Metrics for math.cube on real

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 7 to 5 computations (28.6% saved)

sample541.0ms (6%)

Memory

-19.2MiB live, 654.0MiB allocated

Samples

352.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 131.0ms

ival-mult: 122.0ms (92.9% of total)

ival-true: 6.0ms (4.6% of total)

ival-assert: 3.0ms (2.3% of total)

Bogosity

explain43.0ms (0.5%)

Memory

34.6MiB live, 107.1MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(.f64 (.f64 x x) x)`
-	-	`(*.f64 x x)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

16.0ms

512×

valid

Compiler

Compiled 27 to 13 computations (51.9% saved)

Precisions

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

ival-mult: 7.0ms (95% of total)

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

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

preprocess28.0ms (0.3%)

Memory

-57.2MiB live, 48.3MiB allocated

Algorithm

1×	egg-herbie

Rules

22×	`distribute-lft-neg-in`
22×	`associate-r`
16×	`cancel-sign-sub-inv`
16×	`unsub-neg`
14×	`neg-sub0`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	13
1	23	9
2	60	7
3	127	7
4	148	7
5	156	7
0	3	5
0	5	5
1	6	3
2	8	3
0	8	3

Stop Event

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

Calls

Call 1

Inputs
(.f64 (.f64 x x) x)

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

Symmetry

(negabs x)

Compiler

Compiled 5 to 3 computations (40% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(.f64 (.f64 x x) x)

Compiler

Compiled 5 to 3 computations (40% saved)

simplify3.0ms (0%)

Memory

1.9MiB live, 1.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	-5824	(.f64 (.f64 x x) x)
cost-diff	0	(*.f64 x x)

Rules

6×	`lower-*.f32`
4×	`lift-*.f64`
2×	`lower-*.f64`
2×	`lower-pow.f64`
2×	`cube-unmult`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	3	9
0	5	9
1	6	7
2	8	7
0	8	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 (.f64 x x) x)
(*.f64 x x)
x

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

localize11.0ms (0.1%)

Memory

13.8MiB live, 13.8MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(*.f64 x x)
accuracy	0.0625	(.f64 (.f64 x x) x)

Samples

8.0ms

256×

valid

Compiler

Compiled 11 to 5 computations (54.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-mult: 3.0ms (90.7% of total)

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

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

series3.0ms (0%)

Memory

6.0MiB live, 5.9MiB allocated

Counts

2 → 24

Calls

Call 1

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

Outputs
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (.f64 (.f64 x x) x) (patch (.f64 (.f64 x x) x) #<representation binary64>) () ())) ())

Calls

3 calls:

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

simplify3.0ms (0%)

Memory

5.3MiB live, 5.3MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`lower-*.f64`
6×	`lower-*.f32`
4×	`lower-pow.f64`
4×	`lower-pow.f32`
2×	`cube-mult`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	72
1	8	72
2	10	72
3	12	72
0	12	72

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

Inputs
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)

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

rewrite141.0ms (1.6%)

Memory

1.7MiB live, 114.2MiB allocated

Rules

2 618×	`lower-*.f64`
2 618×	`lower-*.f32`
1 200×	`unpow-prod-down`
1 030×	`log-prod`
922×	`associate-r`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	3	8
0	5	6
1	10	6
2	24	6
3	52	6
4	166	6
5	571	2
6	4059	2
7	4117	2
8	4354	2
9	6881	2
0	8590	2

Stop Event

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

Counts

2 → 4

Calls

Call 1

Inputs
(*.f64 x x)
(.f64 (.f64 x x) x)

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

eval2.0ms (0%)

Memory: 6.8MiB live, 6.7MiB allocated
Compiler: Compiled 128 to 9 computations (93% saved)

prune11.0ms (0.1%)

Memory

-23.8MiB live, 16.1MiB allocated

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	25	3	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	25	4	29

Accuracy

100.0%

Counts

29 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(.f64 (.f64 x x) x)
▶	56.4%	(*.f64 x x)
▶	100.0%	#s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64)))
▶	6.5%	x

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify3.0ms (0%)

Memory

11.8MiB live, 11.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	(pow.f64 x #s(literal 3 binary64))
cost-diff	0	#s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64)))

Rules

6×	`lower-*.f32`
4×	`lower-*.f64`
2×	`cube-mult`
2×	`lift-pow.f64`
2×	`unpow3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
0	8	17
1	10	17
0	10	17

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
x
#s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64)))
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
(*.f64 x x)
x

Outputs
x
#s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64)))
(pow.f64 x #s(literal 3 binary64))
x
#s(literal 3 binary64)
(*.f64 x x)
x

localize19.0ms (0.2%)

Memory

6.6MiB live, 45.1MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0	#s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64)))
accuracy	0.00390625	(pow.f64 x #s(literal 3 binary64))

Samples

14.0ms

256×

valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-mult: 5.0ms (61.7% of total)

ival-pow: 3.0ms (37% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0%)

Memory

6.4MiB live, 6.4MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs

#s(alt #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) (patch #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())

#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())

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

Outputs
#s(alt (pow x 3) (taylor 0 x) (#s(alt #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) (patch #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) (patch #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) (patch #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) (patch #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) (patch #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) (patch #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) (patch #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) (patch #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) (patch #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) (patch #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) (patch #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) (patch #s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 3 binary64)) (patch (pow.f64 x #s(literal 3 binary64)) #<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	((* (* x x) x) (pow x 3) (* x x))
1.0ms	x	@	-inf	((* (* x x) x) (pow x 3) (* x x))
0.0ms	x	@	0	((* (* x x) x) (pow x 3) (* x x))

simplify3.0ms (0%)

Memory

6.1MiB live, 6.1MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`lower-*.f64`
6×	`lower-*.f32`
4×	`lower-pow.f64`
4×	`lower-pow.f32`
2×	`cube-mult`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	108
1	8	108
2	10	108
3	12	108
0	12	108

Stop Event

1×	iter limit
1×	saturated

Counts

36 → 36

Calls

Call 1

Inputs
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

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

rewrite51.0ms (0.6%)

Memory

-4.0MiB live, 70.6MiB allocated

Rules

540×	`lower-*.f32`
538×	`lower-*.f64`
414×	`lower-fma.f64`
414×	`lower-fma.f32`
254×	`lower-pow.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
0	8	13
1	19	13
2	39	13
3	94	13
4	257	13
0	1180	13

Stop Event

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

Counts

3 → 55

Calls

Call 1

Inputs
#s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64)))
(pow.f64 x #s(literal 3 binary64))
(*.f64 x x)

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

eval15.0ms (0.2%)

Memory: -26.9MiB live, 20.9MiB allocated
Compiler: Compiled 585 to 157 computations (73.2% saved)

prune3.0ms (0%)

Memory

8.6MiB live, 8.6MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	90	5	95

Accuracy

100.0%

Counts

95 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(.f64 (.f64 x x) x)
✓	56.4%	(*.f64 x x)
✓	100.0%	#s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64)))
▶	99.8%	#s(approx (* (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)))
✓	6.5%	x

Compiler

Compiled 20 to 16 computations (20% saved)

simplify3.0ms (0%)

Memory

3.6MiB live, 3.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(pow.f64 x #s(literal 5/2 binary64))
cost-diff	0	(*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))
cost-diff	0	#s(approx (* (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)))

Rules

10×	`lower-*.f32`
8×	`lower-*.f64`
4×	`lower-pow.f32`
2×	`lift-sqrt.f64`
2×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	25
0	11	25
1	13	23
2	15	23
0	15	23

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (* (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)))
(*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))
(pow.f64 x #s(literal 5/2 binary64))
x
#s(literal 5/2 binary64)
(sqrt.f64 x)

Outputs
#s(approx (* (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)))
#s(approx (* (* x x) x) (*.f64 (sqrt.f64 x) (pow.f64 x #s(literal 5/2 binary64))))
(*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (pow.f64 x #s(literal 5/2 binary64)))
(pow.f64 x #s(literal 5/2 binary64))
x
#s(literal 5/2 binary64)
(sqrt.f64 x)

localize26.0ms (0.3%)

Memory

-1.3MiB live, 36.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 x #s(literal 5/2 binary64))
accuracy	0	(sqrt.f64 x)
accuracy	0	#s(approx (* (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)))
accuracy	0.1171875	(*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))

Samples

21.0ms

256×

valid

Compiler

Compiled 20 to 9 computations (55% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-pow: 7.0ms (48% of total)

ival-mult: 5.0ms (34.3% of total)

ival-sqrt: 2.0ms (13.7% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.1%)

Memory

13.4MiB live, 13.4MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#s(alt #s(approx (* (* x x) x) (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) (patch #s(approx ( (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) (patch (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal 5/2 binary64)) (patch (pow.f64 x #s(literal 5/2 binary64)) #<representation binary64>) () ())
#s(alt (sqrt.f64 x) (patch (sqrt.f64 x) #<representation binary64>) () ())

Outputs
#s(alt (pow x 3) (taylor 0 x) (#s(alt #s(approx (* (* x x) x) (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) (patch #s(approx ( (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt #s(approx (* (* x x) x) (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) (patch #s(approx ( (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt #s(approx (* (* x x) x) (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) (patch #s(approx ( (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt #s(approx (* (* x x) x) (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) (patch #s(approx ( (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) (patch (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) (patch (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) (patch (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor 0 x) (#s(alt (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) (patch (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (pow x 5)) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 5/2 binary64)) (patch (pow.f64 x #s(literal 5/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (pow x 5)) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 5/2 binary64)) (patch (pow.f64 x #s(literal 5/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (pow x 5)) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 5/2 binary64)) (patch (pow.f64 x #s(literal 5/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (pow x 5)) (taylor 0 x) (#s(alt (pow.f64 x #s(literal 5/2 binary64)) (patch (pow.f64 x #s(literal 5/2 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 (pow x 3) (taylor inf x) (#s(alt #s(approx (* (* x x) x) (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) (patch #s(approx ( (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt #s(approx (* (* x x) x) (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) (patch #s(approx ( (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt #s(approx (* (* x x) x) (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) (patch #s(approx ( (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt #s(approx (* (* x x) x) (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) (patch #s(approx ( (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) (patch (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) (patch (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) (patch (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) (patch (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (sqrt (pow x 5)) (taylor inf x) (#s(alt (pow.f64 x #s(literal 5/2 binary64)) (patch (pow.f64 x #s(literal 5/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (pow x 5)) (taylor inf x) (#s(alt (pow.f64 x #s(literal 5/2 binary64)) (patch (pow.f64 x #s(literal 5/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (pow x 5)) (taylor inf x) (#s(alt (pow.f64 x #s(literal 5/2 binary64)) (patch (pow.f64 x #s(literal 5/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (sqrt (pow x 5)) (taylor inf x) (#s(alt (pow.f64 x #s(literal 5/2 binary64)) (patch (pow.f64 x #s(literal 5/2 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 (pow x 3) (taylor -inf x) (#s(alt #s(approx (* (* x x) x) (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) (patch #s(approx ( (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt #s(approx (* (* x x) x) (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) (patch #s(approx ( (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt #s(approx (* (* x x) x) (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) (patch #s(approx ( (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt #s(approx (* (* x x) x) (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) (patch #s(approx ( (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) (patch (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) (patch (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) (patch (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) (patch (.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (pow x 5)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 5/2 binary64)) (patch (pow.f64 x #s(literal 5/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (pow x 5)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 5/2 binary64)) (patch (pow.f64 x #s(literal 5/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (pow x 5)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 5/2 binary64)) (patch (pow.f64 x #s(literal 5/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (sqrt (pow x 5)) (pow (sqrt -1) 2))) (taylor -inf x) (#s(alt (pow.f64 x #s(literal 5/2 binary64)) (patch (pow.f64 x #s(literal 5/2 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
3.0ms	x	@	-inf	((* (* x x) x) (* (pow x 5/2) (sqrt x)) (pow x 5/2) (sqrt x))
2.0ms	x	@	inf	((* (* x x) x) (* (pow x 5/2) (sqrt x)) (pow x 5/2) (sqrt x))
1.0ms	x	@	0	((* (* x x) x) (* (pow x 5/2) (sqrt x)) (pow x 5/2) (sqrt x))

simplify31.0ms (0.3%)

Memory

-21.1MiB live, 17.0MiB allocated

Algorithm

1×	egg-herbie

Rules

432×	`lower-*.f64`
432×	`lower-fma.f64`
432×	`lower-fma.f32`
432×	`lower-*.f32`
266×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	144
1	36	144
2	102	144
3	247	144
4	594	144
5	844	144
6	1067	144
7	1210	144
8	1232	144
9	1232	144
10	1244	144
11	1246	144
0	1246	144

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

Calls

Call 1

Inputs
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(sqrt (pow x 5))
(sqrt (pow x 5))
(sqrt (pow x 5))
(sqrt (pow x 5))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(sqrt (pow x 5))
(sqrt (pow x 5))
(sqrt (pow x 5))
(sqrt (pow x 5))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* -1 (* (pow x 3) (pow (sqrt -1) 2)))
(* -1 (* (pow x 3) (pow (sqrt -1) 2)))
(* -1 (* (pow x 3) (pow (sqrt -1) 2)))
(* -1 (* (pow x 3) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (pow x 5)) (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 (* (sqrt x) (pow (sqrt -1) 2)))

Outputs
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(sqrt (pow x 5))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(sqrt (pow x 5))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(sqrt (pow x 5))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(sqrt (pow x 5))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(sqrt (pow x 5))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(sqrt (pow x 5))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(sqrt (pow x 5))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(sqrt (pow x 5))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(* -1 (* (pow x 3) (pow (sqrt -1) 2)))
(pow.f64 x #s(literal 3 binary64))
(* -1 (* (pow x 3) (pow (sqrt -1) 2)))
(pow.f64 x #s(literal 3 binary64))
(* -1 (* (pow x 3) (pow (sqrt -1) 2)))
(pow.f64 x #s(literal 3 binary64))
(* -1 (* (pow x 3) (pow (sqrt -1) 2)))
(pow.f64 x #s(literal 3 binary64))
(* -1 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))
(sqrt.f64 (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (sqrt (pow x 5)) (pow (sqrt -1) 2)))
(sqrt.f64 (pow.f64 x #s(literal 5 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)

rewrite70.0ms (0.8%)

Memory

12.5MiB live, 93.3MiB allocated

Rules

1 602×	`lower-fma.f64`
1 602×	`lower-fma.f32`
1 122×	`prod-exp`
976×	`lower-pow.f64`
976×	`lower-pow.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	8	23
0	11	25
1	26	16
2	65	16
3	176	16
4	667	16
5	4842	10
0	9579	10

Stop Event

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

Counts

4 → 306

Calls

Call 1

Inputs
#s(approx (* (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)))
(*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x))
(pow.f64 x #s(literal 5/2 binary64))
(sqrt.f64 x)

Outputs
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eval43.0ms (0.5%)

Memory: -10.6MiB live, 64.8MiB allocated
Compiler: Compiled 3 642 to 788 computations (78.4% saved)

prune7.0ms (0.1%)

Memory

18.2MiB live, 18.2MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	354	0	354
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	354	5	359

Accuracy

100.0%

Counts

359 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(.f64 (.f64 x x) x)
✓	56.4%	(*.f64 x x)
✓	100.0%	#s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64)))
✓	99.8%	#s(approx (* (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)))
✓	6.5%	x

Compiler

Compiled 40 to 27 computations (32.5% saved)

regimes5.0ms (0.1%)

Memory

8.8MiB live, 8.8MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
x
(*.f64 x x)
(.f64 (.f64 x x) x)
#s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64)))
#s(approx (* (* x x) x) (*.f64 (pow.f64 x #s(literal 5/2 binary64)) (sqrt.f64 x)))

Outputs
#s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64)))

Calls

2 calls:

2.0ms	x
2.0ms	(.f64 (.f64 x x) x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(.f64 (.f64 x x) x)`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0%)

Memory

4.9MiB live, 4.9MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs
x
(*.f64 x x)
(.f64 (.f64 x x) x)

Outputs
(.f64 (.f64 x x) x)

Calls

2 calls:

2.0ms	x
2.0ms	(.f64 (.f64 x x) x)

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(.f64 (.f64 x x) x)`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes30.0ms (0.3%)

Memory

-29.6MiB live, 9.6MiB allocated

Counts

2 → 1

Calls

Call 1

Inputs
x
(*.f64 x x)

Outputs
(*.f64 x x)

Calls

2 calls:

28.0ms	(.f64 (.f64 x x) x)
2.0ms	x

Results

Accuracy	Segments	Branch
56.4%	1	`x`
56.4%	1	`(.f64 (.f64 x x) x)`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Memory

5.8MiB live, 5.8MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

2 calls:

1.0ms	x
1.0ms	(.f64 (.f64 x x) x)

Results

Accuracy	Segments	Branch
6.5%	1	`x`
6.5%	1	`(.f64 (.f64 x x) x)`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify29.0ms (0.3%)

Memory

-1.2MiB live, 44.6MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`-commutative-binary64-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	9	18

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64)))
(.f64 (.f64 x x) x)
(*.f64 x x)
x

Outputs
#s(approx (* (* x x) x) (pow.f64 x #s(literal 3 binary64)))
(.f64 (.f64 x x) x)
(*.f64 x x)
x

soundness7.8s (86.6%)

Memory

-9.5MiB live, 103.6MiB allocated

Rules

2 618×	`lower-*.f64`
2 618×	`lower-*.f32`
1 200×	`unpow-prod-down`
1 030×	`log-prod`
922×	`associate-r`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	5	72
1	8	72
2	10	72
3	12	72
0	12	72
0	3	8
0	5	6
1	10	6
2	24	6
3	52	6
4	166	6
5	571	2
6	4059	2
7	4117	2
8	4354	2
9	6881	2
0	8590	2

Stop Event

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

Compiler

Compiled 16 to 9 computations (43.8% saved)

preprocess66.0ms (0.7%)

Memory: 12.0MiB live, 94.7MiB allocated
Remove: (negabs x)
Compiler: Compiled 58 to 40 computations (31% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample541.0ms (6%)

explain43.0ms (0.5%)

preprocess28.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize11.0ms (0.1%)

series3.0ms (0%)

simplify3.0ms (0%)

rewrite141.0ms (1.6%)

eval2.0ms (0%)

prune11.0ms (0.1%)

simplify3.0ms (0%)

localize19.0ms (0.2%)

series3.0ms (0%)

simplify3.0ms (0%)

rewrite51.0ms (0.6%)

eval15.0ms (0.2%)

prune3.0ms (0%)

simplify3.0ms (0%)

localize26.0ms (0.3%)

series7.0ms (0.1%)

simplify31.0ms (0.3%)

rewrite70.0ms (0.8%)

eval43.0ms (0.5%)

prune7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0%)

regimes30.0ms (0.3%)

regimes3.0ms (0%)

simplify29.0ms (0.3%)

soundness7.8s (86.6%)

preprocess66.0ms (0.7%)

end0.0ms (0%)

Profiling