Metrics for sqrt B (should all be same)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

1.1MiB live, 1.1MiB 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)

sample1.1s (21.7%)

Memory

-5.0MiB live, 926.9MiB allocated

Samples

500.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 318.0ms

ival-mult: 212.0ms (66.7% of total)

ival-sqrt: 93.0ms (29.3% of total)

ival-true: 6.0ms (1.9% of total)

exact: 5.0ms (1.6% of total)

ival-assert: 3.0ms (0.9% of total)

Bogosity

explain63.0ms (1.2%)

Memory

-10.9MiB live, 81.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
140	-	1	(-1.357210783666539e-156)	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(.f64 (.f64 #s(literal 2 binary64) x) x)`
0	-	0	-	`(*.f64 #s(literal 2 binary64) x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`	oflow-rescue	70	0
↳	`(*.f64 #s(literal 2 binary64) x)`	overflow	1
↳	`(.f64 (.f64 #s(literal 2 binary64) x) x)`	overflow	70
`sqrt.f64`	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`	uflow-rescue	69	0
↳	`(.f64 (.f64 #s(literal 2 binary64) x) x)`	underflow	69

Confusion

	Predicted +	Predicted -
+	139	1
-	0	116

Precision

1.0

Recall

0.9928571428571429

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	139	0	1
-	0	0	116

Precision?

1.0

Recall?

0.9928571428571429

Freqs

test

number	freq
0	117
1	139

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

31.0ms

512×

valid

Compiler

Compiled 58 to 24 computations (58.6% saved)

Precisions

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

ival-mult: 11.0ms (70.9% of total)

ival-sqrt: 4.0ms (25.8% of total)

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

exact: 0.0ms (0% of total)

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

preprocess42.0ms (0.8%)

Memory

-28.5MiB live, 10.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	21	13
2	62	13
3	149	13
4	214	13
5	231	13
6	233	13
0	5	6
0	8	6
1	12	6
2	13	6
0	13	6

Stop Event

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

Calls

Call 1

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

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

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

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	49.4%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	12	16
2	13	16
0	13	16

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize16.0ms (0.3%)

Memory

10.6MiB live, 10.6MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(.f64 (.f64 #s(literal 2 binary64) x) x)
accuracy	0	(*.f64 #s(literal 2 binary64) x)
accuracy	32.369744221525565	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Samples

11.0ms

256×

valid

Compiler

Compiled 34 to 12 computations (64.7% saved)

Precisions

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

ival-mult: 3.0ms (57% of total)

ival-sqrt: 2.0ms (38% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

3.0MiB live, 3.0MiB allocated

Counts

3 → 36

Calls

Call 1

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

Inputs

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

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

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

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

Calls

3 calls:

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

simplify5.0ms (0.1%)

Memory

2.1MiB live, 2.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	148
1	17	148
2	32	148
3	36	148
4	40	148
5	52	148
6	64	148
7	75	148
8	95	148
9	100	148
0	100	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))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 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))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* -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))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)

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))
(* 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)
(* 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))
(* 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 (* 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))
(* 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)

rewrite223.0ms (4.3%)

Memory

2.0MiB live, 76.7MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	17	14
2	38	13
3	92	12
4	338	12
5	2074	12
0	8672	12

Stop Event

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

Counts

3 → 118

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
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eval18.0ms (0.3%)

Memory: 18.3MiB live, 18.3MiB allocated
Compiler: Compiled 1 927 to 352 computations (81.7% saved)

prune57.0ms (1.1%)

Memory

-17.6MiB live, 25.2MiB allocated

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	146	8	154
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	146	9	155

Accuracy

100.0%

Counts

155 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.0%	(pow.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x)) #s(literal 2 binary64))
▶	99.4%	(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
	64.3%	(.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) (*.f64 x #s(literal 2 binary64)))))
▶	99.3%	(.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))
▶	99.3%	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)))
	99.3%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
▶	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
▶	49.3%	(sqrt.f64 (.f64 (.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)))
✓	49.4%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Compiler

Compiled 148 to 119 computations (19.6% saved)

simplify7.0ms (0.1%)

Memory

11.7MiB live, 11.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
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 1/16 binary64))
cost-diff	320	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
cost-diff	13248	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)))
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	(*.f64 x #s(literal 2 binary64))
cost-diff	0	(.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x))
cost-diff	0	(sqrt.f64 (.f64 (.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)))
cost-diff	1600	(.f64 (.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (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	(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
cost-diff	0	(pow.f64 x #s(literal 3/4 binary64))
cost-diff	0	(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	123
0	40	119
1	60	103
2	88	101
3	139	101
4	209	101
5	211	101
0	211	101

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
(pow.f64 x #s(literal 3/4 binary64))
x
#s(literal 3/4 binary64)
(sqrt.f64 (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(sqrt.f64 x)
#s(literal 2 binary64)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
(sqrt.f64 (.f64 (.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)))
(.f64 (.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x))
(*.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(sqrt.f64 x)
(.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 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)))
(pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64))
#s(literal 4 binary64)
#s(literal 1/16 binary64)
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
(*.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 1/8 binary64)
x

Outputs
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3/4 binary64)))
(pow.f64 x #s(literal 3/4 binary64))
x
#s(literal 3/4 binary64)
(sqrt.f64 (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(sqrt.f64 x)
#s(literal 2 binary64)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
(sqrt.f64 (.f64 (.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)))
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
(.f64 (.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 #s(literal 2 binary64) x) x)
(.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x))
(.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x)) x)
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
x
#s(literal 2 binary64)
(sqrt.f64 x)
(.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)
x
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 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 1/16 binary64))
#s(literal 4 binary64)
#s(literal 1/16 binary64)
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
(*.f64 (pow.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(literal 3 binary64)) x)
(*.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 1/8 binary64)
x

localize107.0ms (2.1%)

Memory

-20.6MiB live, 94.5MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64))
accuracy	0.22265625	(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
accuracy	0.2890625	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
accuracy	0.328125	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)))
accuracy	0	(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
accuracy	0.22265625	(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
accuracy	0.29296875	(.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 x)
accuracy	0.13671875	(.f64 (.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))
accuracy	0.1484375	(.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x))
accuracy	32.369744221525565	(sqrt.f64 (.f64 (.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.44921875	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
accuracy	0	(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
accuracy	0	(sqrt.f64 x)
accuracy	0.10546875	(sqrt.f64 (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
accuracy	0.3717575195368841	(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))))

Samples

74.0ms

256×

valid

Compiler

Compiled 248 to 48 computations (80.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-mult: 14.0ms (42% of total)

ival-pow: 12.0ms (36% of total)

ival-sqrt: 6.0ms (18% of total)

exact: 1.0ms (3% of total)

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

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

series245.0ms (4.7%)

Memory

15.4MiB live, 443.6MiB allocated

Counts

17 → 168

Calls

Call 1

Inputs
#s(alt (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (patch (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) #<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 (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 x) #s(literal 2 binary64)) (patch (.f64 (sqrt.f64 x) #s(literal 2 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 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) (patch (sqrt.f64 (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())
#s(alt (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (patch (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #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 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 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 1/16 binary64)) (patch (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())

Outputs
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (patch (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (patch (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (patch (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (patch (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 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 (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 x) 1/4) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow (* 1 x) 1/4) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow (* 1 x) 1/4) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow (* 1 x) 1/4) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (sqrt x)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) #s(literal 2 binary64)) (patch (.f64 (sqrt.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (sqrt x)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) #s(literal 2 binary64)) (patch (.f64 (sqrt.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (sqrt x)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) #s(literal 2 binary64)) (patch (.f64 (sqrt.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 (sqrt x)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 x) #s(literal 2 binary64)) (patch (.f64 (sqrt.f64 x) #s(literal 2 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 (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (pow x 2)) (taylor 0 x) (#s(alt (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) (patch (sqrt.f64 (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) (patch (sqrt.f64 (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) (patch (sqrt.f64 (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) (patch (sqrt.f64 (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* 2 (sqrt (pow x 3))) (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (patch (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (sqrt (pow x 3))) (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (patch (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (sqrt (pow x 3))) (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (patch (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* 2 (sqrt (pow x 3))) (taylor 0 x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (patch (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) #<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>) () ())) ())
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#s(alt (* (pow 64 1/16) x) (taylor inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1))))) (taylor -inf x) (#s(alt (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (patch (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1))))) (taylor -inf x) (#s(alt (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (patch (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1))))) (taylor -inf x) (#s(alt (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (patch (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1))))) (taylor -inf x) (#s(alt (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (patch (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 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 (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 (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 (* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* -2 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 x) #s(literal 2 binary64)) (patch (.f64 (sqrt.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 x) #s(literal 2 binary64)) (patch (.f64 (sqrt.f64 x) #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 x) #s(literal 2 binary64)) (patch (.f64 (sqrt.f64 x) #s(literal 2 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 (* -2 (* (pow x 2) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (pow x 2) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (pow x 2) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (pow x 2) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) (patch (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) (patch (sqrt.f64 (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) (patch (sqrt.f64 (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) (patch (sqrt.f64 (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (* (sqrt -2) (sqrt -1)))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) (patch (sqrt.f64 (.f64 (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (patch (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (patch (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (patch (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (patch (.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) #<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 (* (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 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.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 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.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 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.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 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow 64 1/16) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 64 1/16) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 64 1/16) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 64 1/16) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) 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 (* (sqrt x) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
127.0ms	x	@	0	((* (pow x 3/4) (sqrt (* (sqrt x) 2))) (pow x 3/4) (sqrt (* (sqrt x) 2)) (* (sqrt x) 2) (* (sqrt 2) x) (sqrt 2) (* (* (* x 2) (sqrt x)) (sqrt x)) (sqrt (* (* (* x 2) (sqrt x)) (sqrt x))) (* (* x 2) (sqrt x)) (* x 2) (* (pow 4 1/8) (* (pow 4 1/8) x)) (pow 4 1/8) (* (pow 4 1/8) x) (* (pow 4 1/16) (* (pow 4 1/16) (* (pow 4 1/8) x))) (* (pow 4 1/16) (* (pow 4 1/8) x)) (pow 4 1/16) (sqrt x))
72.0ms	x	@	-inf	((* (pow x 3/4) (sqrt (* (sqrt x) 2))) (pow x 3/4) (sqrt (* (sqrt x) 2)) (* (sqrt x) 2) (* (sqrt 2) x) (sqrt 2) (* (* (* x 2) (sqrt x)) (sqrt x)) (sqrt (* (* (* x 2) (sqrt x)) (sqrt x))) (* (* x 2) (sqrt x)) (* x 2) (* (pow 4 1/8) (* (pow 4 1/8) x)) (pow 4 1/8) (* (pow 4 1/8) x) (* (pow 4 1/16) (* (pow 4 1/16) (* (pow 4 1/8) x))) (* (pow 4 1/16) (* (pow 4 1/8) x)) (pow 4 1/16) (sqrt x))
41.0ms	x	@	inf	((* (pow x 3/4) (sqrt (* (sqrt x) 2))) (pow x 3/4) (sqrt (* (sqrt x) 2)) (* (sqrt x) 2) (* (sqrt 2) x) (sqrt 2) (* (* (* x 2) (sqrt x)) (sqrt x)) (sqrt (* (* (* x 2) (sqrt x)) (sqrt x))) (* (* x 2) (sqrt x)) (* x 2) (* (pow 4 1/8) (* (pow 4 1/8) x)) (pow 4 1/8) (* (pow 4 1/8) x) (* (pow 4 1/16) (* (pow 4 1/16) (* (pow 4 1/8) x))) (* (pow 4 1/16) (* (pow 4 1/8) x)) (pow 4 1/16) (sqrt x))

Time

Variable

Point

Expression

127.0ms

((* (pow x 3/4) (sqrt (* (sqrt x) 2))) (pow x 3/4) (sqrt (* (sqrt x) 2)) (* (sqrt x) 2) (* (sqrt 2) x) (sqrt 2) (* (* (* x 2) (sqrt x)) (sqrt x)) (sqrt (* (* (* x 2) (sqrt x)) (sqrt x))) (* (* x 2) (sqrt x)) (* x 2) (* (pow 4 1/8) (* (pow 4 1/8) x)) (pow 4 1/8) (* (pow 4 1/8) x) (* (pow 4 1/16) (* (pow 4 1/16) (* (pow 4 1/8) x))) (* (pow 4 1/16) (* (pow 4 1/8) x)) (pow 4 1/16) (sqrt x))

72.0ms

-inf

((* (pow x 3/4) (sqrt (* (sqrt x) 2))) (pow x 3/4) (sqrt (* (sqrt x) 2)) (* (sqrt x) 2) (* (sqrt 2) x) (sqrt 2) (* (* (* x 2) (sqrt x)) (sqrt x)) (sqrt (* (* (* x 2) (sqrt x)) (sqrt x))) (* (* x 2) (sqrt x)) (* x 2) (* (pow 4 1/8) (* (pow 4 1/8) x)) (pow 4 1/8) (* (pow 4 1/8) x) (* (pow 4 1/16) (* (pow 4 1/16) (* (pow 4 1/8) x))) (* (pow 4 1/16) (* (pow 4 1/8) x)) (pow 4 1/16) (sqrt x))

41.0ms

inf

((* (pow x 3/4) (sqrt (* (sqrt x) 2))) (pow x 3/4) (sqrt (* (sqrt x) 2)) (* (sqrt x) 2) (* (sqrt 2) x) (sqrt 2) (* (* (* x 2) (sqrt x)) (sqrt x)) (sqrt (* (* (* x 2) (sqrt x)) (sqrt x))) (* (* x 2) (sqrt x)) (* x 2) (* (pow 4 1/8) (* (pow 4 1/8) x)) (pow 4 1/8) (* (pow 4 1/8) x) (* (pow 4 1/16) (* (pow 4 1/16) (* (pow 4 1/8) x))) (* (pow 4 1/16) (* (pow 4 1/8) x)) (pow 4 1/16) (sqrt x))

simplify195.0ms (3.7%)

Memory

24.8MiB live, 142.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	65	828
1	135	828
2	368	824
3	824	824
4	1055	824
5	1290	824
6	1650	824
7	2239	824
8	2688	824
9	2839	824
10	3088	824
11	3263	824
12	3400	824
13	3556	824
14	3866	824
15	4202	824
16	4494	824
17	5220	824
18	6621	824
19	7937	824
0	8006	824

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

Inputs
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(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)
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (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))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* 2 (sqrt (pow x 3)))
(* 2 (sqrt (pow x 3)))
(* 2 (sqrt (pow x 3)))
(* 2 (sqrt (pow x 3)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 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 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(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)
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* (pow (* 1 x) 1/4) (sqrt 2))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (sqrt x))
(* 2 (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))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* 2 (sqrt (pow x 3)))
(* 2 (sqrt (pow x 3)))
(* 2 (sqrt (pow x 3)))
(* 2 (sqrt (pow x 3)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 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 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(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))))))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* -2 (* (pow x 2) (pow (sqrt -1) 2)))
(* -2 (* (pow x 2) (pow (sqrt -1) 2)))
(* -2 (* (pow x 2) (pow (sqrt -1) 2)))
(* -2 (* (pow x 2) (pow (sqrt -1) 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))))
(* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 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 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) 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)))

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)
(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))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 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)
(* 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))
(* 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 (sqrt (pow x 3)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* 2 (sqrt (pow x 3)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* 2 (sqrt (pow x 3)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* 2 (sqrt (pow x 3)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #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)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 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 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 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 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)
(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))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow (* 1 x) 1/4) (sqrt 2))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* 2 (sqrt x))
(*.f64 (sqrt.f64 x) #s(literal 2 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)
(* 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))
(* 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 (sqrt (pow x 3)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* 2 (sqrt (pow x 3)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* 2 (sqrt (pow x 3)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* 2 (sqrt (pow x 3)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #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)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 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 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 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (pow.f64 #s(literal -1 binary64) #s(literal 37/4 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (pow.f64 #s(literal -1 binary64) #s(literal 37/4 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (pow.f64 #s(literal -1 binary64) #s(literal 37/4 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
(* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1)))))
(.f64 (pow.f64 #s(literal -1 binary64) #s(literal 37/4 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) x)))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)))
(* (pow (* -1 x) 1/4) (* (sqrt (sqrt -1)) (sqrt 2)))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 x) #s(literal 2 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)
(* -2 (* (pow x 2) (pow (sqrt -1) 2)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* -2 (* (pow x 2) (pow (sqrt -1) 2)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* -2 (* (pow x 2) (pow (sqrt -1) 2)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* -2 (* (pow x 2) (pow (sqrt -1) 2)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 x))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 x))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 x))
(* -1 (* x (* (sqrt -2) (sqrt -1))))
(.f64 (.f64 (sqrt.f64 #s(literal -2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 x))
(* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #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)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 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 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 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 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)

rewrite106.0ms (2%)

Memory

2.5MiB live, 201.1MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	99
0	40	101
1	85	97
2	228	61
3	892	51
4	5044	51
0	8591	51

Stop Event

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

Counts

17 → 1 159

Calls

Call 1

Inputs
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
(pow.f64 x #s(literal 3/4 binary64))
(sqrt.f64 (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(.f64 (.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x))
(sqrt.f64 (.f64 (.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)))
(.f64 (.f64 x #s(literal 2 binary64)) (sqrt.f64 x))
(*.f64 x #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)
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)))
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
(pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64))
(sqrt.f64 x)

Outputs
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eval191.0ms (3.7%)

Memory: 10.1MiB live, 364.0MiB allocated
Compiler: Compiled 20 751 to 1 620 computations (92.2% saved)

prune37.0ms (0.7%)

Memory

-20.6MiB live, 99.5MiB allocated

Pruning

10 alts after pruning (5 fresh and 5 done)

	Pruned	Kept	Total
New	1 574	2	1 576
Fresh	0	3	3
Picked	1	4	5
Done	0	1	1
Total	1 575	10	1 585

Accuracy

100.0%

Counts

1 585 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.0%	(pow.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x)) #s(literal 2 binary64))
✓	99.4%	(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
▶	64.3%	(.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) (*.f64 x #s(literal 2 binary64)))))
✓	99.3%	(.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))
▶	99.6%	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)))
▶	99.3%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
▶	20.3%	(*.f64 x #s(literal 1 binary64))
✓	49.3%	(sqrt.f64 (.f64 (.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)))
✓	49.4%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Compiler

Compiled 116 to 100 computations (13.8% saved)

simplify8.0ms (0.2%)

Memory

11.3MiB live, 11.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
cost-diff	0	(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x))
cost-diff	7104	(pow.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x)) #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 x) (.f64 x #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 (.f64 (sqrt.f64 x) (.f64 x #s(literal 2 binary64))))
cost-diff	0	(pow.f64 x #s(literal 1/4 binary64))
cost-diff	0	(.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) (*.f64 x #s(literal 2 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	320	(*.f64 x #s(literal 1 binary64))
cost-diff	0	(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
cost-diff	0	#s(approx (* (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x))
cost-diff	0	(pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64))
cost-diff	0	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	130
0	45	128
1	62	128
2	111	125
3	152	125
4	196	125
5	231	125
6	231	125
0	231	125

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)))
(pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64))
#s(literal 4 binary64)
#s(literal 1/16 binary64)
#s(approx (* (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x))
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64))
#s(literal 64 binary64)
x
(*.f64 x #s(literal 1 binary64))
x
#s(literal 1 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))
x
#s(literal 2 binary64)
(sqrt.f64 x)
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) (*.f64 x #s(literal 2 binary64)))))
(pow.f64 x #s(literal 1/4 binary64))
x
#s(literal 1/4 binary64)
(sqrt.f64 (.f64 (sqrt.f64 x) (.f64 x #s(literal 2 binary64))))
(.f64 (sqrt.f64 x) (.f64 x #s(literal 2 binary64)))
(sqrt.f64 x)
(*.f64 x #s(literal 2 binary64))
#s(literal 2 binary64)
(pow.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x)) #s(literal 2 binary64))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x))
(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
#s(literal 4 binary64)
#s(literal 1/8 binary64)
(sqrt.f64 x)
x
#s(literal 2 binary64)

Outputs
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)))
(.f64 #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 x (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)))) (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)))
(pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64))
#s(literal 4 binary64)
#s(literal 1/16 binary64)
#s(approx (* (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x))
#s(approx (* (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 x (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64))))
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(*.f64 x (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)))
(pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64))
#s(literal 64 binary64)
x
(*.f64 x #s(literal 1 binary64))
x
x
#s(literal 1 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)))
(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)
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) (*.f64 x #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (.f64 (*.f64 (sqrt.f64 x) #s(literal 2 binary64)) x)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 x #s(literal 1/4 binary64))
x
#s(literal 1/4 binary64)
(sqrt.f64 (.f64 (sqrt.f64 x) (.f64 x #s(literal 2 binary64))))
(sqrt.f64 (.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)) x))
(.f64 (sqrt.f64 x) (.f64 x #s(literal 2 binary64)))
(.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)) x)
(sqrt.f64 x)
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
(pow.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x)) #s(literal 2 binary64))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x))
(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
#s(literal 4 binary64)
#s(literal 1/8 binary64)
(sqrt.f64 x)
x
#s(literal 2 binary64)

localize78.0ms (1.5%)

Memory

-18.5MiB live, 97.8MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
accuracy	0	(sqrt.f64 x)
accuracy	0.30859375	(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x))
accuracy	0.49447250976844204	(pow.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x)) #s(literal 2 binary64))
accuracy	0	(sqrt.f64 x)
accuracy	0.1484375	(.f64 (sqrt.f64 x) (.f64 x #s(literal 2 binary64)))
accuracy	0.34765625	(.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) (*.f64 x #s(literal 2 binary64)))))
accuracy	23.345165683592192	(sqrt.f64 (.f64 (sqrt.f64 x) (.f64 x #s(literal 2 binary64))))
accuracy	0	(*.f64 x #s(literal 2 binary64))
accuracy	0	(sqrt.f64 x)
accuracy	0.23827949386657932	(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
accuracy	0.28515625	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
accuracy	0	(*.f64 x #s(literal 1 binary64))
accuracy	0	(pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64))
accuracy	0	#s(approx (* (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x))
accuracy	0.109375	(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
accuracy	0.328125	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)))

Samples

51.0ms

256×

valid

Compiler

Compiled 232 to 53 computations (77.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-pow: 15.0ms (40.4% of total)

ival-mult: 13.0ms (35% of total)

ival-sqrt: 5.0ms (13.5% of total)

ival-pow2: 2.0ms (5.4% of total)

exact: 1.0ms (2.7% of total)

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

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

series179.0ms (3.4%)

Memory

30.8MiB live, 261.3MiB allocated

Counts

16 → 168

Calls

Call 1

Inputs
#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x))) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx (* (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x))) #<representation binary64>) () ())
#s(alt (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (patch (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (* (pow 4 1/16) (* (pow 4 1/8) x)) (.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)) (patch #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x) (patch (.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1 binary64)) (patch (.f64 x #s(literal 1 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 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) (.f64 x #s(literal 2 binary64))))) (patch (.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) (.f64 x #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal 1/4 binary64)) (patch (pow.f64 x #s(literal 1/4 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (sqrt.f64 x) (.f64 x #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 (sqrt.f64 x) (.f64 x #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 x) (.f64 x #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 x) (.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x)) #s(literal 2 binary64)) (patch (pow.f64 (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 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>) () ())

Outputs
#s(alt (* (pow 256 1/16) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x))) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx (* (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow 256 1/16) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x))) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx (* (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow 256 1/16) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x))) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx (* (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow 256 1/16) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x))) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx (* (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow 64 1/16) x) (taylor 0 x) (#s(alt #s(approx (* (pow 4 1/16) (* (pow 4 1/8) x)) (.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)) (patch #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 64 1/16) x) (taylor 0 x) (#s(alt #s(approx (* (pow 4 1/16) (* (pow 4 1/8) x)) (.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)) (patch #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 64 1/16) x) (taylor 0 x) (#s(alt #s(approx (* (pow 4 1/16) (* (pow 4 1/8) x)) (.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)) (patch #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)) #<representation binary64>) () ())) ())
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Calls

3 calls:

Time

Variable

Point

Expression

63.0ms

((* (pow 4 1/16) (* (pow 4 1/16) (* (pow 4 1/8) x))) (pow 4 1/16) (* (pow 4 1/16) (* (pow 4 1/8) x)) (* (pow 64 1/16) x) (* x 1) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x) (* (pow x 1/4) (sqrt (* (sqrt x) (* x 2)))) (pow x 1/4) (sqrt (* (sqrt x) (* x 2))) (* (sqrt x) (* x 2)) (pow (* (pow 4 1/8) (sqrt x)) 2) (* (pow 4 1/8) (sqrt x)) (pow 4 1/8))

61.0ms

-inf

((* (pow 4 1/16) (* (pow 4 1/16) (* (pow 4 1/8) x))) (pow 4 1/16) (* (pow 4 1/16) (* (pow 4 1/8) x)) (* (pow 64 1/16) x) (* x 1) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x) (* (pow x 1/4) (sqrt (* (sqrt x) (* x 2)))) (pow x 1/4) (sqrt (* (sqrt x) (* x 2))) (* (sqrt x) (* x 2)) (pow (* (pow 4 1/8) (sqrt x)) 2) (* (pow 4 1/8) (sqrt x)) (pow 4 1/8))

50.0ms

inf

((* (pow 4 1/16) (* (pow 4 1/16) (* (pow 4 1/8) x))) (pow 4 1/16) (* (pow 4 1/16) (* (pow 4 1/8) x)) (* (pow 64 1/16) x) (* x 1) (* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x) (* (pow x 1/4) (sqrt (* (sqrt x) (* x 2)))) (pow x 1/4) (sqrt (* (sqrt x) (* x 2))) (* (sqrt x) (* x 2)) (pow (* (pow 4 1/8) (sqrt x)) 2) (* (pow 4 1/8) (sqrt x)) (pow 4 1/8))

simplify137.0ms (2.6%)

Memory

-20.0MiB live, 110.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	67	832
1	149	832
2	458	828
3	1037	828
4	1525	828
5	2525	828
6	3566	828
7	5220	828
8	7450	828
0	8202	828

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 156

Calls

Call 1

Inputs
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
x
x
x
x
(* 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))
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(* (pow (* 1 (pow x 3)) 1/4) (sqrt 2))
(* (pow (* 1 (pow x 3)) 1/4) (sqrt 2))
(* (pow (* 1 (pow x 3)) 1/4) (sqrt 2))
(* (pow (* 1 (pow x 3)) 1/4) (sqrt 2))
(* 2 (sqrt (pow x 3)))
(* 2 (sqrt (pow x 3)))
(* 2 (sqrt (pow x 3)))
(* 2 (sqrt (pow x 3)))
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/8) (sqrt x))
(* (pow 4 1/8) (sqrt x))
(* (pow 4 1/8) (sqrt x))
(* (pow 4 1/8) (sqrt x))
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
x
x
x
x
(* 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))
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(* (pow (* 1 (pow x 3)) 1/4) (sqrt 2))
(* (pow (* 1 (pow x 3)) 1/4) (sqrt 2))
(* (pow (* 1 (pow x 3)) 1/4) (sqrt 2))
(* (pow (* 1 (pow x 3)) 1/4) (sqrt 2))
(* 2 (sqrt (pow x 3)))
(* 2 (sqrt (pow x 3)))
(* 2 (sqrt (pow x 3)))
(* 2 (sqrt (pow x 3)))
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/8) (sqrt x))
(* (pow 4 1/8) (sqrt x))
(* (pow 4 1/8) (sqrt x))
(* (pow 4 1/8) (sqrt x))
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
(* (pow 64 1/16) x)
x
x
x
x
(* -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 (* (pow -1 1/4) (* (* x (sqrt -2)) (sqrt (sqrt -1)))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt -2)) (sqrt (sqrt -1)))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt -2)) (sqrt (sqrt -1)))))
(* -1 (* (pow -1 1/4) (* (* x (sqrt -2)) (sqrt (sqrt -1)))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(* (pow (* -1 (pow x 3)) 1/4) (* (sqrt -2) (sqrt (sqrt -1))))
(* (pow (* -1 (pow x 3)) 1/4) (* (sqrt -2) (sqrt (sqrt -1))))
(* (pow (* -1 (pow x 3)) 1/4) (* (sqrt -2) (sqrt (sqrt -1))))
(* (pow (* -1 (pow x 3)) 1/4) (* (sqrt -2) (sqrt (sqrt -1))))
(* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* -1 (* (pow 4 1/4) (* x (pow (sqrt -1) 2))))
(* -1 (* (pow 4 1/4) (* x (pow (sqrt -1) 2))))
(* -1 (* (pow 4 1/4) (* x (pow (sqrt -1) 2))))
(* -1 (* (pow 4 1/4) (* x (pow (sqrt -1) 2))))
(* -1 (* (pow 4 1/8) (* (sqrt x) (pow (sqrt -1) 2))))
(* -1 (* (pow 4 1/8) (* (sqrt x) (pow (sqrt -1) 2))))
(* -1 (* (pow 4 1/8) (* (sqrt x) (pow (sqrt -1) 2))))
(* -1 (* (pow 4 1/8) (* (sqrt x) (pow (sqrt -1) 2))))

Outputs
(* (pow 256 1/16) x)
(*.f64 x (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)))
(* (pow 256 1/16) x)
(*.f64 x (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)))
(* (pow 256 1/16) x)
(*.f64 x (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)))
(* (pow 256 1/16) x)
(*.f64 x (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)))
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
x
x
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)
(* (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)
(pow (* 1 x) 1/4)
(pow.f64 x #s(literal 1/4 binary64))
(pow (* 1 x) 1/4)
(pow.f64 x #s(literal 1/4 binary64))
(pow (* 1 x) 1/4)
(pow.f64 x #s(literal 1/4 binary64))
(pow (* 1 x) 1/4)
(pow.f64 x #s(literal 1/4 binary64))
(* (pow (* 1 (pow x 3)) 1/4) (sqrt 2))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow (* 1 (pow x 3)) 1/4) (sqrt 2))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow (* 1 (pow x 3)) 1/4) (sqrt 2))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow (* 1 (pow x 3)) 1/4) (sqrt 2))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 2 (sqrt (pow x 3)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* 2 (sqrt (pow x 3)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* 2 (sqrt (pow x 3)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* 2 (sqrt (pow x 3)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/8) (sqrt x))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x))
(* (pow 4 1/8) (sqrt x))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x))
(* (pow 4 1/8) (sqrt x))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x))
(* (pow 4 1/8) (sqrt x))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x))
(* (pow 256 1/16) x)
(*.f64 x (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)))
(* (pow 256 1/16) x)
(*.f64 x (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)))
(* (pow 256 1/16) x)
(*.f64 x (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)))
(* (pow 256 1/16) x)
(*.f64 x (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)))
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
x
x
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)
(* (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)
(pow (* 1 x) 1/4)
(pow.f64 x #s(literal 1/4 binary64))
(pow (* 1 x) 1/4)
(pow.f64 x #s(literal 1/4 binary64))
(pow (* 1 x) 1/4)
(pow.f64 x #s(literal 1/4 binary64))
(pow (* 1 x) 1/4)
(pow.f64 x #s(literal 1/4 binary64))
(* (pow (* 1 (pow x 3)) 1/4) (sqrt 2))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow (* 1 (pow x 3)) 1/4) (sqrt 2))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow (* 1 (pow x 3)) 1/4) (sqrt 2))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow (* 1 (pow x 3)) 1/4) (sqrt 2))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 2 (sqrt (pow x 3)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* 2 (sqrt (pow x 3)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* 2 (sqrt (pow x 3)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* 2 (sqrt (pow x 3)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/4) x)
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* (pow 4 1/8) (sqrt x))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x))
(* (pow 4 1/8) (sqrt x))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x))
(* (pow 4 1/8) (sqrt x))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x))
(* (pow 4 1/8) (sqrt x))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x))
(* (pow 256 1/16) x)
(*.f64 x (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)))
(* (pow 256 1/16) x)
(*.f64 x (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)))
(* (pow 256 1/16) x)
(*.f64 x (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)))
(* (pow 256 1/16) x)
(*.f64 x (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)))
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(* (pow 64 1/16) x)
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
x
x
x
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 (* (pow -1 1/4) (* (* x (sqrt -2)) (sqrt (sqrt -1)))))
(.f64 (pow.f64 #s(literal -1 binary64) #s(literal -5/4 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) x)))
(* -1 (* (pow -1 1/4) (* (* x (sqrt -2)) (sqrt (sqrt -1)))))
(.f64 (pow.f64 #s(literal -1 binary64) #s(literal -5/4 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) x)))
(* -1 (* (pow -1 1/4) (* (* x (sqrt -2)) (sqrt (sqrt -1)))))
(.f64 (pow.f64 #s(literal -1 binary64) #s(literal -5/4 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) x)))
(* -1 (* (pow -1 1/4) (* (* x (sqrt -2)) (sqrt (sqrt -1)))))
(.f64 (pow.f64 #s(literal -1 binary64) #s(literal -5/4 binary64)) (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 #s(literal -2 binary64)) x)))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(pow.f64 x #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(pow.f64 x #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(pow.f64 x #s(literal 1/4 binary64))
(exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x))))))
(pow.f64 x #s(literal 1/4 binary64))
(* (pow (* -1 (pow x 3)) 1/4) (* (sqrt -2) (sqrt (sqrt -1))))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64))) (pow.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal 1/4 binary64)))
(* (pow (* -1 (pow x 3)) 1/4) (* (sqrt -2) (sqrt (sqrt -1))))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64))) (pow.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal 1/4 binary64)))
(* (pow (* -1 (pow x 3)) 1/4) (* (sqrt -2) (sqrt (sqrt -1))))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64))) (pow.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal 1/4 binary64)))
(* (pow (* -1 (pow x 3)) 1/4) (* (sqrt -2) (sqrt (sqrt -1))))
(.f64 (.f64 (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -2 binary64))) (pow.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal 1/4 binary64)))
(* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* -2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64))
(* -1 (* (pow 4 1/4) (* x (pow (sqrt -1) 2))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* -1 (* (pow 4 1/4) (* x (pow (sqrt -1) 2))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* -1 (* (pow 4 1/4) (* x (pow (sqrt -1) 2))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* -1 (* (pow 4 1/4) (* x (pow (sqrt -1) 2))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/4 binary64)) x)
(* -1 (* (pow 4 1/8) (* (sqrt x) (pow (sqrt -1) 2))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x))
(* -1 (* (pow 4 1/8) (* (sqrt x) (pow (sqrt -1) 2))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x))
(* -1 (* (pow 4 1/8) (* (sqrt x) (pow (sqrt -1) 2))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x))
(* -1 (* (pow 4 1/8) (* (sqrt x) (pow (sqrt -1) 2))))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x))

rewrite123.0ms (2.3%)

Memory

8.2MiB live, 169.5MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	105
0	45	96
1	103	86
2	316	86
3	1390	35
4	5825	35
0	8194	35

Stop Event

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

Counts

16 → 1 345

Calls

Call 1

Inputs
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)))
(pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64))
#s(approx (* (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x))
(*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)
(*.f64 x #s(literal 1 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)
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) (*.f64 x #s(literal 2 binary64)))))
(pow.f64 x #s(literal 1/4 binary64))
(sqrt.f64 (.f64 (sqrt.f64 x) (.f64 x #s(literal 2 binary64))))
(.f64 (sqrt.f64 x) (.f64 x #s(literal 2 binary64)))
(pow.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x)) #s(literal 2 binary64))
(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x))
(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))

Outputs
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eval376.0ms (7.2%)

Memory: 20.8MiB live, 362.9MiB allocated
Compiler: Compiled 23 519 to 2 808 computations (88.1% saved)

prune41.0ms (0.8%)

Memory

-18.2MiB live, 109.4MiB allocated

Pruning

11 alts after pruning (2 fresh and 9 done)

	Pruned	Kept	Total
New	1 862	2	1 864
Fresh	0	0	0
Picked	1	4	5
Done	0	5	5
Total	1 863	11	1 874

Accuracy

100.0%

Counts

1 874 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.0%	(pow.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x)) #s(literal 2 binary64))
✓	99.4%	(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
✓	64.3%	(.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) (*.f64 x #s(literal 2 binary64)))))
✓	99.3%	(.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))
✓	99.6%	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)))
✓	99.3%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
▶	64.2%	(.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (.f64 (sqrt.f64 x) (*.f64 x #s(literal 2 binary64)))))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	49.3%	(sqrt.f64 (.f64 (.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)))
✓	49.4%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
▶	20.3%	x

Compiler

Compiled 86 to 71 computations (17.4% saved)

simplify3.0ms (0.1%)

Memory

5.5MiB live, 5.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	35
0	14	35
1	19	35
2	26	35
3	28	35
0	28	35

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize25.0ms (0.5%)

Memory

4.1MiB live, 43.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.1484375	(.f64 (sqrt.f64 x) (.f64 x #s(literal 2 binary64)))
accuracy	0.1484375	(sqrt.f64 (sqrt.f64 x))
accuracy	0.34765625	(.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (.f64 (sqrt.f64 x) (*.f64 x #s(literal 2 binary64)))))
accuracy	23.345165683592192	(sqrt.f64 (.f64 (sqrt.f64 x) (.f64 x #s(literal 2 binary64))))

Samples

17.0ms

256×

valid

Compiler

Compiled 72 to 18 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-sqrt: 5.0ms (49.8% of total)

ival-mult: 4.0ms (39.8% of total)

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

exact: 0.0ms (0% of total)

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

series51.0ms (1%)

Memory

-2.1MiB live, 81.1MiB allocated

Counts

5 → 60

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

17.0ms

((* (sqrt (sqrt x)) (sqrt (* (sqrt x) (* x 2)))) (sqrt (sqrt x)) (sqrt x) (sqrt (* (sqrt x) (* x 2))) (* (sqrt x) (* x 2)))

16.0ms

inf

((* (sqrt (sqrt x)) (sqrt (* (sqrt x) (* x 2)))) (sqrt (sqrt x)) (sqrt x) (sqrt (* (sqrt x) (* x 2))) (* (sqrt x) (* x 2)))

16.0ms

-inf

((* (sqrt (sqrt x)) (sqrt (* (sqrt x) (* x 2)))) (sqrt (sqrt x)) (sqrt x) (sqrt (* (sqrt x) (* x 2))) (* (sqrt x) (* x 2)))

simplify72.0ms (1.4%)

Memory

-4.4MiB live, 34.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	332
1	74	332
2	185	332
3	318	332
4	462	332
5	589	332
6	762	332
7	1124	332
8	1652	332
9	1703	332
10	1839	332
11	1967	332
12	2053	332
13	2207	332
14	2273	332
15	2367	332
16	2383	332
17	2387	332
18	2393	332
19	2397	332
20	2397	332
0	2397	332

Stop Event

1×	iter limit
1×	saturated

Counts

60 → 60

Calls

Call 1

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

rewrite36.0ms (0.7%)

Memory

-3.5MiB live, 35.2MiB allocated

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	8	29
0	14	24
1	27	21
2	76	21
3	277	21
4	1532	7
0	8402	7

Stop Event

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

Counts

5 → 39

Calls

Call 1

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

eval17.0ms (0.3%)

Memory: -5.9MiB live, 34.7MiB allocated
Compiler: Compiled 1 162 to 112 computations (90.4% saved)

prune8.0ms (0.2%)

Memory

24.4MiB live, 24.4MiB allocated

Pruning

11 alts after pruning (0 fresh and 11 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	0	0
Picked	0	2	2
Done	0	9	9
Total	113	11	124

Accuracy

100.0%

Counts

124 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.0%	(pow.f64 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x)) #s(literal 2 binary64))
✓	99.4%	(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
✓	64.3%	(.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) (*.f64 x #s(literal 2 binary64)))))
✓	99.3%	(.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))
✓	99.6%	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)))
✓	99.3%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
✓	64.2%	(.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (.f64 (sqrt.f64 x) (*.f64 x #s(literal 2 binary64)))))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	49.3%	(sqrt.f64 (.f64 (.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)))
✓	49.4%	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
✓	20.3%	x

Compiler

Compiled 188 to 115 computations (38.8% saved)

regimes13.0ms (0.3%)

Memory

-8.7MiB live, 30.4MiB allocated

Counts

13 → 1

Calls

Call 1

Inputs
x
(*.f64 x #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(sqrt.f64 (.f64 (.f64 (*.f64 x #s(literal 2 binary64)) (sqrt.f64 x)) (sqrt.f64 x)))
(.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (.f64 (sqrt.f64 x) (*.f64 x #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) (*.f64 x #s(literal 2 binary64)))))
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)))
(.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 (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (sqrt.f64 x)) #s(literal 2 binary64))
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) (*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)))

Outputs
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)))

Calls

3 calls:

5.0ms	(.f64 (.f64 #s(literal 2 binary64) x) x)
4.0ms	x
4.0ms	(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`
99.6%	1	`(.f64 (.f64 #s(literal 2 binary64) x) x)`

Compiler

Compiled 12 to 10 computations (16.7% saved)

regimes11.0ms (0.2%)

Memory

-21.8MiB live, 17.3MiB allocated

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 12 to 10 computations (16.7% saved)

regimes8.0ms (0.2%)

Memory

15.2MiB live, 15.2MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(sqrt.f64 (.f64 (.f64 #s(literal 2 binary64) x) x))`
99.3%	1	`(.f64 (.f64 #s(literal 2 binary64) x) x)`

Compiler

Compiled 12 to 10 computations (16.7% saved)

regimes5.0ms (0.1%)

Memory

10.1MiB live, 10.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

2 → 1

Calls

Call 1

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

Outputs
x

Calls

3 calls:

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

Results

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

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify22.0ms (0.4%)

Memory

-1.7MiB live, 37.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	33
1	28	33

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
x

Outputs
(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)) #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)) x)))
(.f64 #s(approx ( (pow 4 1/16) (* (pow 4 1/8) x)) (*.f64 x (pow.f64 #s(literal 64 binary64) #s(literal 1/16 binary64)))) (pow.f64 #s(literal 4 binary64) #s(literal 1/16 binary64)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 x))) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
x

soundness1.5s (29.1%)

Memory

13.8MiB live, 406.7MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	17	14
2	38	13
3	92	12
4	338	12
5	2074	12
0	8672	12
0	23	99
0	40	101
1	85	97
2	228	61
3	892	51
4	5044	51
0	8591	51
0	65	828
1	135	828
2	368	824
3	824	824
4	1055	824
5	1290	824
6	1650	824
7	2239	824
8	2688	824
9	2839	824
10	3088	824
11	3263	824
12	3400	824
13	3556	824
14	3866	824
15	4202	824
16	4494	824
17	5220	824
18	6621	824
19	7937	824
0	8006	824
0	29	105
0	45	96
1	103	86
2	316	86
3	1390	35
4	5825	35
0	8194	35

Stop Event

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

Compiler

Compiled 65 to 51 computations (21.5% saved)

preprocess39.0ms (0.7%)

Memory: -9.4MiB live, 65.6MiB allocated
Compiler: Compiled 120 to 100 computations (16.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	9	148
1	17	148
2	32	148
3	36	148
4	40	148
5	52	148
6	64	148
7	75	148
8	95	148
9	100	148
0	100	148

Iter	Nodes	Cost
0	29	130
0	45	128
1	62	128
2	111	125
3	152	125
4	196	125
5	231	125
6	231	125
0	231	125

Iter	Nodes	Cost
0	9	148
1	17	148
2	32	148
3	36	148
4	40	148
5	52	148
6	64	148
7	75	148
8	95	148
9	100	148
0	100	148

Iter	Nodes	Cost
0	29	130
0	45	128
1	62	128
2	111	125
3	152	125
4	196	125
5	231	125
6	231	125
0	231	125

start0.0ms (0%)

analyze0.0ms (0%)

sample1.1s (21.7%)

explain63.0ms (1.2%)

preprocess42.0ms (0.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize16.0ms (0.3%)

series4.0ms (0.1%)

simplify5.0ms (0.1%)

rewrite223.0ms (4.3%)

eval18.0ms (0.3%)

prune57.0ms (1.1%)

simplify7.0ms (0.1%)

localize107.0ms (2.1%)

series245.0ms (4.7%)

simplify195.0ms (3.7%)

rewrite106.0ms (2%)

eval191.0ms (3.7%)

prune37.0ms (0.7%)

simplify8.0ms (0.2%)

localize78.0ms (1.5%)

series179.0ms (3.4%)

simplify137.0ms (2.6%)

rewrite123.0ms (2.3%)

eval376.0ms (7.2%)

prune41.0ms (0.8%)

simplify3.0ms (0.1%)

localize25.0ms (0.5%)

series51.0ms (1%)

simplify72.0ms (1.4%)

rewrite36.0ms (0.7%)

eval17.0ms (0.3%)

prune8.0ms (0.2%)

regimes13.0ms (0.3%)

regimes11.0ms (0.2%)

regimes8.0ms (0.2%)

regimes5.0ms (0.1%)

simplify22.0ms (0.4%)

soundness1.5s (29.1%)

preprocess39.0ms (0.7%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	9	148
1	17	148
2	32	148
3	36	148
4	40	148
5	52	148
6	64	148
7	75	148
8	95	148
9	100	148
0	100	148

Iter	Nodes	Cost
0	29	130
0	45	128
1	62	128
2	111	125
3	152	125
4	196	125
5	231	125
6	231	125
0	231	125