Metrics for sqrt C (should all be same)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.8MiB live, 0.8MiB 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)

sample883.0ms (6.2%)

Memory

-3.5MiB live, 858.9MiB allocated

Samples

472.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 273.0ms

ival-mult: 173.0ms (63.3% of total)

ival-sqrt: 85.0ms (31.1% of total)

ival-true: 7.0ms (2.6% of total)

exact: 5.0ms (1.8% of total)

ival-assert: 3.0ms (1.1% of total)

Bogosity

explain67.0ms (0.5%)

Memory

3.1MiB live, 78.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
125	-	2	(8.399297044586115e-159)	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`(.f64 #s(literal 2 binary64) (.f64 x x))`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`	oflow-rescue	63	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	overflow	63
↳	`(*.f64 x x)`	overflow	63
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))`	uflow-rescue	60	0
↳	`(.f64 #s(literal 2 binary64) (.f64 x x))`	underflow	60
↳	`(*.f64 x x)`	underflow	60

Confusion

	Predicted +	Predicted -
+	123	2
-	0	131

Precision

1.0

Recall

0.984

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	123	0	2
-	0	0	131

Precision?

1.0

Recall?

0.984

Freqs

test

number	freq
0	133
1	123

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

22.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-mult: 7.0ms (59.3% of total)

ival-sqrt: 4.0ms (33.9% of total)

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

exact: 0.0ms (0% of total)

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

preprocess14.0ms (0.1%)

Memory

22.6MiB live, 22.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0%)

Memory

4.2MiB live, 4.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize35.0ms (0.2%)

Memory

-4.5MiB live, 33.4MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(.f64 #s(literal 2 binary64) (.f64 x x))
accuracy	28.85397330075771	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Samples

29.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

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

ival-mult: 3.0ms (52.4% of total)

ival-sqrt: 2.0ms (34.9% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0%)

Memory

8.3MiB live, 8.3MiB allocated

Counts

3 → 36

Calls

Call 1

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

Inputs

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

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

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

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

Calls

3 calls:

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

simplify12.0ms (0.1%)

Memory

-45.7MiB live, 8.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

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

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

rewrite148.0ms (1%)

Memory

14.9MiB live, 199.9MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

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

Counts

3 → 226

Calls

Call 1

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

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

eval37.0ms (0.3%)

Memory: 10.6MiB live, 81.1MiB allocated
Compiler: Compiled 3 146 to 747 computations (76.3% saved)

prune11.0ms (0.1%)

Memory

29.2MiB live, 29.2MiB allocated

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	254	8	262
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	254	9	263

Accuracy

100.0%

Counts

263 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
▶	99.4%	(.f64 (pow.f64 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))))
▶	99.4%	(.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))))
	99.2%	(.f64 (pow.f64 x #s(literal 3/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 (*.f64 x #s(literal 2 binary64)))))
	99.2%	(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #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))
	99.4%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
▶	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	54.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 154 to 131 computations (14.9% saved)

simplify14.0ms (0.1%)

Memory

-24.9MiB live, 17.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
cost-diff	0	(pow.f64 x #s(literal 5/8 binary64))
cost-diff	0	(.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))))
cost-diff	0	(*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)))
cost-diff	0	(pow.f64 x #s(literal 7/8 binary64))
cost-diff	0	(.f64 (pow.f64 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))))
cost-diff	0	(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
cost-diff	0	(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
cost-diff	6784	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
cost-diff	0	(pow.f64 x #s(literal 3/4 binary64))
cost-diff	0	(*.f64 #s(literal 4 binary64) x)
cost-diff	0	(pow.f64 (*.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64))
cost-diff	0	(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	129
0	48	129
1	62	125
2	70	125
0	70	125

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(pow.f64 (*.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64))
(*.f64 #s(literal 4 binary64) x)
#s(literal 4 binary64)
x
#s(literal 1/4 binary64)
(pow.f64 x #s(literal 3/4 binary64))
#s(literal 3/4 binary64)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
(.f64 (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 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))))
(pow.f64 x #s(literal 7/8 binary64))
x
#s(literal 7/8 binary64)
(sqrt.f64 (*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
#s(literal 2 binary64)
(.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))))
(pow.f64 x #s(literal 5/8 binary64))
x
#s(literal 5/8 binary64)
(sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(sqrt.f64 x)
#s(literal 2 binary64)

Outputs
(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 (.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (*.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64))
(pow.f64 (*.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
(*.f64 #s(literal 4 binary64) x)
(*.f64 x #s(literal 4 binary64))
#s(literal 4 binary64)
x
#s(literal 1/4 binary64)
(pow.f64 x #s(literal 3/4 binary64))
#s(literal 3/4 binary64)
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
x
(.f64 (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 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))) (pow.f64 x #s(literal 7/8 binary64)))
(pow.f64 x #s(literal 7/8 binary64))
x
#s(literal 7/8 binary64)
(sqrt.f64 (*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 x #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
#s(literal 2 binary64)
(.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (.f64 (*.f64 (sqrt.f64 x) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))) (pow.f64 x #s(literal 5/8 binary64)))
(pow.f64 x #s(literal 5/8 binary64))
x
#s(literal 5/8 binary64)
(sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(pow.f64 x #s(literal 1/4 binary64))
#s(literal 1/4 binary64)
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(sqrt.f64 x)
#s(literal 2 binary64)

localize101.0ms (0.7%)

Memory

36.0MiB live, 228.3MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(pow.f64 x #s(literal 1/4 binary64))
accuracy	0.12109375	(sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
accuracy	0.3046875	(.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))))
accuracy	0.35546875	(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))
accuracy	0.00390625	(pow.f64 x #s(literal 7/8 binary64))
accuracy	0.0078125	(pow.f64 x #s(literal 1/4 binary64))
accuracy	0.15234375	(sqrt.f64 (*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)))
accuracy	0.352226269536884	(.f64 (pow.f64 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))))
accuracy	0	(pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64))
accuracy	0.203125	(*.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)
accuracy	0.3203125	(.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x))
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.453125	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
accuracy	0	(pow.f64 (*.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64))
accuracy	0	(pow.f64 x #s(literal 3/4 binary64))
accuracy	0	(*.f64 #s(literal 4 binary64) x)
accuracy	0.3515625	(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))

Samples

83.0ms

256×

valid

Compiler

Compiled 131 to 30 computations (77.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 65.0ms

ival-pow: 29.0ms (44.7% of total)

ival-mult: 21.0ms (32.3% of total)

ival-sqrt: 13.0ms (20% of total)

exact: 1.0ms (1.5% of total)

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

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

series690.0ms (4.9%)

Memory

-26.7MiB live, 586.3MiB allocated

Counts

18 → 192

Calls

Call 1

Inputs
#s(alt (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) (patch (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (patch (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 4 binary64) x) (patch (.f64 #s(literal 4 binary64) x) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal 3/4 binary64)) (patch (pow.f64 x #s(literal 3/4 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) x) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 2 binary64)) (patch (sqrt.f64 #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (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 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)))) (patch (.f64 (pow.f64 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal 7/8 binary64)) (patch (pow.f64 x #s(literal 7/8 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) (patch (.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))) (patch (.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal 5/8 binary64)) (patch (pow.f64 x #s(literal 5/8 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (patch (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.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>) () ())

Outputs
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) (patch (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) (patch (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) (patch (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) (patch (.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log 4) (log x)))) (taylor 0 x) (#s(alt (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (patch (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log 4) (log x)))) (taylor 0 x) (#s(alt (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (patch (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log 4) (log x)))) (taylor 0 x) (#s(alt (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (patch (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log 4) (log x)))) (taylor 0 x) (#s(alt (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (patch (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 4 x) (taylor 0 x) (#s(alt (.f64 #s(literal 4 binary64) x) (patch (.f64 #s(literal 4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 4 x) (taylor 0 x) (#s(alt (.f64 #s(literal 4 binary64) x) (patch (.f64 #s(literal 4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 4 x) (taylor 0 x) (#s(alt (.f64 #s(literal 4 binary64) x) (patch (.f64 #s(literal 4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* 4 x) (taylor 0 x) (#s(alt (.f64 #s(literal 4 binary64) x) (patch (.f64 #s(literal 4 binary64) x) #<representation binary64>) () ())) ())
#s(alt (pow (* 1 (pow x 3)) 1/4) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3/4 binary64)) (patch (pow.f64 x #s(literal 3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (* 1 (pow x 3)) 1/4) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3/4 binary64)) (patch (pow.f64 x #s(literal 3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (* 1 (pow x 3)) 1/4) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3/4 binary64)) (patch (pow.f64 x #s(literal 3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow (* 1 (pow x 3)) 1/4) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3/4 binary64)) (patch (pow.f64 x #s(literal 3/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 #s(literal 2 binary64)) x) (patch (.f64 (sqrt.f64 #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/4) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt (* (pow 4 1/8) x) (taylor 0 x) (#s(alt (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) (patch (.f64 (pow.f64 #s(literal 4 binary64) #s(literal 1/8 binary64)) x) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* (pow -1 1/4) (* (* x (sqrt 2)) (sqrt (sqrt -1))))) (taylor -inf x) (#s(alt (.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))) (patch (.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.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 5/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))) (patch (.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 5/8 binary64)) (patch (pow.f64 x #s(literal 5/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 5/8 binary64)) (patch (pow.f64 x #s(literal 5/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 5/8 binary64)) (patch (pow.f64 x #s(literal 5/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 5/8 binary64)) (patch (pow.f64 x #s(literal 5/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (* (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x)))))) (sqrt 2)) (sqrt (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (* (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x)))))) (sqrt 2)) (sqrt (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (* (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x)))))) (sqrt 2)) (sqrt (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (* (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x)))))) (sqrt 2)) (sqrt (sqrt -1))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x)))))) (sqrt -1))) (taylor -inf x) (#s(alt (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (patch (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x)))))) (sqrt -1))) (taylor -inf x) (#s(alt (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (patch (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x)))))) (sqrt -1))) (taylor -inf x) (#s(alt (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (patch (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x)))))) (sqrt -1))) (taylor -inf x) (#s(alt (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (patch (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 1/4 binary64)) (patch (pow.f64 x #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 1/4 binary64)) (patch (pow.f64 x #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 1/4 binary64)) (patch (pow.f64 x #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())
#s(alt (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 1/4 binary64)) (patch (pow.f64 x #s(literal 1/4 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
349.0ms	x	@	inf	((* (pow (* 4 x) 1/4) (pow x 3/4)) (pow (* 4 x) 1/4) (* 4 x) (pow x 3/4) (* (sqrt 2) x) (sqrt 2) (* (pow 4 1/8) (* (pow 4 1/8) x)) (pow 4 1/8) (* (pow 4 1/8) x) (* (pow x 7/8) (sqrt (* (pow x 1/4) 2))) (pow x 7/8) (sqrt (* (pow x 1/4) 2)) (* (pow x 1/4) 2) (* (pow x 5/8) (sqrt (* (pow x 1/4) (* (sqrt x) 2)))) (pow x 5/8) (sqrt (* (pow x 1/4) (* (sqrt x) 2))) (* (pow x 1/4) (* (sqrt x) 2)) (pow x 1/4))
228.0ms	x	@	0	((* (pow (* 4 x) 1/4) (pow x 3/4)) (pow (* 4 x) 1/4) (* 4 x) (pow x 3/4) (* (sqrt 2) x) (sqrt 2) (* (pow 4 1/8) (* (pow 4 1/8) x)) (pow 4 1/8) (* (pow 4 1/8) x) (* (pow x 7/8) (sqrt (* (pow x 1/4) 2))) (pow x 7/8) (sqrt (* (pow x 1/4) 2)) (* (pow x 1/4) 2) (* (pow x 5/8) (sqrt (* (pow x 1/4) (* (sqrt x) 2)))) (pow x 5/8) (sqrt (* (pow x 1/4) (* (sqrt x) 2))) (* (pow x 1/4) (* (sqrt x) 2)) (pow x 1/4))
108.0ms	x	@	-inf	((* (pow (* 4 x) 1/4) (pow x 3/4)) (pow (* 4 x) 1/4) (* 4 x) (pow x 3/4) (* (sqrt 2) x) (sqrt 2) (* (pow 4 1/8) (* (pow 4 1/8) x)) (pow 4 1/8) (* (pow 4 1/8) x) (* (pow x 7/8) (sqrt (* (pow x 1/4) 2))) (pow x 7/8) (sqrt (* (pow x 1/4) 2)) (* (pow x 1/4) 2) (* (pow x 5/8) (sqrt (* (pow x 1/4) (* (sqrt x) 2)))) (pow x 5/8) (sqrt (* (pow x 1/4) (* (sqrt x) 2))) (* (pow x 1/4) (* (sqrt x) 2)) (pow x 1/4))

Time

Variable

Point

Expression

349.0ms

inf

((* (pow (* 4 x) 1/4) (pow x 3/4)) (pow (* 4 x) 1/4) (* 4 x) (pow x 3/4) (* (sqrt 2) x) (sqrt 2) (* (pow 4 1/8) (* (pow 4 1/8) x)) (pow 4 1/8) (* (pow 4 1/8) x) (* (pow x 7/8) (sqrt (* (pow x 1/4) 2))) (pow x 7/8) (sqrt (* (pow x 1/4) 2)) (* (pow x 1/4) 2) (* (pow x 5/8) (sqrt (* (pow x 1/4) (* (sqrt x) 2)))) (pow x 5/8) (sqrt (* (pow x 1/4) (* (sqrt x) 2))) (* (pow x 1/4) (* (sqrt x) 2)) (pow x 1/4))

228.0ms

((* (pow (* 4 x) 1/4) (pow x 3/4)) (pow (* 4 x) 1/4) (* 4 x) (pow x 3/4) (* (sqrt 2) x) (sqrt 2) (* (pow 4 1/8) (* (pow 4 1/8) x)) (pow 4 1/8) (* (pow 4 1/8) x) (* (pow x 7/8) (sqrt (* (pow x 1/4) 2))) (pow x 7/8) (sqrt (* (pow x 1/4) 2)) (* (pow x 1/4) 2) (* (pow x 5/8) (sqrt (* (pow x 1/4) (* (sqrt x) 2)))) (pow x 5/8) (sqrt (* (pow x 1/4) (* (sqrt x) 2))) (* (pow x 1/4) (* (sqrt x) 2)) (pow x 1/4))

108.0ms

-inf

((* (pow (* 4 x) 1/4) (pow x 3/4)) (pow (* 4 x) 1/4) (* 4 x) (pow x 3/4) (* (sqrt 2) x) (sqrt 2) (* (pow 4 1/8) (* (pow 4 1/8) x)) (pow 4 1/8) (* (pow 4 1/8) x) (* (pow x 7/8) (sqrt (* (pow x 1/4) 2))) (pow x 7/8) (sqrt (* (pow x 1/4) 2)) (* (pow x 1/4) 2) (* (pow x 5/8) (sqrt (* (pow x 1/4) (* (sqrt x) 2)))) (pow x 5/8) (sqrt (* (pow x 1/4) (* (sqrt x) 2))) (* (pow x 1/4) (* (sqrt x) 2)) (pow x 1/4))

simplify164.0ms (1.2%)

Memory

6.6MiB live, 159.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	91	1212
1	218	1212
2	509	1132
3	995	1108
4	1452	1088
5	1839	1088
6	2705	1088
7	4576	1088
8	7001	1088
0	8062	1088

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

Inputs
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(exp (* 1/4 (+ (log 4) (log x))))
(exp (* 1/4 (+ (log 4) (log x))))
(exp (* 1/4 (+ (log 4) (log x))))
(exp (* 1/4 (+ (log 4) (log x))))
(* 4 x)
(* 4 x)
(* 4 x)
(* 4 x)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* (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)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(pow (* 1 (pow x 7)) 1/8)
(pow (* 1 (pow x 7)) 1/8)
(pow (* 1 (pow x 7)) 1/8)
(pow (* 1 (pow x 7)) 1/8)
(* (pow (* 1 x) 1/8) (sqrt 2))
(* (pow (* 1 x) 1/8) (sqrt 2))
(* (pow (* 1 x) 1/8) (sqrt 2))
(* (pow (* 1 x) 1/8) (sqrt 2))
(* 2 (pow (* 1 x) 1/4))
(* 2 (pow (* 1 x) 1/4))
(* 2 (pow (* 1 x) 1/4))
(* 2 (pow (* 1 x) 1/4))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(pow (* 1 (pow x 5)) 1/8)
(pow (* 1 (pow x 5)) 1/8)
(pow (* 1 (pow x 5)) 1/8)
(pow (* 1 (pow x 5)) 1/8)
(* (pow (* 1 (pow x 3)) 1/8) (sqrt 2))
(* (pow (* 1 (pow x 3)) 1/8) (sqrt 2))
(* (pow (* 1 (pow x 3)) 1/8) (sqrt 2))
(* (pow (* 1 (pow x 3)) 1/8) (sqrt 2))
(* 2 (pow (* 1 (pow x 3)) 1/4))
(* 2 (pow (* 1 (pow x 3)) 1/4))
(* 2 (pow (* 1 (pow x 3)) 1/4))
(* 2 (pow (* 1 (pow x 3)) 1/4))
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(* (pow 4 1/4) x)
(exp (* 1/4 (+ (log 4) (* -1 (log (/ 1 x))))))
(exp (* 1/4 (+ (log 4) (* -1 (log (/ 1 x))))))
(exp (* 1/4 (+ (log 4) (* -1 (log (/ 1 x))))))
(exp (* 1/4 (+ (log 4) (* -1 (log (/ 1 x))))))
(* 4 x)
(* 4 x)
(* 4 x)
(* 4 x)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(pow (* 1 (pow x 3)) 1/4)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* (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)
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(pow (* 1 (pow x 7)) 1/8)
(pow (* 1 (pow x 7)) 1/8)
(pow (* 1 (pow x 7)) 1/8)
(pow (* 1 (pow x 7)) 1/8)
(* (pow (* 1 x) 1/8) (sqrt 2))
(* (pow (* 1 x) 1/8) (sqrt 2))
(* (pow (* 1 x) 1/8) (sqrt 2))
(* (pow (* 1 x) 1/8) (sqrt 2))
(* 2 (pow (* 1 x) 1/4))
(* 2 (pow (* 1 x) 1/4))
(* 2 (pow (* 1 x) 1/4))
(* 2 (pow (* 1 x) 1/4))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(pow (* 1 (pow x 5)) 1/8)
(pow (* 1 (pow x 5)) 1/8)
(pow (* 1 (pow x 5)) 1/8)
(pow (* 1 (pow x 5)) 1/8)
(* (pow (* 1 (pow x 3)) 1/8) (sqrt 2))
(* (pow (* 1 (pow x 3)) 1/8) (sqrt 2))
(* (pow (* 1 (pow x 3)) 1/8) (sqrt 2))
(* (pow (* 1 (pow x 3)) 1/8) (sqrt 2))
(* 2 (pow (* 1 (pow x 3)) 1/4))
(* 2 (pow (* 1 (pow x 3)) 1/4))
(* 2 (pow (* 1 (pow x 3)) 1/4))
(* 2 (pow (* 1 (pow x 3)) 1/4))
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(* -1 (* (pow 4 1/4) x))
(* -1 (* (pow 4 1/4) x))
(* -1 (* (pow 4 1/4) x))
(* -1 (* (pow 4 1/4) x))
(exp (* 1/4 (+ (log -4) (* -1 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -4) (* -1 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -4) (* -1 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -4) (* -1 (log (/ -1 x))))))
(* 4 x)
(* 4 x)
(* 4 x)
(* 4 x)
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x))))))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* (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)
(* -1 (* (pow -1 1/4) (* x (sqrt 2))))
(* -1 (* (pow -1 1/4) (* x (sqrt 2))))
(* -1 (* (pow -1 1/4) (* x (sqrt 2))))
(* -1 (* (pow -1 1/4) (* x (sqrt 2))))
(exp (* 1/8 (+ (log -1) (* -7 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -7 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -7 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -7 (log (/ -1 x))))))
(* (exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x)))))) (sqrt 2))
(* (exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x)))))) (sqrt 2))
(* (exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x)))))) (sqrt 2))
(* (exp (* 1/8 (+ (log -1) (* -1 (log (/ -1 x)))))) (sqrt 2))
(* 2 (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))))
(* 2 (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))))
(* 2 (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 x)))))))
(* 2 (exp (* 1/4 (+ (log -1) (* -1 (log (/ -1 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 (* 1/8 (+ (log -1) (* -5 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x))))))
(* (* (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x)))))) (sqrt 2)) (sqrt (sqrt -1)))
(* (* (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x)))))) (sqrt 2)) (sqrt (sqrt -1)))
(* (* (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x)))))) (sqrt 2)) (sqrt (sqrt -1)))
(* (* (exp (* 1/8 (+ (log -1) (* -3 (log (/ -1 x)))))) (sqrt 2)) (sqrt (sqrt -1)))
(* 2 (* (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x)))))) (sqrt -1)))
(* 2 (* (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x)))))) (sqrt -1)))
(* 2 (* (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x)))))) (sqrt -1)))
(* 2 (* (exp (* 1/4 (+ (log -1) (* -3 (log (/ -1 x)))))) (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))))))

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

rewrite193.0ms (1.4%)

Memory

12.7MiB live, 272.6MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	103
0	48	103
1	109	97
2	310	81
3	1320	71
4	4617	71
0	8102	71

Stop Event

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

Counts

18 → 1 059

Calls

Call 1

Inputs
(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(pow.f64 (*.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64))
(*.f64 #s(literal 4 binary64) x)
(pow.f64 x #s(literal 3/4 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 #s(literal 2 binary64))
(.f64 (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 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))))
(pow.f64 x #s(literal 7/8 binary64))
(sqrt.f64 (*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))))
(pow.f64 x #s(literal 5/8 binary64))
(sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 1/4 binary64))

Outputs
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eval291.0ms (2.1%)

Memory: 17.7MiB live, 286.9MiB allocated
Compiler: Compiled 18 326 to 2 295 computations (87.5% saved)

prune197.0ms (1.4%)

Memory

-33.8MiB live, 80.4MiB allocated

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	1 353	4	1 357
Fresh	2	1	3
Picked	4	1	5
Done	0	1	1
Total	1 359	7	1 366

Accuracy

100.0%

Counts

1 366 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x)
▶	99.4%	(.f64 (pow.f64 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))))
▶	99.4%	(.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))))
▶	99.4%	(.f64 (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
▶	99.4%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	54.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 102 to 89 computations (12.7% saved)

simplify5.0ms (0%)

Memory

6.2MiB live, 6.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64))
cost-diff	0	(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x)
cost-diff	6464	(pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64))
cost-diff	0	(.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))
cost-diff	0	(sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
cost-diff	0	(pow.f64 x #s(literal 5/8 binary64))
cost-diff	0	(.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))))
cost-diff	0	(*.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64)))
cost-diff	0	(pow.f64 x #s(literal 7/8 binary64))
cost-diff	0	(.f64 (pow.f64 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))))
cost-diff	0	(sqrt.f64 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	(.f64 (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(*.f64 x #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	140
0	47	140
1	59	136
2	71	136
3	73	136
0	73	136

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.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 (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))
(sqrt.f64 x)
x
#s(literal 2 binary64)
(pow.f64 x #s(literal 3/4 binary64))
#s(literal 3/4 binary64)
(.f64 (pow.f64 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))))
(pow.f64 x #s(literal 7/8 binary64))
x
#s(literal 7/8 binary64)
(sqrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))
(sqrt.f64 (sqrt.f64 x))
(sqrt.f64 x)
#s(literal 2 binary64)
(.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))))
(pow.f64 x #s(literal 5/8 binary64))
x
#s(literal 5/8 binary64)
(sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(sqrt.f64 (sqrt.f64 x))
(sqrt.f64 x)
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x)
(pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64))
#s(literal 256 binary64)
#s(literal 1/32 binary64)
#s(literal 2 binary64)
x

Outputs
(.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 (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
(sqrt.f64 (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
(sqrt.f64 x)
x
#s(literal 2 binary64)
(pow.f64 x #s(literal 3/4 binary64))
#s(literal 3/4 binary64)
(.f64 (pow.f64 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))) (pow.f64 x #s(literal 7/8 binary64)))
(pow.f64 x #s(literal 7/8 binary64))
x
#s(literal 7/8 binary64)
(sqrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))
(sqrt.f64 (sqrt.f64 x))
(sqrt.f64 x)
#s(literal 2 binary64)
(.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (pow.f64 x #s(literal 5/8 binary64)))
(pow.f64 x #s(literal 5/8 binary64))
x
#s(literal 5/8 binary64)
(sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(sqrt.f64 (sqrt.f64 x))
(sqrt.f64 x)
(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x)
(*.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64)) x)
(pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 256 binary64) #s(literal 1/16 binary64))
(pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64))
#s(literal 256 binary64)
#s(literal 1/32 binary64)
#s(literal 2 binary64)
x

localize6.7s (47.5%)

Memory

2.2MiB live, 112.2MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64))
accuracy	0.453125	(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x)
accuracy	1.0	(pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64))
accuracy	0.12109375	(sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
accuracy	0.15625	(sqrt.f64 (sqrt.f64 x))
accuracy	0.3046875	(.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))))
accuracy	0.35546875	(.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))
accuracy	0.00390625	(pow.f64 x #s(literal 7/8 binary64))
accuracy	0.15234375	(sqrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64)))
accuracy	0.15625	(sqrt.f64 (sqrt.f64 x))
accuracy	0.352226269536884	(.f64 (pow.f64 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))))
accuracy	0	(*.f64 (sqrt.f64 x) #s(literal 2 binary64))
accuracy	0	(sqrt.f64 x)
accuracy	0.1015625	(sqrt.f64 (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))
accuracy	0.3515625	(.f64 (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
accuracy	0	(*.f64 x #s(literal 2 binary64))
accuracy	0	(sqrt.f64 (*.f64 x #s(literal 2 binary64)))
accuracy	0	(sqrt.f64 x)
accuracy	0.35775375976844204	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))

Samples

60.0ms

256×

valid

Compiler

Compiled 142 to 29 computations (79.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-pow: 18.0ms (40.7% of total)

ival-mult: 13.0ms (29.4% of total)

ival-sqrt: 10.0ms (22.6% of total)

ival-pow2: 2.0ms (4.5% of total)

exact: 1.0ms (2.3% of total)

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

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

series2.1s (14.9%)

Memory

-3.6MiB live, 607.3MiB allocated

Counts

19 → 204

Calls

Call 1

Inputs
#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 (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (pow.f64 x #s(literal 3/4 binary64))) (patch (.f64 (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (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 (pow.f64 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64)))) (patch (.f64 (pow.f64 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal 7/8 binary64)) (patch (pow.f64 x #s(literal 7/8 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64)) (patch (.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))) (patch (.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal 5/8 binary64)) (patch (pow.f64 x #s(literal 5/8 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())
#s(alt (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) (patch (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (sqrt.f64 x)) (patch (sqrt.f64 (sqrt.f64 x)) #<representation binary64>) () ())

Outputs
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) (patch (.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 x #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 x #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 x #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt x) (sqrt 2)) (taylor 0 x) (#s(alt (sqrt.f64 (.f64 x #s(literal 2 binary64))) (patch (sqrt.f64 (.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 2 x) (taylor 0 x) (#s(alt (.f64 x #s(literal 2 binary64)) (patch (.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (sqrt x) (taylor 0 x) (#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (pow.f64 x #s(literal 3/4 binary64))) (patch (.f64 (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (pow.f64 x #s(literal 3/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (pow.f64 x #s(literal 3/4 binary64))) (patch (.f64 (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (pow.f64 x #s(literal 3/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (pow.f64 x #s(literal 3/4 binary64))) (patch (.f64 (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (pow.f64 x #s(literal 3/4 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 2)) (taylor 0 x) (#s(alt (.f64 (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (pow.f64 x #s(literal 3/4 binary64))) (patch (.f64 (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (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>) () ())) ())
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#s(alt (exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x)))))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 5/8 binary64)) (patch (pow.f64 x #s(literal 5/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow (* -1 (pow x 3)) 1/8) (* (pow (* 1 (pow (sqrt -1) 3)) 1/4) (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow (* -1 (pow x 3)) 1/8) (* (pow (* 1 (pow (sqrt -1) 3)) 1/4) (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow (* -1 (pow x 3)) 1/8) (* (pow (* 1 (pow (sqrt -1) 3)) 1/4) (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow (* -1 (pow x 3)) 1/8) (* (pow (* 1 (pow (sqrt -1) 3)) 1/4) (sqrt 2))) (taylor -inf x) (#s(alt (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) (patch (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (pow (* -1 (pow x 3)) 1/4) (sqrt (pow (sqrt -1) 3)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (pow (* -1 (pow x 3)) 1/4) (sqrt (pow (sqrt -1) 3)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (pow (* -1 (pow x 3)) 1/4) (sqrt (pow (sqrt -1) 3)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 2 (* (pow (* -1 (pow x 3)) 1/4) (sqrt (pow (sqrt -1) 3)))) (taylor -inf x) (#s(alt (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (patch (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* (pow 256 1/16) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 256 1/16) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 256 1/16) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow 256 1/16) x) (taylor -inf x) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) (patch (.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* (pow (* -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>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

1.9s

((* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x) (* (sqrt (* (sqrt x) 2)) (pow x 3/4)) (sqrt (* (sqrt x) 2)) (* (sqrt x) 2) (* (pow x 7/8) (sqrt (* (sqrt (sqrt x)) 2))) (pow x 7/8) (sqrt (* (sqrt (sqrt x)) 2)) (* (sqrt (sqrt x)) 2) (* (pow x 5/8) (sqrt (* (sqrt (sqrt x)) (* (sqrt x) 2)))) (pow x 5/8) (sqrt (* (sqrt (sqrt x)) (* (sqrt x) 2))) (* (sqrt (sqrt x)) (* (sqrt x) 2)) (pow (pow 256 1/32) 2) (* (pow (pow 256 1/32) 2) x) (pow 256 1/32) (sqrt (sqrt x)))

179.0ms

-inf

((* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x) (* (sqrt (* (sqrt x) 2)) (pow x 3/4)) (sqrt (* (sqrt x) 2)) (* (sqrt x) 2) (* (pow x 7/8) (sqrt (* (sqrt (sqrt x)) 2))) (pow x 7/8) (sqrt (* (sqrt (sqrt x)) 2)) (* (sqrt (sqrt x)) 2) (* (pow x 5/8) (sqrt (* (sqrt (sqrt x)) (* (sqrt x) 2)))) (pow x 5/8) (sqrt (* (sqrt (sqrt x)) (* (sqrt x) 2))) (* (sqrt (sqrt x)) (* (sqrt x) 2)) (pow (pow 256 1/32) 2) (* (pow (pow 256 1/32) 2) x) (pow 256 1/32) (sqrt (sqrt x)))

56.0ms

inf

((* (sqrt (* x 2)) (sqrt x)) (sqrt (* x 2)) (* x 2) (sqrt x) (* (sqrt (* (sqrt x) 2)) (pow x 3/4)) (sqrt (* (sqrt x) 2)) (* (sqrt x) 2) (* (pow x 7/8) (sqrt (* (sqrt (sqrt x)) 2))) (pow x 7/8) (sqrt (* (sqrt (sqrt x)) 2)) (* (sqrt (sqrt x)) 2) (* (pow x 5/8) (sqrt (* (sqrt (sqrt x)) (* (sqrt x) 2)))) (pow x 5/8) (sqrt (* (sqrt (sqrt x)) (* (sqrt x) 2))) (* (sqrt (sqrt x)) (* (sqrt x) 2)) (pow (pow 256 1/32) 2) (* (pow (pow 256 1/32) 2) x) (pow 256 1/32) (sqrt (sqrt x)))

simplify222.0ms (1.6%)

Memory

15.9MiB live, 134.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 16 (0.0ms)

Iter	Nodes	Cost
0	96	1316
1	220	1316
2	578	1268
3	1350	1268
4	1779	1260
5	2231	1260
6	2700	1260
7	2957	1260
8	3211	1260
9	3750	1260
10	3923	1260
11	4113	1260
12	4186	1260
13	4247	1260
14	4294	1260
15	4552	1260
16	4799	1252
17	5142	1252
18	5797	1252
19	6691	1252
20	7725	1252
0	8010	1252

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
(* 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) (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))
(pow (* 1 (pow x 7)) 1/8)
(pow (* 1 (pow x 7)) 1/8)
(pow (* 1 (pow x 7)) 1/8)
(pow (* 1 (pow x 7)) 1/8)
(* (pow (* 1 x) 1/8) (sqrt 2))
(* (pow (* 1 x) 1/8) (sqrt 2))
(* (pow (* 1 x) 1/8) (sqrt 2))
(* (pow (* 1 x) 1/8) (sqrt 2))
(* 2 (pow (* 1 x) 1/4))
(* 2 (pow (* 1 x) 1/4))
(* 2 (pow (* 1 x) 1/4))
(* 2 (pow (* 1 x) 1/4))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(pow (* 1 (pow x 5)) 1/8)
(pow (* 1 (pow x 5)) 1/8)
(pow (* 1 (pow x 5)) 1/8)
(pow (* 1 (pow x 5)) 1/8)
(* (pow (* 1 (pow x 3)) 1/8) (sqrt 2))
(* (pow (* 1 (pow x 3)) 1/8) (sqrt 2))
(* (pow (* 1 (pow x 3)) 1/8) (sqrt 2))
(* (pow (* 1 (pow x 3)) 1/8) (sqrt 2))
(* 2 (pow (* 1 (pow x 3)) 1/4))
(* 2 (pow (* 1 (pow x 3)) 1/4))
(* 2 (pow (* 1 (pow x 3)) 1/4))
(* 2 (pow (* 1 (pow x 3)) 1/4))
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(* 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) (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))
(pow (* 1 (pow x 7)) 1/8)
(pow (* 1 (pow x 7)) 1/8)
(pow (* 1 (pow x 7)) 1/8)
(pow (* 1 (pow x 7)) 1/8)
(* (pow (* 1 x) 1/8) (sqrt 2))
(* (pow (* 1 x) 1/8) (sqrt 2))
(* (pow (* 1 x) 1/8) (sqrt 2))
(* (pow (* 1 x) 1/8) (sqrt 2))
(* 2 (pow (* 1 x) 1/4))
(* 2 (pow (* 1 x) 1/4))
(* 2 (pow (* 1 x) 1/4))
(* 2 (pow (* 1 x) 1/4))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(* x (sqrt 2))
(pow (* 1 (pow x 5)) 1/8)
(pow (* 1 (pow x 5)) 1/8)
(pow (* 1 (pow x 5)) 1/8)
(pow (* 1 (pow x 5)) 1/8)
(* (pow (* 1 (pow x 3)) 1/8) (sqrt 2))
(* (pow (* 1 (pow x 3)) 1/8) (sqrt 2))
(* (pow (* 1 (pow x 3)) 1/8) (sqrt 2))
(* (pow (* 1 (pow x 3)) 1/8) (sqrt 2))
(* 2 (pow (* 1 (pow x 3)) 1/4))
(* 2 (pow (* 1 (pow x 3)) 1/4))
(* 2 (pow (* 1 (pow x 3)) 1/4))
(* 2 (pow (* 1 (pow x 3)) 1/4))
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(pow (* 1 x) 1/4)
(* -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)))))
(* (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)))
(* -1 (* (pow -1 1/8) (* (pow (* 1 (sqrt -1)) 1/4) (* x (sqrt 2)))))
(* -1 (* (pow -1 1/8) (* (pow (* 1 (sqrt -1)) 1/4) (* x (sqrt 2)))))
(* -1 (* (pow -1 1/8) (* (pow (* 1 (sqrt -1)) 1/4) (* x (sqrt 2)))))
(* -1 (* (pow -1 1/8) (* (pow (* 1 (sqrt -1)) 1/4) (* x (sqrt 2)))))
(exp (* 1/8 (+ (log -1) (* -7 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -7 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -7 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -7 (log (/ -1 x))))))
(* (pow (* -1 x) 1/8) (* (pow (* 1 (sqrt -1)) 1/4) (sqrt 2)))
(* (pow (* -1 x) 1/8) (* (pow (* 1 (sqrt -1)) 1/4) (sqrt 2)))
(* (pow (* -1 x) 1/8) (* (pow (* 1 (sqrt -1)) 1/4) (sqrt 2)))
(* (pow (* -1 x) 1/8) (* (pow (* 1 (sqrt -1)) 1/4) (sqrt 2)))
(* 2 (* (pow (* -1 x) 1/4) (sqrt (sqrt -1))))
(* 2 (* (pow (* -1 x) 1/4) (sqrt (sqrt -1))))
(* 2 (* (pow (* -1 x) 1/4) (sqrt (sqrt -1))))
(* 2 (* (pow (* -1 x) 1/4) (sqrt (sqrt -1))))
(* -1 (* (pow -1 1/8) (* (pow (* 1 (pow (sqrt -1) 3)) 1/4) (* x (sqrt 2)))))
(* -1 (* (pow -1 1/8) (* (pow (* 1 (pow (sqrt -1) 3)) 1/4) (* x (sqrt 2)))))
(* -1 (* (pow -1 1/8) (* (pow (* 1 (pow (sqrt -1) 3)) 1/4) (* x (sqrt 2)))))
(* -1 (* (pow -1 1/8) (* (pow (* 1 (pow (sqrt -1) 3)) 1/4) (* x (sqrt 2)))))
(exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x))))))
(exp (* 1/8 (+ (log -1) (* -5 (log (/ -1 x))))))
(* (pow (* -1 (pow x 3)) 1/8) (* (pow (* 1 (pow (sqrt -1) 3)) 1/4) (sqrt 2)))
(* (pow (* -1 (pow x 3)) 1/8) (* (pow (* 1 (pow (sqrt -1) 3)) 1/4) (sqrt 2)))
(* (pow (* -1 (pow x 3)) 1/8) (* (pow (* 1 (pow (sqrt -1) 3)) 1/4) (sqrt 2)))
(* (pow (* -1 (pow x 3)) 1/8) (* (pow (* 1 (pow (sqrt -1) 3)) 1/4) (sqrt 2)))
(* 2 (* (pow (* -1 (pow x 3)) 1/4) (sqrt (pow (sqrt -1) 3))))
(* 2 (* (pow (* -1 (pow x 3)) 1/4) (sqrt (pow (sqrt -1) 3))))
(* 2 (* (pow (* -1 (pow x 3)) 1/4) (sqrt (pow (sqrt -1) 3))))
(* 2 (* (pow (* -1 (pow x 3)) 1/4) (sqrt (pow (sqrt -1) 3))))
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (pow 256 1/16) x)
(* (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)))

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)
(* (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) (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)
(pow (* 1 (pow x 7)) 1/8)
(pow.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 1/8 binary64))
(pow (* 1 (pow x 7)) 1/8)
(pow.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 1/8 binary64))
(pow (* 1 (pow x 7)) 1/8)
(pow.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 1/8 binary64))
(pow (* 1 (pow x 7)) 1/8)
(pow.f64 (pow.f64 x #s(literal 7 binary64)) #s(literal 1/8 binary64))
(* (pow (* 1 x) 1/8) (sqrt 2))
(*.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow (* 1 x) 1/8) (sqrt 2))
(*.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow (* 1 x) 1/8) (sqrt 2))
(*.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* (pow (* 1 x) 1/8) (sqrt 2))
(*.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(* 2 (pow (* 1 x) 1/4))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(* 2 (pow (* 1 x) 1/4))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(* 2 (pow (* 1 x) 1/4))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(* 2 (pow (* 1 x) 1/4))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) #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)
(pow (* 1 (pow x 5)) 1/8)
(pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/8 binary64))
(pow (* 1 (pow x 5)) 1/8)
(pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/8 binary64))
(pow (* 1 (pow x 5)) 1/8)
(pow.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 1/8 binary64))
(pow (* 1 (pow x 5)) 1/8)
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(.f64 (.f64 (pow.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* 2 (* (pow (* -1 (pow x 3)) 1/4) (sqrt (pow (sqrt -1) 3))))
(.f64 (.f64 (pow.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64)))))
(* (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 (* -1 x) 1/4) (sqrt (sqrt -1)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))))
(* (pow (* -1 x) 1/4) (sqrt (sqrt -1)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))))
(* (pow (* -1 x) 1/4) (sqrt (sqrt -1)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))))
(* (pow (* -1 x) 1/4) (sqrt (sqrt -1)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) (sqrt.f64 (sqrt.f64 #s(literal -1 binary64))))

rewrite142.0ms (1%)

Memory

-4.9MiB live, 189.9MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	109
0	47	90
1	110	86
2	293	76
3	982	70
4	6414	70
0	8166	70

Stop Event

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

Counts

19 → 907

Calls

Call 1

Inputs
(.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 (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 (pow.f64 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))))
(pow.f64 x #s(literal 7/8 binary64))
(sqrt.f64 (*.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))
(.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))))
(pow.f64 x #s(literal 5/8 binary64))
(sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64))))
(.f64 (sqrt.f64 (sqrt.f64 x)) (.f64 (sqrt.f64 x) #s(literal 2 binary64)))
(pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64))
(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x)
(pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64))
(sqrt.f64 (sqrt.f64 x))

Outputs
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eval223.0ms (1.6%)

Memory: 22.4MiB live, 292.6MiB allocated
Compiler: Compiled 19 167 to 2 053 computations (89.3% saved)

prune33.0ms (0.2%)

Memory

-32.0MiB live, 93.2MiB allocated

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	1 338	2	1 340
Fresh	0	0	0
Picked	0	5	5
Done	0	2	2
Total	1 338	9	1 347

Accuracy

100.0%

Counts

1 347 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x)
✓	99.4%	(.f64 (pow.f64 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))))
✓	99.4%	(.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))))
▶	99.0%	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
✓	99.4%	(.f64 (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
✓	99.4%	(.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))
✓	54.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))

Compiler

Compiled 67 to 58 computations (13.4% saved)

simplify4.0ms (0%)

Memory

5.8MiB live, 5.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
cost-diff	1600	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
cost-diff	320	(*.f64 x #s(literal 1 binary64))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	24
0	13	22
1	19	22
2	23	18
3	25	18
4	36	18
5	40	18
6	41	18
0	41	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize23.0ms (0.2%)

Memory

-1.7MiB live, 35.9MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 x)
accuracy	0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.35775375976844204	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
accuracy	0.4645500488422101	(*.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64)))
accuracy	0	(*.f64 x #s(literal 1 binary64))

Samples

17.0ms

256×

valid

Compiler

Compiled 26 to 10 computations (61.5% saved)

Precisions

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

ival-mult: 6.0ms (57.1% of total)

ival-sqrt: 3.0ms (28.5% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0%)

Memory

9.5MiB live, 9.5MiB allocated

Counts

5 → 48

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

-inf

((* x 1) (* (* (sqrt x) (sqrt 2)) (sqrt x)) (* (sqrt x) (sqrt 2)) (sqrt x) (sqrt 2))

1.0ms

inf

((* x 1) (* (* (sqrt x) (sqrt 2)) (sqrt x)) (* (sqrt x) (sqrt 2)) (sqrt x) (sqrt 2))

1.0ms

((* x 1) (* (* (sqrt x) (sqrt 2)) (sqrt x)) (* (sqrt x) (sqrt 2)) (sqrt x) (sqrt 2))

simplify24.0ms (0.2%)

Memory

19.8MiB live, 19.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	144
1	37	144
2	134	144
3	266	144
4	665	144
5	873	144
6	1002	144
7	1031	144
8	1033	144
9	1033	144
0	1033	144

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 36

Calls

Call 1

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

rewrite90.0ms (0.6%)

Memory

1.5MiB live, 75.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
0	13	8
1	24	8
2	56	8
3	156	8
4	708	8
5	5192	8
0	8250	8

Stop Event

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

Counts

5 → 133

Calls

Call 1

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

Outputs
#<batchref>
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eval29.0ms (0.2%)

Memory: -0.7MiB live, 40.1MiB allocated
Compiler: Compiled 1 893 to 251 computations (86.7% saved)

prune12.0ms (0.1%)

Memory

-15.8MiB live, 21.2MiB allocated

Pruning

9 alts after pruning (1 fresh and 8 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	0	0	0
Picked	1	1	2
Done	0	7	7
Total	183	9	192

Accuracy

100.0%

Counts

192 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) x)
✓	99.4%	(.f64 (pow.f64 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))))
✓	99.4%	(.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))))
✓	99.0%	(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
✓	99.4%	(.f64 (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
✓	99.4%	(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
✓	99.3%	(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
✓	54.9%	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
	20.3%	x

Compiler

Compiled 196 to 115 computations (41.3% saved)

regimes23.0ms (0.2%)

Memory

1.7MiB live, 37.7MiB allocated

Counts

16 → 1

Calls

Call 1

Inputs
x
(*.f64 x #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
(.f64 (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))))
(.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 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))
(.f64 (pow.f64 (.f64 #s(literal 4 binary64) x) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 3/4 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (pow.f64 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))))
(.f64 (pow.f64 x #s(literal 3/8 binary64)) (.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 (*.f64 x #s(literal 2 binary64)))))
(.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (pow.f64 x #s(literal 1/4 binary64)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))))

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

Calls

4 calls:

8.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
5.0ms	x
5.0ms	(*.f64 x x)
4.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))

Results

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

Compiler

Compiled 15 to 12 computations (20% saved)

regimes17.0ms (0.1%)

Memory

-6.4MiB live, 31.8MiB allocated

Counts

11 → 1

Calls

Call 1

Inputs
x
(*.f64 x #s(literal 1 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) x)
(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
(.f64 (sqrt.f64 (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))
(.f64 (.f64 (sqrt.f64 x) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 x))
(.f64 (sqrt.f64 (.f64 (sqrt.f64 x) #s(literal 2 binary64))) (pow.f64 x #s(literal 3/4 binary64)))
(.f64 (pow.f64 x #s(literal 7/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) #s(literal 2 binary64))))
(.f64 (pow.f64 x #s(literal 5/8 binary64)) (sqrt.f64 (.f64 (sqrt.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 2 binary64)))))
(*.f64 (pow.f64 (pow.f64 #s(literal 256 binary64) #s(literal 1/32 binary64)) #s(literal 2 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))

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

Calls

4 calls:

6.0ms	x
4.0ms	(*.f64 x x)
3.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (.f64 x x)))
3.0ms	(.f64 #s(literal 2 binary64) (.f64 x x))

Results

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

Compiler

Compiled 15 to 12 computations (20% saved)

regimes8.0ms (0.1%)

Memory

20.3MiB live, 20.3MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 15 to 12 computations (20% saved)

regimes6.0ms (0%)

Memory

13.4MiB live, 13.4MiB 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

4 calls:

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

Results

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

Compiler

Compiled 15 to 12 computations (20% saved)

simplify27.0ms (0.2%)

Memory

-38.1MiB live, 45.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	20	21

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.5s (10.8%)

Memory

13.6MiB live, 483.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	103
0	48	103
1	109	97
2	310	81
3	1320	71
4	4617	71
0	8102	71
0	8	20
0	13	8
1	24	8
2	56	8
3	156	8
4	708	8
5	5192	8
0	8250	8
0	27	109
0	47	90
1	110	86
2	293	76
3	982	70
4	6414	70
0	8166	70
0	5	14
0	8	14
1	17	13
2	46	12
3	123	12
4	580	12
5	3914	12
0	8179	12

Stop Event

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

Compiler

Compiled 82 to 60 computations (26.8% saved)

preprocess33.0ms (0.2%)

Memory: 30.7MiB live, 68.8MiB allocated
Compiler: Compiled 108 to 88 computations (18.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

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

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

start0.0ms (0%)

analyze0.0ms (0%)

sample883.0ms (6.2%)

explain67.0ms (0.5%)

preprocess14.0ms (0.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize35.0ms (0.2%)

series4.0ms (0%)

simplify12.0ms (0.1%)

rewrite148.0ms (1%)

eval37.0ms (0.3%)

prune11.0ms (0.1%)

simplify14.0ms (0.1%)

localize101.0ms (0.7%)

series690.0ms (4.9%)

simplify164.0ms (1.2%)

rewrite193.0ms (1.4%)

eval291.0ms (2.1%)

prune197.0ms (1.4%)

simplify5.0ms (0%)

localize6.7s (47.5%)

series2.1s (14.9%)

simplify222.0ms (1.6%)

rewrite142.0ms (1%)

eval223.0ms (1.6%)

prune33.0ms (0.2%)

simplify4.0ms (0%)

localize23.0ms (0.2%)

series4.0ms (0%)

simplify24.0ms (0.2%)

rewrite90.0ms (0.6%)

eval29.0ms (0.2%)

prune12.0ms (0.1%)

regimes23.0ms (0.2%)

regimes17.0ms (0.1%)

regimes8.0ms (0.1%)

regimes6.0ms (0%)

simplify27.0ms (0.2%)

soundness1.5s (10.8%)

preprocess33.0ms (0.2%)

end0.0ms (0%)

Profiling

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