Metrics for Statistics.Correlation.Kendall:numOfTiesBy from math-functions-0.1.5.2

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample538.0ms (26.5%)

Memory

14.7MiB live, 832.9MiB allocated

Samples

353.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 168.0ms

ival-sub: 90.0ms (53.5% of total)

ival-mult: 64.0ms (38% of total)

ival-true: 6.0ms (3.6% of total)

exact: 5.0ms (3% of total)

ival-assert: 3.0ms (1.8% of total)

Bogosity

explain51.0ms (2.5%)

Memory

-15.3MiB live, 56.8MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(*.f64 x (-.f64 x #s(literal 1 binary64)))`
-	-	`(-.f64 x #s(literal 1 binary64))`
-	-	`#s(literal 1 binary64)`
-	-	`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

17.0ms

512×

valid

Compiler

Compiled 29 to 16 computations (44.8% saved)

Precisions

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

ival-sub: 3.0ms (39.7% of total)

ival-mult: 3.0ms (39.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess20.0ms (1%)

Memory

-14.6MiB live, 24.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	22	11
2	55	10
3	161	10
4	210	10
5	218	10
0	4	5
0	6	5
1	12	5
2	18	5
3	21	5
4	23	5
5	28	5
6	38	5
7	56	5
8	113	5
9	199	5
10	228	5
11	228	5
0	228	5

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 5 to 4 computations (20% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 x (-.f64 x #s(literal 1 binary64)))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify7.0ms (0.4%)

Memory

7.7MiB live, 7.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	6	10
1	12	10
2	18	10
3	21	10
4	23	10
5	28	10
6	38	10
7	56	10
8	113	10
9	199	10
10	228	10
11	228	10
0	228	10

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize14.0ms (0.7%)

Memory

-12.6MiB live, 25.6MiB allocated

Localize:

Found 2 expressions of interest:

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

Samples

11.0ms

256×

valid

Compiler

Compiled 12 to 6 computations (50% saved)

Precisions

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

ival-mult: 3.0ms (60.9% of total)

ival-sub: 1.0ms (20.3% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Memory

2.6MiB live, 2.6MiB allocated

Counts

2 → 24

Calls

Call 1

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

Inputs

#s(alt (*.f64 x (-.f64 x #s(literal 1 binary64))) (patch (*.f64 x (-.f64 x #s(literal 1 binary64))) #<representation binary64>) () ())

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

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

Calls

3 calls:

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

simplify167.0ms (8.2%)

Memory

24.1MiB live, 102.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	83
1	32	83
2	75	83
3	133	83
4	381	83
5	1592	83
6	2757	83
7	3875	83
8	5224	83
9	6705	83
10	7600	83
0	8010	83

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 22

Calls

Call 1

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

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

rewrite156.0ms (7.7%)

Memory

-11.7MiB live, 181.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	25	8
2	138	8
3	1250	8
0	8952	8

Stop Event

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

Counts

2 → 299

Calls

Call 1

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

Outputs
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eval42.0ms (2.1%)

Memory: 13.6MiB live, 51.4MiB allocated
Compiler: Compiled 6 888 to 877 computations (87.3% saved)

prune24.0ms (1.2%)

Memory

-20.2MiB live, 18.8MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	319	2	321
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	319	3	322

Accuracy

100.0%

Counts

322 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 x (-.f64 x #s(literal 1 binary64)))
▶	54.2%	#s(approx (* x (- x 1)) (*.f64 x x))
▶	48.1%	#s(approx (* x (- x 1)) (neg.f64 x))

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify8.0ms (0.4%)

Memory

12.9MiB live, 12.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (* x (- x 1)) (*.f64 x x))
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (* x (- x 1)) (neg.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
0	10	24
1	18	24
2	23	24
3	30	24
4	38	24
5	50	24
6	91	24
7	147	24
8	199	24
9	221	24
10	221	24
0	221	24

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (* x (- x 1)) (neg.f64 x))
(neg.f64 x)
x
#s(approx (* x (- x 1)) (*.f64 x x))
(*.f64 x x)
x

Outputs
#s(approx (* x (- x 1)) (neg.f64 x))
(neg.f64 x)
x
#s(approx (* x (- x 1)) (*.f64 x x))
(*.f64 x x)
x

localize22.0ms (1.1%)

Memory

-10.8MiB live, 31.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	29.314323639130556	#s(approx (* x (- x 1)) (*.f64 x x))
accuracy	0	(neg.f64 x)
accuracy	33.22442587122713	#s(approx (* x (- x 1)) (neg.f64 x))

Samples

13.0ms

256×

valid

Compiler

Compiled 19 to 8 computations (57.9% saved)

Precisions

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

ival-mult: 3.0ms (46.4% of total)

ival-sub: 2.0ms (30.9% of total)

ival-neg: 1.0ms (15.5% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

5.1MiB live, 5.1MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#s(alt #s(approx (* x (- x 1)) (neg.f64 x)) (patch #s(approx (* x (- x 1)) (neg.f64 x)) #<representation binary64>) () ())
#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())
#s(alt #s(approx (* x (- x 1)) (.f64 x x)) (patch #s(approx ( x (- x 1)) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())

Outputs
#s(alt (* -1 x) (taylor 0 x) (#s(alt #s(approx (* x (- x 1)) (neg.f64 x)) (patch #s(approx (* x (- x 1)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- x 1)) (taylor 0 x) (#s(alt #s(approx (* x (- x 1)) (neg.f64 x)) (patch #s(approx (* x (- x 1)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- x 1)) (taylor 0 x) (#s(alt #s(approx (* x (- x 1)) (neg.f64 x)) (patch #s(approx (* x (- x 1)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* x (- x 1)) (taylor 0 x) (#s(alt #s(approx (* x (- x 1)) (neg.f64 x)) (patch #s(approx (* x (- x 1)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt #s(approx (* x (- x 1)) (.f64 x x)) (patch #s(approx ( x (- x 1)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* x (- x 1)) (taylor 0 x) (#s(alt #s(approx (* x (- x 1)) (.f64 x x)) (patch #s(approx ( x (- x 1)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* x (- x 1)) (taylor 0 x) (#s(alt #s(approx (* x (- x 1)) (.f64 x x)) (patch #s(approx ( x (- x 1)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* x (- x 1)) (taylor 0 x) (#s(alt #s(approx (* x (- x 1)) (.f64 x x)) (patch #s(approx ( x (- x 1)) (*.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 (pow x 2) (taylor inf x) (#s(alt #s(approx (* x (- x 1)) (neg.f64 x)) (patch #s(approx (* x (- x 1)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (* x (- x 1)) (neg.f64 x)) (patch #s(approx (* x (- x 1)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (* x (- x 1)) (neg.f64 x)) (patch #s(approx (* x (- x 1)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (* x (- x 1)) (neg.f64 x)) (patch #s(approx (* x (- x 1)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt #s(approx (* x (- x 1)) (.f64 x x)) (patch #s(approx ( x (- x 1)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (* x (- x 1)) (.f64 x x)) (patch #s(approx ( x (- x 1)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (* x (- x 1)) (.f64 x x)) (patch #s(approx ( x (- x 1)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (* x (- x 1)) (.f64 x x)) (patch #s(approx ( x (- x 1)) (*.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 (pow x 2) (taylor -inf x) (#s(alt #s(approx (* x (- x 1)) (neg.f64 x)) (patch #s(approx (* x (- x 1)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor -inf x) (#s(alt #s(approx (* x (- x 1)) (neg.f64 x)) (patch #s(approx (* x (- x 1)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor -inf x) (#s(alt #s(approx (* x (- x 1)) (neg.f64 x)) (patch #s(approx (* x (- x 1)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor -inf x) (#s(alt #s(approx (* x (- x 1)) (neg.f64 x)) (patch #s(approx (* x (- x 1)) (neg.f64 x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (neg.f64 x) (patch (neg.f64 x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (* x (- x 1)) (.f64 x x)) (patch #s(approx ( x (- x 1)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor -inf x) (#s(alt #s(approx (* x (- x 1)) (.f64 x x)) (patch #s(approx ( x (- x 1)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor -inf x) (#s(alt #s(approx (* x (- x 1)) (.f64 x x)) (patch #s(approx ( x (- x 1)) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 x))) (taylor -inf x) (#s(alt #s(approx (* x (- x 1)) (.f64 x x)) (patch #s(approx ( x (- x 1)) (*.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	((* x (- x 1)) (neg x) (* x (- x 1)) (* x x))
1.0ms	x	@	-inf	((* x (- x 1)) (neg x) (* x (- x 1)) (* x x))
0.0ms	x	@	0	((* x (- x 1)) (neg x) (* x (- x 1)) (* x x))

simplify126.0ms (6.2%)

Memory

25.4MiB live, 136.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	166
1	22	166
2	40	166
3	82	166
4	191	166
5	373	166
6	698	166
7	2322	166
8	3755	166
9	5759	166
10	7525	166
0	8089	166

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

rewrite226.0ms (11.1%)

Memory

-5.0MiB live, 196.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
0	10	22
1	32	22
2	159	22
3	1391	22
0	8503	22

Stop Event

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

Counts

4 → 71

Calls

Call 1

Inputs
#s(approx (* x (- x 1)) (neg.f64 x))
(neg.f64 x)
#s(approx (* x (- x 1)) (*.f64 x x))
(*.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>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval32.0ms (1.6%)

Memory: -9.2MiB live, 24.6MiB allocated
Compiler: Compiled 959 to 227 computations (76.3% saved)

prune5.0ms (0.3%)

Memory

15.9MiB live, 15.9MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	119	3	122

Accuracy

100.0%

Counts

122 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 x (-.f64 x #s(literal 1 binary64)))
✓	54.2%	#s(approx (* x (- x 1)) (*.f64 x x))
✓	48.1%	#s(approx (* x (- x 1)) (neg.f64 x))

Compiler

Compiled 24 to 18 computations (25% saved)

regimes27.0ms (1.3%)

Memory

-28.6MiB live, 10.8MiB allocated

Counts

3 → 1

Calls

Call 1

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

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

Calls

2 calls:

25.0ms	x
2.0ms	(*.f64 x (-.f64 x #s(literal 1 binary64)))

Results

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

regimes3.0ms (0.2%)

Memory

9.1MiB live, 9.1MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (* x (- x 1)) (neg.f64 x))
#s(approx (* x (- x 1)) (*.f64 x x))

Outputs
#s(approx (* x (- x 1)) (neg.f64 x))
#s(approx (* x (- x 1)) (*.f64 x x))

Calls

2 calls:

2.0ms	(*.f64 x (-.f64 x #s(literal 1 binary64)))
1.0ms	x

Results

Accuracy	Segments	Branch
97.5%	3	`x`
97.5%	2	`(*.f64 x (-.f64 x #s(literal 1 binary64)))`

Compiler

Compiled 6 to 5 computations (16.7% saved)

regimes3.0ms (0.1%)

Memory

10.0MiB live, 10.0MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (* x (- x 1)) (neg.f64 x))

Outputs
#s(approx (* x (- x 1)) (neg.f64 x))

Calls

2 calls:

1.0ms	x
1.0ms	(*.f64 x (-.f64 x #s(literal 1 binary64)))

Results

Accuracy	Segments	Branch
48.1%	1	`x`
48.1%	1	`(*.f64 x (-.f64 x #s(literal 1 binary64)))`

Compiler

Compiled 6 to 5 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.8209764168017877	576344417.9390048

Compiler

Compiled 8 to 8 computations (0% saved)

simplify68.0ms (3.3%)

Memory

13.1MiB live, 52.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	38
1	22	38
2	27	38
3	33	38
4	40	38
5	49	38

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(if (<=.f64 (*.f64 x (-.f64 x #s(literal 1 binary64))) #s(literal 2 binary64)) #s(approx (* x (- x 1)) (neg.f64 x)) #s(approx (* x (- x 1)) (*.f64 x x)))

#s(approx (* x (- x 1)) (neg.f64 x))

Outputs
(*.f64 x (-.f64 x #s(literal 1 binary64)))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
(if (<=.f64 (.f64 x (-.f64 x #s(literal 1 binary64))) #s(literal 2 binary64)) #s(approx ( x (- x 1)) (neg.f64 x)) #s(approx (* x (- x 1)) (*.f64 x x)))
(if (<=.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x) #s(literal 2 binary64)) #s(approx ( x (- x 1)) (neg.f64 x)) #s(approx (* x (- x 1)) (*.f64 x x)))
#s(approx (* x (- x 1)) (neg.f64 x))

soundness427.0ms (21%)

Memory

-35.8MiB live, 88.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	83
1	32	83
2	75	83
3	133	83
4	381	83
5	1592	83
6	2757	83
7	3875	83
8	5224	83
9	6705	83
10	7600	83
0	8010	83

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 30 to 17 computations (43.3% saved)

preprocess58.0ms (2.8%)

Memory: 25.9MiB live, 64.6MiB allocated
Compiler: Compiled 66 to 36 computations (45.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	6	15
1	22	11
2	55	10
3	161	10
4	210	10
5	218	10
0	4	5
0	6	5
1	12	5
2	18	5
3	21	5
4	23	5
5	28	5
6	38	5
7	56	5
8	113	5
9	199	5
10	228	5
11	228	5
0	228	5

Iter	Nodes	Cost
0	4	10
0	6	10
1	12	10
2	18	10
3	21	10
4	23	10
5	28	10
6	38	10
7	56	10
8	113	10
9	199	10
10	228	10
11	228	10
0	228	10

Iter	Nodes	Cost
0	8	24
0	10	24
1	18	24
2	23	24
3	30	24
4	38	24
5	50	24
6	91	24
7	147	24
8	199	24
9	221	24
10	221	24
0	221	24

Iter	Nodes	Cost
0	6	15
1	22	11
2	55	10
3	161	10
4	210	10
5	218	10
0	4	5
0	6	5
1	12	5
2	18	5
3	21	5
4	23	5
5	28	5
6	38	5
7	56	5
8	113	5
9	199	5
10	228	5
11	228	5
0	228	5

Iter	Nodes	Cost
0	4	10
0	6	10
1	12	10
2	18	10
3	21	10
4	23	10
5	28	10
6	38	10
7	56	10
8	113	10
9	199	10
10	228	10
11	228	10
0	228	10

Iter	Nodes	Cost
0	8	24
0	10	24
1	18	24
2	23	24
3	30	24
4	38	24
5	50	24
6	91	24
7	147	24
8	199	24
9	221	24
10	221	24
0	221	24

start0.0ms (0%)

analyze0.0ms (0%)

sample538.0ms (26.5%)

explain51.0ms (2.5%)

preprocess20.0ms (1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify7.0ms (0.4%)

localize14.0ms (0.7%)

series2.0ms (0.1%)

simplify167.0ms (8.2%)

rewrite156.0ms (7.7%)

eval42.0ms (2.1%)

prune24.0ms (1.2%)

simplify8.0ms (0.4%)

localize22.0ms (1.1%)

series3.0ms (0.1%)

simplify126.0ms (6.2%)

rewrite226.0ms (11.1%)

eval32.0ms (1.6%)

prune5.0ms (0.3%)

regimes27.0ms (1.3%)

regimes3.0ms (0.2%)

regimes3.0ms (0.1%)

bsearch0.0ms (0%)

simplify68.0ms (3.3%)

soundness427.0ms (21%)

preprocess58.0ms (2.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	6	15
1	22	11
2	55	10
3	161	10
4	210	10
5	218	10
0	4	5
0	6	5
1	12	5
2	18	5
3	21	5
4	23	5
5	28	5
6	38	5
7	56	5
8	113	5
9	199	5
10	228	5
11	228	5
0	228	5

Iter	Nodes	Cost
0	4	10
0	6	10
1	12	10
2	18	10
3	21	10
4	23	10
5	28	10
6	38	10
7	56	10
8	113	10
9	199	10
10	228	10
11	228	10
0	228	10

Iter	Nodes	Cost
0	8	24
0	10	24
1	18	24
2	23	24
3	30	24
4	38	24
5	50	24
6	91	24
7	147	24
8	199	24
9	221	24
10	221	24
0	221	24