Metrics for Data.Random.Dice:roll from dice-0.1

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB 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)

sample759.0ms (21.6%)

Memory

-2.7MiB live, 714.1MiB allocated

Samples

468.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 176.0ms

ival-mult: 121.0ms (68.6% of total)

ival-sub: 42.0ms (23.8% of total)

ival-true: 6.0ms (3.4% of total)

exact: 5.0ms (2.8% of total)

ival-assert: 3.0ms (1.7% of total)

Bogosity

explain65.0ms (1.9%)

Memory

17.9MiB live, 56.5MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`#s(literal 1 binary64)`
-	-	`(*.f64 x x)`
-	-	`(-.f64 (*.f64 x x) #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: 7.0ms

ival-mult: 4.0ms (55.4% of total)

ival-sub: 2.0ms (27.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess475.0ms (13.5%)

Memory

17.6MiB live, 243.7MiB allocated

Algorithm

1×	egg-herbie

Rules

31 314×	`lower-fma.f64`
31 314×	`lower-fma.f32`
4 314×	`lower-*.f32`
4 312×	`lower-*.f64`
2 860×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	23	11
2	65	10
3	163	10
4	405	10
5	712	10
6	1225	10
7	2225	10
8	3127	10
9	3701	10
10	3980	10
11	4274	10
12	4428	10
13	4501	10
14	4712	10
15	5479	10
16	5677	10
17	7349	10
18	7872	10
0	4	5
0	6	5
1	14	5
2	18	5
3	33	5
4	62	5
5	123	5
6	283	5
7	562	5
8	2053	5
9	3150	5
10	4387	5
11	5032	5
12	5290	5
13	5441	5
14	5523	5
15	5837	5
16	6383	5
17	7494	5
18	7928	5
0	8115	4

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 5 to 4 computations (20% saved)

eval0.0ms (0%)

Memory: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 5 to 4 computations (20% saved)

simplify332.0ms (9.5%)

Memory

-20.9MiB live, 348.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 x x)
cost-diff	128	(-.f64 (*.f64 x x) #s(literal 1 binary64))

Rules

31 314×	`lower-fma.f64`
31 314×	`lower-fma.f32`
4 314×	`lower-*.f32`
4 312×	`lower-*.f64`
2 860×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	6	10
1	14	10
2	18	10
3	33	10
4	62	10
5	123	10
6	283	10
7	562	10
8	2053	10
9	3150	10
10	4387	10
11	5032	10
12	5290	10
13	5441	10
14	5523	10
15	5837	10
16	6383	10
17	7494	10
18	7928	10
0	8115	9

Stop Event

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

Calls

Call 1

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

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

localize14.0ms (0.4%)

Memory

-7.4MiB live, 31.6MiB allocated

Localize:

Found 2 expressions of interest:

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

Samples

10.0ms

256×

valid

Compiler

Compiled 12 to 6 computations (50% saved)

Precisions

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

ival-sub: 3.0ms (59.5% of total)

ival-mult: 2.0ms (39.7% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Memory

2.6MiB live, 2.6MiB allocated

Counts

2 → 24

Calls

Call 1

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

Inputs

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

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

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

simplify138.0ms (3.9%)

Memory

5.2MiB live, 164.7MiB allocated

Algorithm

1×	egg-herbie

Rules

13 152×	`lower-fma.f64`
13 152×	`lower-fma.f32`
3 644×	`lower-*.f64`
3 644×	`lower-*.f32`
1 814×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	88
1	17	88
2	39	88
3	88	88
4	283	88
5	498	88
6	905	88
7	2793	88
8	5014	88
0	8287	79

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

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

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

rewrite208.0ms (5.9%)

Memory

7.0MiB live, 198.1MiB allocated

Rules

5 468×	`lower-fma.f64`
5 468×	`lower-fma.f32`
5 046×	`lower-/.f64`
5 046×	`lower-/.f32`
3 098×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	29	8
2	164	8
3	1504	8
0	8468	7

Stop Event

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

Counts

2 → 340

Calls

Call 1

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

Outputs
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eval55.0ms (1.6%)

Memory: -9.4MiB live, 75.2MiB allocated
Compiler: Compiled 8 186 to 854 computations (89.6% saved)

prune5.0ms (0.2%)

Memory

19.4MiB live, 19.4MiB allocated

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	361	3	364
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	362	3	365

Accuracy

100.0%

Counts

365 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 x x #s(literal -1 binary64))
▶	45.9%	#s(approx (- (* x x) 1) (*.f64 x x))
▶	53.7%	#s(approx (- (* x x) 1) #s(literal -1 binary64))

Compiler

Compiled 10 to 9 computations (10% saved)

simplify295.0ms (8.4%)

Memory

-0.0MiB live, 226.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

31 314×	`lower-fma.f32`
31 312×	`lower-fma.f64`
4 314×	`lower-*.f32`
4 312×	`lower-*.f64`
2 860×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
0	11	25
1	18	25
2	21	25
3	36	25
4	67	25
5	128	25
6	288	25
7	568	25
8	2045	25
9	3146	25
10	4401	25
11	5058	25
12	5317	25
13	5468	25
14	5550	25
15	5864	25
16	6410	25
17	7521	25
18	7955	25
0	8142	25

Stop Event

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

Calls

Call 1

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

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

localize17.0ms (0.5%)

Memory

-8.2MiB live, 29.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x x #s(literal -1 binary64))
accuracy	0	(*.f64 x x)
accuracy	34.59341326074665	#s(approx (- (* x x) 1) (*.f64 x x))
accuracy	29.622864039421085	#s(approx (- (* x x) 1) #s(literal -1 binary64))

Samples

12.0ms

256×

valid

Compiler

Compiled 24 to 8 computations (66.7% saved)

Precisions

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

ival-mult: 4.0ms (60.5% of total)

ival-sub: 1.0ms (15.1% of total)

ival-add: 1.0ms (15.1% 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

4.1MiB live, 4.1MiB allocated

Counts

4 → 48

Calls

Call 1

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

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

Calls

3 calls:

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

simplify184.0ms (5.2%)

Memory

11.3MiB live, 165.8MiB allocated

Algorithm

1×	egg-herbie

Rules

13 152×	`lower-fma.f64`
13 152×	`lower-fma.f32`
3 644×	`lower-*.f64`
3 644×	`lower-*.f32`
1 814×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	192
1	17	192
2	39	192
3	88	192
4	283	192
5	498	192
6	905	192
7	2793	192
8	5014	192
0	8287	165

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

rewrite274.0ms (7.8%)

Memory

-46.8MiB live, 222.9MiB allocated

Rules

6 802×	`lower-fma.f32`
6 800×	`lower-fma.f64`
3 730×	`lower-/.f64`
3 730×	`lower-/.f32`
2 872×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
0	11	21
1	42	21
2	234	21
3	2264	21
0	9463	21

Stop Event

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

Counts

4 → 274

Calls

Call 1

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

Outputs
#<batchref>
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eval75.0ms (2.1%)

Memory: 5.2MiB live, 76.8MiB allocated
Compiler: Compiled 5 900 to 731 computations (87.6% saved)

prune7.0ms (0.2%)

Memory

31.0MiB live, 31.0MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	322	0	322
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	322	3	325

Accuracy

100.0%

Counts

325 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x x #s(literal -1 binary64))
✓	45.9%	#s(approx (- (* x x) 1) (*.f64 x x))
✓	53.7%	#s(approx (- (* x x) 1) #s(literal -1 binary64))

Compiler

Compiled 25 to 17 computations (32% saved)

regimes12.0ms (0.3%)

Memory

-36.2MiB live, 13.5MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

8.0ms	(-.f64 (*.f64 x x) #s(literal 1 binary64))
2.0ms	x
2.0ms	(*.f64 x x)

Results

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes4.0ms (0.1%)

Memory

7.4MiB live, 7.4MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.8%	2	`x`
97.8%	2	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`
97.8%	2	`(*.f64 x x)`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes4.0ms (0.1%)

Memory

7.7MiB live, 7.7MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

Outputs
#s(approx (- (* x x) 1) #s(literal -1 binary64))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
53.7%	1	`x`
53.7%	1	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`
53.7%	1	`(*.f64 x x)`

Compiler

Compiled 9 to 7 computations (22.2% saved)

bsearch9.0ms (0.3%)

Memory

16.7MiB live, 16.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
8.0ms	0.11284686238773584	31356.306601387903

Samples

3.0ms

144×

valid

Compiler

Compiled 44 to 71 computations (-61.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-sub: 1.0ms (101.7% of total)

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

exact: 0.0ms (0% of total)

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

simplify25.0ms (0.7%)

Memory

-23.7MiB live, 51.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	33
1	14	33

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

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

#s(approx (- (* x x) 1) #s(literal -1 binary64))

Outputs

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

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

#s(approx (- (* x x) 1) #s(literal -1 binary64))

soundness452.0ms (12.8%)

Memory

36.3MiB live, 219.7MiB allocated

Rules

13 152×	`lower-fma.f64`
13 152×	`lower-fma.f32`
5 468×	`lower-fma.f64`
5 468×	`lower-fma.f32`
5 046×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	88
1	17	88
2	39	88
3	88	88
4	283	88
5	498	88
6	905	88
7	2793	88
8	5014	88
0	8287	79
0	4	8
0	6	8
1	29	8
2	164	8
3	1504	8
0	8468	7

Stop Event

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

Compiler

Compiled 32 to 21 computations (34.4% saved)

preprocess103.0ms (2.9%)

Memory: -31.5MiB live, 100.8MiB allocated
Remove: (abs x)
Compiler: Compiled 54 to 32 computations (40.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample759.0ms (21.6%)

explain65.0ms (1.9%)

preprocess475.0ms (13.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify332.0ms (9.5%)

localize14.0ms (0.4%)

series2.0ms (0.1%)

simplify138.0ms (3.9%)

rewrite208.0ms (5.9%)

eval55.0ms (1.6%)

prune5.0ms (0.2%)

simplify295.0ms (8.4%)

localize17.0ms (0.5%)

series2.0ms (0.1%)

simplify184.0ms (5.2%)

rewrite274.0ms (7.8%)

eval75.0ms (2.1%)

prune7.0ms (0.2%)

regimes12.0ms (0.3%)

regimes4.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch9.0ms (0.3%)

simplify25.0ms (0.7%)

soundness452.0ms (12.8%)

preprocess103.0ms (2.9%)

end0.0ms (0%)

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