Metrics for Examples.Basics.BasicTests:f2 from sbv-4.4

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample993.0ms (30.4%)

Memory

-0.4MiB live, 1 142.4MiB allocated

Samples

719.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 237.0ms

ival-mult: 154.0ms (64.9% of total)

ival-sub: 74.0ms (31.2% of total)

ival-true: 6.0ms (2.5% of total)

ival-assert: 4.0ms (1.7% of total)

Bogosity

explain65.0ms (2%)

Memory

5.4MiB live, 50.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
18	-	-	`(-.f64 (.f64 x x) (.f64 y y))`
0	-	-	`y`
0	-	-	`(*.f64 y y)`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (.f64 x x) (.f64 y y))`	nan-rescue	18	0
↳	`(*.f64 x x)`	overflow	59
↳	`(*.f64 y y)`	overflow	61

Confusion

	Predicted +	Predicted -
+	18	0
-	0	238

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	18	0	0
-	0	0	238

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	238
1	18

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

33.0ms

512×

valid

Compiler

Compiled 41 to 19 computations (53.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-mult: 7.0ms (74.4% of total)

ival-sub: 2.0ms (21.3% of total)

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

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

preprocess117.0ms (3.6%)

Memory

0.6MiB live, 47.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	38
1	48	35
2	215	35
3	371	35
4	909	35
5	1923	35
6	2926	35
7	3269	35
8	3347	35
9	3347	35
10	3546	35
0	5	7
0	8	7
1	21	7
2	81	7
3	223	7
4	403	7
5	836	7
6	1385	7
7	2069	7
8	2898	7
9	3208	7
10	3270	7
11	3270	7
12	3348	7
0	3348	7

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (.f64 y y))

Outputs
(-.f64 (.f64 x x) (.f64 y y))
(*.f64 (-.f64 x y) (+.f64 y x))

Symmetry

(abs y)

(abs x)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	93.0%	(-.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify90.0ms (2.8%)

Memory

-26.9MiB live, 29.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	21	15
2	81	15
3	223	15
4	403	15
5	836	15
6	1385	15
7	2069	15
8	2898	15
9	3208	15
10	3270	15
11	3270	15
12	3348	15
0	3348	15

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (.f64 y y))
(*.f64 x x)
x
(*.f64 y y)
y

Outputs
(-.f64 (.f64 x x) (.f64 y y))
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 x x)
x
(*.f64 y y)
y

localize14.0ms (0.4%)

Memory

16.1MiB live, 16.1MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 y y)
accuracy	0.0	(*.f64 x x)
accuracy	4.156227294132265	(-.f64 (.f64 x x) (.f64 y y))

Samples

10.0ms

256×

valid

Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-mult: 3.0ms (67.9% of total)

ival-sub: 1.0ms (22.6% of total)

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

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

series3.0ms (0.1%)

Memory

4.0MiB live, 4.0MiB allocated

Counts

3 → 7

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (.f64 y y))
(*.f64 x x)
(*.f64 y y)

Outputs
(* -1 (pow y 2))
(- (pow x 2) (pow y 2))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(+ (* -1 (pow y 2)) (pow x 2))
(pow y 2)
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))

Calls

6 calls:

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

simplify89.0ms (2.7%)

Memory

-7.8MiB live, 39.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	44
1	40	44
2	136	44
3	829	44
4	3437	44
0	8613	43

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 7

Calls

Call 1

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

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

rewrite133.0ms (4.1%)

Memory

-13.9MiB live, 32.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	37	13
2	329	13
3	4470	13
0	8291	12

Stop Event

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

Counts

3 → 91

Calls

Call 1

Inputs
(-.f64 (.f64 x x) (.f64 y y))
(*.f64 x x)
(*.f64 y y)

Outputs
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 y y (.f64 x x)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 (.f64 y x) #s(literal 4 binary64))))) (-.f64 (pow.f64 (*.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (+.f64 (pow.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 (+.f64 y x) (-.f64 x y))
(.f64 (fma.f64 y y (.f64 x x)) (/.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x))))
(.f64 (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 y y (.f64 x x)) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 x y)) (+.f64 y x))
(/.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (+.f64 y x)) (-.f64 x y))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 y x)) (fma.f64 y (+.f64 y x) (.f64 x x)))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (-.f64 x y)) (fma.f64 y (+.f64 y x) (.f64 x x)))
(/.f64 (.f64 (-.f64 x y) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y (+.f64 y x) (.f64 x x)))
(/.f64 (.f64 (-.f64 x y) (fma.f64 y y (.f64 x x))) (-.f64 x y))
(/.f64 (.f64 (+.f64 y x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y (+.f64 y x) (.f64 x x)))
(/.f64 (.f64 (+.f64 y x) (fma.f64 y y (.f64 x x))) (+.f64 y x))
(/.f64 (.f64 (fma.f64 y y (.f64 x x)) (-.f64 x y)) (-.f64 x y))
(/.f64 (.f64 (fma.f64 y y (.f64 x x)) (+.f64 y x)) (+.f64 y x))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) #s(literal 2 binary64))) (fma.f64 y y (*.f64 x x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64))) (fma.f64 y y (*.f64 x x)))
(/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 y y (*.f64 x x)))
(/.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64))) (/.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (*.f64 x x)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (-.f64 (pow.f64 (*.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) (fma.f64 y (+.f64 y x) (.f64 x x))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y y (.f64 x x))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))
(/.f64 (.f64 (fma.f64 y y (.f64 x x)) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (.f64 (+.f64 y x) (fma.f64 y (+.f64 y x) (.f64 x x))))
(/.f64 (.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y y (.f64 x x))) (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))
(/.f64 (.f64 (fma.f64 y y (.f64 x x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (.f64 (-.f64 x y) (fma.f64 y (+.f64 y x) (.f64 x x))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (.f64 (fma.f64 y y (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 6 binary64)))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 (*.f64 y x) #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 3 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 y #s(literal 18 binary64))) (.f64 (+.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (.f64 y x) #s(literal 6 binary64))) (-.f64 (pow.f64 (*.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 (.f64 y x) #s(literal 4 binary64)))) (fma.f64 y y (*.f64 x x))))
(/.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (+.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) (fma.f64 y (+.f64 y x) (*.f64 x x))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (-.f64 (pow.f64 (*.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (fma.f64 y y (*.f64 x x)))
(neg.f64 (fma.f64 y y (*.f64 x x)))
(fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 (pow.f64 y #s(literal 8 binary64)) (pow.f64 (.f64 y x) #s(literal 4 binary64))))) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (-.f64 (pow.f64 (*.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 y y (.f64 x x)) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 x (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))
(fma.f64 (-.f64 x y) y (*.f64 (-.f64 x y) x))
(fma.f64 (-.f64 x y) x (*.f64 (-.f64 x y) y))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 (.f64 x x) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (-.f64 (pow.f64 (*.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 y (-.f64 x y) (*.f64 x (-.f64 x y)))
(fma.f64 y y (*.f64 x x))
(fma.f64 (.f64 x x) (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (-.f64 (pow.f64 (*.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(fma.f64 (.f64 x x) (/.f64 (.f64 x x) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))
(fma.f64 x (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))
(fma.f64 x (-.f64 x y) (*.f64 y (-.f64 x y)))
(fma.f64 x x (*.f64 y y))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (.f64 y y) (.f64 x x))
(-.f64 (.f64 x x) (.f64 y y))
(+.f64 (.f64 y (-.f64 x y)) (.f64 x (-.f64 x y)))
(+.f64 (.f64 x (-.f64 x y)) (.f64 y (-.f64 x y)))
(+.f64 (.f64 (-.f64 x y) y) (.f64 (-.f64 x y) x))
(+.f64 (.f64 (-.f64 x y) x) (.f64 (-.f64 x y) y))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 y (+.f64 y x)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(+.f64 (.f64 y y) (.f64 x x))
(+.f64 (.f64 x x) (.f64 y y))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 x x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 x x))
(exp.f64 (/.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
(*.f64 y y)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 y))
(pow.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(neg.f64 (*.f64 y y))
(sqrt.f64 (pow.f64 y #s(literal 4 binary64)))
(fabs.f64 (*.f64 y y))
(exp.f64 (/.f64 (*.f64 #s(literal 4 binary64) (log.f64 y)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 y) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 y) #s(literal 2 binary64))))

eval9.0ms (0.3%)

Memory: 7.5MiB live, 7.5MiB allocated
Compiler: Compiled 1 864 to 265 computations (85.8% saved)

prune2.0ms (0.1%)

Memory

3.9MiB live, 3.9MiB allocated

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	2	97

Accuracy

100.0%

Counts

97 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 (-.f64 x y) (+.f64 y x))
▶	55.9%	#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))

Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify106.0ms (3.2%)

Memory

0.9MiB live, 47.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
0	16	34
1	35	34
2	101	34
3	248	34
4	431	34
5	861	34
6	1399	34
7	2083	34
8	2913	34
9	3223	34
10	3285	34
11	3285	34
12	3363	34
0	3363	34

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize76.0ms (2.3%)

Memory

-26.1MiB live, 25.6MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0.0	(-.f64 x y)
accuracy	0.0	(+.f64 y x)
accuracy	0.0	(*.f64 (-.f64 x y) (+.f64 y x))
accuracy	0.0	(*.f64 (neg.f64 y) y)
accuracy	0.0	(neg.f64 y)
accuracy	28.203623348438715	#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))

Samples

30.0ms

256×

valid

Compiler

Compiled 31 to 12 computations (61.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-mult: 18.0ms (78.6% of total)

ival-sub: 2.0ms (8.7% of total)

ival-add: 1.0ms (4.4% of total)

ival-neg: 1.0ms (4.4% of total)

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

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

series6.0ms (0.2%)

Memory

6.7MiB live, 6.7MiB allocated

Counts

6 → 31

Calls

Call 1

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

Outputs
(* -1 (pow y 2))
(- (pow x 2) (pow y 2))
(+ (* -1 (pow y 2)) (* x (+ y (* -1 y))))
(+ (* -1 (pow y 2)) (* x (+ x (+ y (* -1 y)))))
(* -1 y)
(- x y)
y
(+ x y)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (/ y x))))
(* (pow x 2) (+ 1 (+ (* -1 (/ y x)) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
x
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (/ y x)))
(* (pow x 2) (+ 1 (* -1 (/ (+ (* -1 (+ y (* -1 y))) (/ (pow y 2) x)) x))))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+ (* -1 (pow y 2)) (pow x 2))
(+ (* y (+ x (* -1 x))) (pow x 2))
(+ (* y (+ x (+ (* -1 x) (* -1 y)))) (pow x 2))
(+ x (* -1 y))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))
(* (pow y 2) (- (+ (* -1 (/ x y)) (/ x y)) 1))
(* (pow y 2) (- (+ (* -1 (/ x y)) (+ (/ x y) (/ (pow x 2) (pow y 2)))) 1))
(* y (- (/ x y) 1))
(* y (+ 1 (/ x y)))
(* (pow y 2) (- (* -1 (/ (+ x (* -1 x)) y)) 1))
(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (- (* -1 (/ x y)) 1)))

Calls

6 calls:

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

simplify157.0ms (4.8%)

Memory

8.8MiB live, 141.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	211
1	299	206
2	1084	205
3	4475	205
0	8193	200

Stop Event

1×	iter limit
1×	node limit

Counts

31 → 29

Calls

Call 1

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

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

rewrite246.0ms (7.5%)

Memory

12.1MiB live, 152.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	31
0	16	31
1	68	31
2	610	31
0	9914	31

Stop Event

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

Counts

6 → 500

Calls

Call 1

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

Outputs
#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))
(*.f64 (neg.f64 (neg.f64 (neg.f64 y))) (neg.f64 (neg.f64 y)))
(*.f64 (neg.f64 (neg.f64 y)) (neg.f64 (neg.f64 (neg.f64 y))))
(*.f64 (neg.f64 (neg.f64 y)) (neg.f64 y))
(*.f64 (neg.f64 y) (neg.f64 (neg.f64 y)))
(*.f64 (neg.f64 y) y)
(*.f64 y (neg.f64 y))
(neg.f64 (*.f64 y y))
(neg.f64 y)
(*.f64 (neg.f64 (+.f64 y (neg.f64 x))) (-.f64 y (neg.f64 x)))
(*.f64 (+.f64 (neg.f64 (neg.f64 y)) (neg.f64 (neg.f64 x))) (-.f64 (neg.f64 (neg.f64 y)) (neg.f64 (neg.f64 x))))
(*.f64 (+.f64 (neg.f64 (neg.f64 y)) (neg.f64 x)) (-.f64 (neg.f64 (neg.f64 y)) (neg.f64 x)))
(*.f64 (+.f64 (neg.f64 (neg.f64 y)) x) (-.f64 (neg.f64 (neg.f64 y)) x))
(*.f64 (+.f64 (neg.f64 y) (neg.f64 (neg.f64 x))) (-.f64 (neg.f64 y) (neg.f64 (neg.f64 x))))
(*.f64 (+.f64 y (neg.f64 (neg.f64 x))) (-.f64 y (neg.f64 (neg.f64 x))))
(*.f64 (+.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 y))) (-.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 y))))
(*.f64 (+.f64 (neg.f64 (neg.f64 x)) (neg.f64 y)) (-.f64 (neg.f64 (neg.f64 x)) (neg.f64 y)))
(*.f64 (+.f64 (neg.f64 (neg.f64 x)) y) (-.f64 (neg.f64 (neg.f64 x)) y))
(*.f64 (+.f64 (neg.f64 x) (neg.f64 (neg.f64 y))) (-.f64 (neg.f64 x) (neg.f64 (neg.f64 y))))
(*.f64 (+.f64 x (neg.f64 (neg.f64 y))) (-.f64 x (neg.f64 (neg.f64 y))))
(*.f64 (-.f64 y (neg.f64 x)) (+.f64 y (neg.f64 x)))
(*.f64 (+.f64 y (neg.f64 x)) (neg.f64 (-.f64 y (neg.f64 x))))
(*.f64 (+.f64 y (neg.f64 x)) (-.f64 y (neg.f64 x)))
(*.f64 (-.f64 y x) (-.f64 y x))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x)))) (.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))) (*.f64 (-.f64 y x) (-.f64 y x)))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 y y) (fma.f64 y y (.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 y y) (fma.f64 y y (.f64 x x)) (pow.f64 x #s(literal 4 binary64))))) (.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (.f64 y y) (fma.f64 y y (.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (.f64 y y) (fma.f64 y y (.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))) (*.f64 (-.f64 y x) (-.f64 y x)))
(/.f64 (-.f64 (pow.f64 (.f64 (-.f64 y x) x) #s(literal 2 binary64)) (pow.f64 (.f64 (-.f64 y x) y) #s(literal 2 binary64))) (*.f64 (-.f64 y x) (-.f64 y x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (*.f64 x x)))))))
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(fma.f64 (.f64 y y) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (.f64 (.f64 (-.f64 y x) x) (/.f64 (*.f64 (-.f64 y x) (-.f64 y x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (-.f64 y x)) (/.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (-.f64 y x)))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 y y) (fma.f64 y y (.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 y x)) (/.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (.f64 y y) (fma.f64 y y (.f64 x x)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 y x)))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (fma.f64 y y (.f64 x x)) (-.f64 y x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (fma.f64 y y (.f64 x x)) (-.f64 y x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (fma.f64 (.f64 y y) (fma.f64 y y (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 y x))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (.f64 (fma.f64 (.f64 y y) (fma.f64 y y (.f64 x x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 y x))))
(-.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (fma.f64 x x (.f64 y x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 y y (fma.f64 x x (.f64 y x)))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (.f64 x x))))
(-.f64 (/.f64 (.f64 (-.f64 y x) y) (-.f64 y x)) (/.f64 (.f64 (-.f64 y x) x) (-.f64 y x)))
(-.f64 (/.f64 (.f64 y y) (-.f64 y x)) (/.f64 (.f64 x x) (-.f64 y x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 y x)) (/.f64 (.f64 y y) (-.f64 y x)))
(-.f64 (neg.f64 x) (neg.f64 y))
(-.f64 (neg.f64 x) y)
(-.f64 (neg.f64 y) (neg.f64 x))
(-.f64 (neg.f64 y) x)
(-.f64 y x)
(-.f64 x (neg.f64 y))
(-.f64 x y)
(+.f64 (.f64 (.f64 (-.f64 y x) x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (.f64 (.f64 y y) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))))
(+.f64 (.f64 (.f64 y y) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (.f64 (.f64 (-.f64 y x) x) (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))))
(+.f64 (.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (.f64 (-.f64 y x) x)) (.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (.f64 y y)))
(+.f64 (.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (.f64 y y)) (.f64 (/.f64 (.f64 (-.f64 y x) (-.f64 y x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (.f64 (-.f64 y x) x)))
(+.f64 (neg.f64 (/.f64 (.f64 (-.f64 y x) y) (-.f64 y x))) (neg.f64 (/.f64 (.f64 (-.f64 y x) x) (-.f64 y x))))
(+.f64 (neg.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (.f64 x x)))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (.f64 x x)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 y y (.f64 (neg.f64 x) y)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x x (fma.f64 y y (.f64 (neg.f64 x) y)))))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 x x (fma.f64 y y (.f64 (neg.f64 x) y)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 y y (.f64 (neg.f64 x) y)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (fma.f64 y y (.f64 x x)) (-.f64 y x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (fma.f64 y y (.f64 x x)) (-.f64 y x))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (.f64 x x))))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 y x) y (.f64 x x))))
(+.f64 (/.f64 (.f64 (-.f64 y x) x) (-.f64 y x)) (/.f64 (.f64 (-.f64 y x) y) (-.f64 y x)))
(+.f64 (/.f64 (.f64 (-.f64 y x) y) (-.f64 y x)) (/.f64 (.f64 (-.f64 y x) x) (-.f64 y x)))
(+.f64 (/.f64 (.f64 y y) (-.f64 y x)) (/.f64 (.f64 x x) (-.f64 y x)))
(+.f64 (/.f64 (.f64 x x) (-.f64 y x)) (/.f64 (.f64 y y) (-.f64 y x)))
(+.f64 (neg.f64 x) (neg.f64 y))
(+.f64 (neg.f64 x) y)
(+.f64 (neg.f64 y) (neg.f64 x))
(+.f64 (neg.f64 y) x)
(+.f64 y x)
(+.f64 x (neg.f64 y))
(+.f64 x y)

eval73.0ms (2.2%)

Memory: 15.9MiB live, 60.6MiB allocated
Compiler: Compiled 11 437 to 1 065 computations (90.7% saved)

prune42.0ms (1.3%)

Memory

-25.1MiB live, 28.7MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	410	1	411
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	410	3	413

Accuracy

100.0%

Counts

413 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (-.f64 x y) (+.f64 y x))
✓	55.9%	#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))
▶	53.7%	#s(approx (- (* x x) (* y y)) (*.f64 x x))

Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify91.0ms (2.8%)

Memory

21.2MiB live, 68.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
0	8	15
1	21	15
2	81	15
3	223	15
4	401	15
5	828	15
6	1379	15
7	2063	15
8	2900	15
9	3210	15
10	3272	15
11	3272	15
12	3350	15
0	3350	15

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (- (* x x) (* y y)) (*.f64 x x))
(*.f64 x x)
x

Outputs
#s(approx (- (* x x) (* y y)) (*.f64 x x))
(*.f64 x x)
x

localize40.0ms (1.2%)

Memory

-10.2MiB live, 36.4MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(*.f64 x x)
accuracy	29.622097173853934	#s(approx (- (* x x) (* y y)) (*.f64 x x))

Samples

12.0ms

256×

valid

Compiler

Compiled 13 to 7 computations (46.2% saved)

Precisions

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

ival-mult: 3.0ms (66.5% of total)

ival-sub: 1.0ms (22.2% of total)

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

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

series2.0ms (0.1%)

Memory

3.3MiB live, 3.3MiB allocated

Counts

2 → 6

Calls

Call 1

Inputs
#s(approx (- (* x x) (* y y)) (*.f64 x x))
(*.f64 x x)

Outputs
(* -1 (pow y 2))
(- (pow x 2) (pow y 2))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ (pow y 2) (pow x 2)))))
(+ (* -1 (pow y 2)) (pow x 2))
(* (pow y 2) (- (/ (pow x 2) (pow y 2)) 1))

Calls

6 calls:

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

simplify125.0ms (3.8%)

Memory

10.1MiB live, 106.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	41
1	40	41
2	136	41
3	829	41
4	3437	41
0	8613	40

Stop Event

1×	iter limit
1×	node limit

Counts

6 → 6

Calls

Call 1

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

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

rewrite97.0ms (3%)

Memory

-26.3MiB live, 64.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
0	8	14
1	37	14
2	329	14
3	4477	14
0	8306	13

Stop Event

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

Counts

2 → 13

Calls

Call 1

Inputs
#s(approx (- (* x x) (* y y)) (*.f64 x x))
(*.f64 x x)

Outputs
#s(approx (- (* x x) (* y y)) (*.f64 x x))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 x x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 x x))
(exp.f64 (/.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))

eval2.0ms (0.1%)

Memory: 5.7MiB live, 5.7MiB allocated
Compiler: Compiled 232 to 56 computations (75.9% saved)

prune2.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	17	0	17
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	17	3	20

Accuracy

100.0%

Counts

20 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (-.f64 x y) (+.f64 y x))
✓	55.9%	#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))
✓	53.7%	#s(approx (- (* x x) (* y y)) (*.f64 x x))

Compiler

Compiled 67 to 35 computations (47.8% saved)

regimes10.0ms (0.3%)

Memory

24.5MiB live, 24.5MiB allocated

Counts

4 → 1

Calls

Call 1

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

Outputs
(*.f64 (-.f64 x y) (+.f64 y x))

Calls

5 calls:

2.0ms	x
2.0ms	y
2.0ms	(*.f64 y y)
2.0ms	(-.f64 (.f64 x x) (.f64 y y))
2.0ms	(*.f64 x x)

Results

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

Compiler

Compiled 15 to 15 computations (0% saved)

regimes9.0ms (0.3%)

Memory

-28.1MiB live, 17.0MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

5 calls:

3.0ms	y
2.0ms	x
1.0ms	(-.f64 (.f64 x x) (.f64 y y))
1.0ms	(*.f64 y y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
77.5%	2	`x`
79.8%	2	`y`
95.3%	2	`(-.f64 (.f64 x x) (.f64 y y))`
77.5%	2	`(*.f64 x x)`
79.8%	2	`(*.f64 y y)`

Compiler

Compiled 15 to 15 computations (0% saved)

regimes5.0ms (0.2%)

Memory

15.1MiB live, 15.1MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (* x x) (* y y)) (*.f64 x x))

Outputs
#s(approx (- (* x x) (* y y)) (*.f64 x x))

Calls

5 calls:

1.0ms	x
1.0ms	y
1.0ms	(-.f64 (.f64 x x) (.f64 y y))
1.0ms	(*.f64 x x)
1.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
53.7%	1	`x`
53.7%	1	`(*.f64 x x)`
53.7%	1	`y`
53.7%	1	`(*.f64 y y)`
53.7%	1	`(-.f64 (.f64 x x) (.f64 y y))`

Compiler

Compiled 15 to 15 computations (0% saved)

bsearch0.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.3780038094251327e-299	0.0

Compiler

Compiled 10 to 10 computations (0% saved)

simplify72.0ms (2.2%)

Memory

-12.1MiB live, 42.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	51
1	39	51
2	104	51
3	247	51
4	425	51
5	860	51
6	1409	51
7	2093	51
8	2924	51
9	3234	51
10	3296	51
11	3296	51
12	3374	51

Stop Event

1×

saturated

Calls

Call 1

Inputs

(*.f64 (-.f64 x y) (+.f64 y x))

(if (<=.f64 (-.f64 (*.f64 x x) (*.f64 y y)) #s(literal -7540071506325551/754007150632555106105265567894716959631281531468563222724576883120202793061715911671371697267283217963528178126800104645601692562497382897388239949720868877774169386463487004356335504882384897549598543638261948036260930759551721433617559655193833844143189700366403049053003693428749228016236154394768201795621617664 binary64)) #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #s(approx (- (* x x) (* y y)) (*.f64 x x)))

#s(approx (- (* x x) (* y y)) (*.f64 x x))

Outputs

(*.f64 (-.f64 x y) (+.f64 y x))

(if (<=.f64 (-.f64 (*.f64 x x) (*.f64 y y)) #s(literal -7540071506325551/754007150632555106105265567894716959631281531468563222724576883120202793061715911671371697267283217963528178126800104645601692562497382897388239949720868877774169386463487004356335504882384897549598543638261948036260930759551721433617559655193833844143189700366403049053003693428749228016236154394768201795621617664 binary64)) #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)) #s(approx (- (* x x) (* y y)) (*.f64 x x)))

#s(approx (- (* x x) (* y y)) (*.f64 x x))

soundness493.0ms (15.1%)

Memory

2.9MiB live, 286.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	13
0	8	13
1	37	13
2	329	13
3	4470	13
0	8291	12
0	17	44
1	40	44
2	136	44
3	829	44
4	3437	44
0	8613	43
0	92	211
1	299	206
2	1084	205
3	4475	205
0	8193	200

Stop Event

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

Compiler

Compiled 83 to 44 computations (47% saved)

preprocess99.0ms (3%)

Memory

-6.4MiB live, 39.2MiB allocated

Remove

(abs x)

(abs y)

Compiler

Compiled 144 to 66 computations (54.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample993.0ms (30.4%)

explain65.0ms (2%)

preprocess117.0ms (3.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify90.0ms (2.8%)

localize14.0ms (0.4%)

series3.0ms (0.1%)

simplify89.0ms (2.7%)

rewrite133.0ms (4.1%)

eval9.0ms (0.3%)

prune2.0ms (0.1%)

simplify106.0ms (3.2%)

localize76.0ms (2.3%)

series6.0ms (0.2%)

simplify157.0ms (4.8%)

rewrite246.0ms (7.5%)

eval73.0ms (2.2%)

prune42.0ms (1.3%)

simplify91.0ms (2.8%)

localize40.0ms (1.2%)

series2.0ms (0.1%)

simplify125.0ms (3.8%)

rewrite97.0ms (3%)

eval2.0ms (0.1%)

prune2.0ms (0.1%)

regimes10.0ms (0.3%)

regimes9.0ms (0.3%)

regimes5.0ms (0.2%)

bsearch0.0ms (0%)

simplify72.0ms (2.2%)

soundness493.0ms (15.1%)

preprocess99.0ms (3%)

end0.0ms (0%)

Profiling