pow.f64 x #s(literal 3/4 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
(*.f64 x #s(literal 2 binary64))
(sqrt.f64 x)
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
(*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64)))
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
(pow.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64))
(*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64)))
(pow.f64 x #s(literal 4 binary64))

Outputs
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eval88.0ms (0.7%)

Memory: 0.5MiB live, 123.3MiB allocated
Compiler: Compiled 4 955 to 344 computations (93.1% saved)

prune27.0ms (0.2%)

Memory

26.9MiB live, 61.5MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	572	2	574
Fresh	1	1	2
Picked	1	4	5
Done	0	1	1
Total	574	8	582

Accuracy

100.0%

Counts

582 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.1%	(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x)
✓	99.5%	(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
▶	99.2%	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
✓	99.5%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
✓	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	56.3%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
✓	56.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
▶	5.5%	(sqrt.f64 #s(literal 2 binary64))

Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify10.0ms (0.1%)

Memory

-19.5MiB live, 13.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64))
cost-diff	0	(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x)
cost-diff	6464	(pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64))
cost-diff	0	(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
cost-diff	0	(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
cost-diff	6784	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))

Rules

28×	`lower-*.f32`
22×	`lower-*.f64`
10×	`*-commutative`
10×	`lower-pow.f32`
6×	`lift-pow.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	42
0	20	42
1	26	34
2	37	34
3	38	34
0	38	34

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
#s(literal 4 binary64)
#s(literal 1/8 binary64)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
x
(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x)
(pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64))
#s(literal 256 binary64)
#s(literal 1/32 binary64)
#s(literal 2 binary64)
x

Outputs
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
#s(literal 4 binary64)
#s(literal 1/8 binary64)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)))
x
(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x)
(*.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)) x)
(pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64))
(pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64))
#s(literal 256 binary64)
#s(literal 1/32 binary64)
#s(literal 2 binary64)
x

localize47.0ms (0.4%)

Memory

1.2MiB live, 82.5MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64))
accuracy	0.39453125	(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x)
accuracy	1.0	(pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64))
accuracy	0	(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
accuracy	0.2109375	(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
accuracy	0.33203125	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))

Samples

26.0ms

256×

valid

Compiler

Compiled 44 to 15 computations (65.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-pow: 6.0ms (38% of total)

ival-mult: 4.0ms (25.3% of total)

ival-sqrt: 2.0ms (12.7% of total)

ival-pow2: 2.0ms (12.7% of total)

exact: 1.0ms (6.3% of total)

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

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

series64.0ms (0.5%)

Memory

30.5MiB live, 188.2MiB allocated

Counts

7 → 36

Calls

Call 1

Inputs
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())
#s(alt (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (patch (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())
#s(alt (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())
#s(alt (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) (patch (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/8) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/8) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/8) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/8) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 256 1/16) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 256 1/16) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 256 1/16) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 256 1/16) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/8) x) (taylor inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/8) x) (taylor inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/8) x) (taylor inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/8) x) (taylor inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 256 1/16) x) (taylor inf x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 256 1/16) x) (taylor inf x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 256 1/16) x) (taylor inf x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 256 1/16) x) (taylor inf x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/8) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/8) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/8) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/8) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 256 1/16) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 256 1/16) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 256 1/16) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 256 1/16) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

32.0ms

((sqrt 2) (* (pow 4 1/8) (* (pow 4 1/8) x)) (pow 4 1/8) (* (pow 4 1/8) x) (pow (pow 256 1/32) 2) (* (pow (pow 256 1/32) 2) x) (pow 256 1/32))

17.0ms

-inf

((sqrt 2) (* (pow 4 1/8) (* (pow 4 1/8) x)) (pow 4 1/8) (* (pow 4 1/8) x) (pow (pow 256 1/32) 2) (* (pow (pow 256 1/32) 2) x) (pow 256 1/32))

15.0ms

inf

((sqrt 2) (* (pow 4 1/8) (* (pow 4 1/8) x)) (pow 4 1/8) (* (pow 4 1/8) x) (pow (pow 256 1/32) 2) (* (pow (pow 256 1/32) 2) x) (pow 256 1/32))

simplify4.0ms (0%)

Memory

6.1MiB live, 6.1MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`lower-*.f64`
12×	`lower-*.f32`
6×	`*-commutative`
6×	`lower-pow.f64`
6×	`lower-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	180
1	15	180
0	15	180

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

Inputs
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/8) x)
(* (pow 4 1/8) x)
(* (pow 4 1/8) x)
(* (pow 4 1/8) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/8) x)
(* (pow 4 1/8) x)
(* (pow 4 1/8) x)
(* (pow 4 1/8) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/8) x)
(* (pow 4 1/8) x)
(* (pow 4 1/8) x)
(* (pow 4 1/8) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)

Outputs
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/8) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
(* (pow 4 1/8) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
(* (pow 4 1/8) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
(* (pow 4 1/8) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
(* (pow 256 1/16) x)
(*.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)) x)
(* (pow 256 1/16) x)
(*.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)) x)
(* (pow 256 1/16) x)
(*.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)) x)
(* (pow 256 1/16) x)
(*.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/8) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
(* (pow 4 1/8) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
(* (pow 4 1/8) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
(* (pow 4 1/8) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
(* (pow 256 1/16) x)
(*.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)) x)
(* (pow 256 1/16) x)
(*.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)) x)
(* (pow 256 1/16) x)
(*.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)) x)
(* (pow 256 1/16) x)
(*.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/4) x)
(*.f64 x (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)))
(* (pow 4 1/8) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
(* (pow 4 1/8) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
(* (pow 4 1/8) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
(* (pow 4 1/8) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
(* (pow 256 1/16) x)
(*.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)) x)
(* (pow 256 1/16) x)
(*.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)) x)
(* (pow 256 1/16) x)
(*.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)) x)
(* (pow 256 1/16) x)
(*.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)) x)

rewrite61.0ms (0.5%)

Memory

-18.3MiB live, 58.5MiB allocated

Rules

430×	`lower-*.f32`
426×	`lower-*.f64`
348×	`associate-r`
278×	`associate-l`
238×	`prod-exp`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	34
0	20	35
1	51	23
2	146	20
3	471	13
0	2304	13

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

7 → 82

Calls

Call 1

Inputs
(sqrt.f64 #s(literal 2 binary64))
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
(pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64))
(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x)
(pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64))

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval11.0ms (0.1%)

Memory: 16.6MiB live, 16.6MiB allocated
Compiler: Compiled 1 081 to 96 computations (91.1% saved)

prune24.0ms (0.2%)

Memory

-20.9MiB live, 18.0MiB allocated

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	0	0	0
Picked	1	2	3
Done	0	5	5
Total	118	9	127

Accuracy

100.0%

Counts

127 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.1%	(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x)
✓	99.5%	(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
✓	99.2%	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
✓	99.5%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
✓	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
▶	20.3%	(*.f64 x #s(literal 1 binary64))
✓	56.3%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
✓	56.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
▶	5.5%	#s(literal 1 binary64)

Compiler

Compiled 53 to 48 computations (9.4% saved)

simplify3.0ms (0%)

Memory

6.7MiB live, 6.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

New	Metric	Score	Program
cost-diff	320	(*.f64 x #s(literal 1 binary64))

Rules

4×	`lower-*.f32`
2×	`*-commutative`
2×	`lower-*.f64`
2×	`*-rgt-identity`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	6
0	4	4
1	7	4
2	8	4
0	8	4

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize14.0ms (0.1%)

Memory

-17.4MiB live, 21.7MiB allocated

Localize:

Found 1 expressions of interest:

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

Samples

6.0ms

256×

valid

Compiler

Compiled 8 to 5 computations (37.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-mult: 2.0ms (99.8% 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

1.0MiB live, 1.0MiB allocated

Counts

1 → 12

Calls

Call 1

Inputs
#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 (.f64 x #s(literal 1 binary64)) (patch (.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 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 0 x) (#s(alt (.f64 x #s(literal 1 binary64)) (patch (.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())
#s(alt 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 (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 (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 (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 (taylor -inf x) (#s(alt (.f64 x #s(literal 1 binary64)) (patch (.f64 x #s(literal 1 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

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

simplify2.0ms (0%)

Memory

2.6MiB live, 2.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	12
0	1	12

Stop Event

1×	saturated
1×	saturated

Counts

12 → 0

Calls

Call 1

Inputs
x
x
x
x
x
x
x
x
x
x
x
x

Outputs
x
x
x
x
x
x
x
x
x
x
x
x

rewrite6.0ms (0.1%)

Memory

6.4MiB live, 6.4MiB allocated

Rules

4×	`lower-*.f32`
2×	`lower-*.f64`
2×	`*-rgt-identity`
2×	`*-commutative`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
0	4	1
1	7	1
2	8	1
0	8	1

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Counts

1 → 3

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>

eval0.0ms (0%)

Memory: 0.9MiB live, 0.9MiB allocated
Compiler: Compiled 7 to 4 computations (42.9% saved)

prune5.0ms (0%)

Memory

8.5MiB live, 8.5MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	2	1	3
Fresh	0	0	0
Picked	2	0	2
Done	0	7	7
Total	4	8	12

Accuracy

100.0%

Counts

12 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.1%	(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x)
✓	99.5%	(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
✓	99.2%	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
✓	99.5%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
✓	99.4%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	56.3%	(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
✓	56.6%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
	20.3%	x

Compiler

Compiled 123 to 85 computations (30.9% saved)

regimes21.0ms (0.2%)

Memory

-14.8MiB live, 22.7MiB allocated

Counts

13 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
x
(*.f64 x #s(literal 1 binary64))
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x)
(pow.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64))
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))))

Outputs
(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))

Calls

4 calls:

9.0ms	x
4.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
4.0ms	(*.f64 x x)
4.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
99.5%	1	`(.f64 #s(literal 2 binary64) (.f64 x x))`
99.5%	1	`(*.f64 x x)`

Compiler

Compiled 15 to 12 computations (20% saved)

regimes15.0ms (0.1%)

Memory

25.0MiB live, 25.0MiB allocated

Counts

11 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
x
(*.f64 x #s(literal 1 binary64))
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (pow.f64 (sqrt.f64 x) #s(literal 4 binary64))))
(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x)
(pow.f64 (*.f64 #s(literal 4 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/4 binary64))
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))

Outputs
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))

Calls

4 calls:

4.0ms	x
4.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
3.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
99.5%	1	`(.f64 #s(literal 2 binary64) (.f64 x x))`
99.5%	1	`(*.f64 x x)`

Compiler

Compiled 15 to 12 computations (20% saved)

regimes61.0ms (0.5%)

Memory

-16.9MiB live, 20.2MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
x
(*.f64 x #s(literal 1 binary64))
(sqrt.f64 #s(literal 2 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Outputs
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)

Calls

4 calls:

53.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
3.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))

Results

Accuracy	Segments	Branch
99.4%	1	`x`
99.4%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
99.4%	1	`(.f64 #s(literal 2 binary64) (.f64 x x))`
99.4%	1	`(*.f64 x x)`

Compiler

Compiled 15 to 12 computations (20% saved)

regimes8.0ms (0.1%)

Memory

14.3MiB live, 14.3MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
x
(*.f64 x #s(literal 1 binary64))
(sqrt.f64 #s(literal 2 binary64))

Outputs
x

Calls

4 calls:

2.0ms	x
2.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
2.0ms	(*.f64 x x)
2.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))

Results

Accuracy	Segments	Branch
20.3%	1	`x`
20.3%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
20.3%	1	`(.f64 #s(literal 2 binary64) (.f64 x x))`
20.3%	1	`(*.f64 x x)`

Compiler

Compiled 15 to 12 computations (20% saved)

regimes5.0ms (0%)

Memory

10.7MiB live, 10.7MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)

Calls

4 calls:

1.0ms	x
1.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
1.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
5.5%	1	`x`
5.5%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
5.5%	1	`(.f64 #s(literal 2 binary64) (.f64 x x))`
5.5%	1	`(*.f64 x x)`

Compiler

Compiled 15 to 12 computations (20% saved)

simplify25.0ms (0.2%)

Memory

-10.1MiB live, 28.2MiB allocated

Algorithm

1×	egg-herbie

Rules

10×	`-commutative-binary64-.f64`
2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	22
1	24	22

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
x
#s(literal 1 binary64)

Outputs
(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 (.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 #s(literal 2 binary64) x)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
x
#s(literal 1 binary64)

soundness9.5s (80.7%)

Memory

-32.4MiB live, 448.8MiB allocated

Rules

6 020×	`lower-fma.f64`
6 020×	`lower-fma.f32`
3 692×	`lower-*.f32`
3 688×	`lower-*.f64`
1 894×	`lower-pow.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	74
0	37	96
1	88	96
2	253	56
3	1125	24
4	5525	24
0	8095	24
0	13	34
0	20	35
1	51	23
2	146	20
3	471	13
0	2304	13
0	3	3
0	4	1
1	7	1
2	8	1
0	8	1
0	5	14
0	8	14
1	17	13
2	46	12
3	123	12
4	580	12
5	3914	12
0	8179	12

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	saturated
1×	iter limit
1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 67 to 50 computations (25.4% saved)

preprocess43.0ms (0.4%)

Memory: 18.2MiB live, 139.0MiB allocated
Compiler: Compiled 110 to 90 computations (18.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148

start0.0ms (0%)

analyze0.0ms (0%)

sample792.0ms (6.7%)

explain60.0ms (0.5%)

preprocess15.0ms (0.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize27.0ms (0.2%)

series4.0ms (0%)

simplify5.0ms (0%)

rewrite212.0ms (1.8%)

eval33.0ms (0.3%)

prune13.0ms (0.1%)

simplify5.0ms (0%)

localize71.0ms (0.6%)

series239.0ms (2%)

simplify150.0ms (1.3%)

rewrite103.0ms (0.9%)

eval88.0ms (0.7%)

prune27.0ms (0.2%)

simplify10.0ms (0.1%)

localize47.0ms (0.4%)

series64.0ms (0.5%)

simplify4.0ms (0%)

rewrite61.0ms (0.5%)

eval11.0ms (0.1%)

prune24.0ms (0.2%)

simplify3.0ms (0%)

localize14.0ms (0.1%)

series1.0ms (0%)

simplify2.0ms (0%)

rewrite6.0ms (0.1%)

eval0.0ms (0%)

prune5.0ms (0%)

regimes21.0ms (0.2%)

regimes15.0ms (0.1%)

regimes61.0ms (0.5%)

regimes8.0ms (0.1%)

regimes5.0ms (0%)

simplify25.0ms (0.2%)

soundness9.5s (80.7%)

preprocess43.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	148
1	15	148
2	32	148
3	38	148
4	42	148
5	54	148
6	66	148
7	77	148
8	97	148
9	102	148
0	102	148