Metrics for Examples.Basics.ProofTests:f4 from sbv-4.4

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

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 15 to 11 computations (26.7% saved)

sample4.0s (58.6%)

Memory

-282.1MiB live, 1 407.3MiB allocated; 4.0s collecting garbage

Samples

3.6s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 509.0ms

ival-mult: 290.0ms (56.9% of total)

ival-add: 203.0ms (39.9% of total)

exact: 6.0ms (1.2% of total)

ival-true: 5.0ms (1% of total)

ival-assert: 3.0ms (0.6% of total)

adjust: 2.0ms (0.4% of total)

Bogosity

explain194.0ms (2.8%)

Memory

4.1MiB live, 327.5MiB allocated; 41ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
13	-	-	`(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))`
7	-	-	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`
0	-	-	`(*.f64 x #s(literal 2 binary64))`
0	-	-	`(*.f64 x x)`
0	-	-	`(.f64 (.f64 x #s(literal 2 binary64)) y)`
0	-	-	`y`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`(*.f64 y y)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`+.f64`	`(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))`	nan-rescue	13	0
↳	`(*.f64 x x)`	overflow	65
↳	`(*.f64 x #s(literal 2 binary64))`	overflow	1
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	overflow	33
`+.f64`	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`	nan-rescue	7	0
↳	`(*.f64 x #s(literal 2 binary64))`	overflow	1
↳	`(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))`	overflow	73
↳	`(*.f64 x x)`	overflow	65
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	overflow	33
↳	`(*.f64 y y)`	overflow	64

Confusion

	Predicted +	Predicted -
+	16	0
-	0	240

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	16	0	0
-	0	0	240

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	240
1	12
2	4

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

68.0ms

512×

valid

Compiler

Compiled 95 to 31 computations (67.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-mult: 15.0ms (70.9% of total)

ival-add: 4.0ms (18.9% of total)

ival-assert: 1.0ms (4.7% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

preprocess168.0ms (2.5%)

Memory

-16.5MiB live, 126.1MiB allocated; 28ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	23	71
1	95	57
2	314	57
3	611	55
4	1031	55
5	1555	35
6	2248	35
7	3008	35
8	3674	35
9	3996	35
10	4004	35
11	4004	35
12	4046	35
13	4088	35
14	4102	35
0	9	13
0	15	13
1	38	11
2	127	11
3	330	11
4	634	11
5	971	7
6	1297	7
7	1855	7
8	2503	7
9	2794	7
10	3048	7
11	3066	7
0	3066	7

Stop Event

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

Calls

Call 1

Inputs
(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

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

Symmetry

(sort x y)

Compiler

Compiled 13 to 9 computations (30.8% saved)

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

2.5MiB live, 2.5MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	93.7%	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify59.0ms (0.9%)

Memory

31.0MiB live, 75.6MiB allocated; 5ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (.f64 x #s(literal 2 binary64)) y)
cost-diff	0	(*.f64 x x)
cost-diff	3	(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))
cost-diff	3	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	39
0	15	39
1	38	35
2	127	35
3	330	35
4	634	35
5	971	31
6	1297	31
7	1855	31
8	2503	31
9	2794	31
10	3048	31
11	3066	31
0	3066	30

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

Outputs
(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
(*.f64 (+.f64 y x) (+.f64 y x))
(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(*.f64 x x)
x
(.f64 (.f64 x #s(literal 2 binary64)) y)
(.f64 y (.f64 #s(literal 2 binary64) x))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
y
(*.f64 y y)

localize83.0ms (1.2%)

Memory

-23.4MiB live, 76.4MiB allocated; 18ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.0	(*.f64 x #s(literal 2 binary64))
accuracy	1.3984375000000002	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
accuracy	2.542962557490618	(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))

Samples

69.0ms

256×

valid

Compiler

Compiled 41 to 11 computations (73.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 61.0ms

ival-mult: 59.0ms (96.3% of total)

ival-add: 2.0ms (3.3% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series7.0ms (0.1%)

Memory

14.2MiB live, 14.2MiB allocated; 0ms collecting garbage

Counts

5 → 17

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (+ (* x x) (* (* x 2) y)) (* x x) (* (* x 2) y) (* x 2))
1.0ms	x	@	0	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (+ (* x x) (* (* x 2) y)) (* x x) (* (* x 2) y) (* x 2))
1.0ms	y	@	0	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (+ (* x x) (* (* x 2) y)) (* x x) (* (* x 2) y) (* x 2))
1.0ms	x	@	-inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (+ (* x x) (* (* x 2) y)) (* x x) (* (* x 2) y) (* x 2))
1.0ms	y	@	inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (+ (* x x) (* (* x 2) y)) (* x x) (* (* x 2) y) (* x 2))

simplify174.0ms (2.6%)

Memory

5.0MiB live, 205.3MiB allocated; 37ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	177
1	194	169
2	746	157
3	3571	149
0	8118	140

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 17

Calls

Call 1

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

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

rewrite273.0ms (4%)

Memory

-43.1MiB live, 339.0MiB allocated; 39ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
0	15	33
1	65	29
2	568	29
0	9286	26

Stop Event

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

Counts

5 → 255

Calls

Call 1

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

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

eval45.0ms (0.7%)

Memory: 35.9MiB live, 79.8MiB allocated; 5ms collecting garbage
Compiler: Compiled 8 056 to 793 computations (90.2% saved)

prune6.0ms (0.1%)

Memory

-25.1MiB live, 19.7MiB allocated; 4ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	265	3	268
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	266	3	269

Accuracy

100.0%

Counts

269 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	57.7%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))
▶	100.0%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
▶	56.3%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Status

Accuracy

Program

▶

57.7%

#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))

▶

100.0%

#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))

▶

56.3%

#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Compiler

Compiled 58 to 36 computations (37.9% saved)

simplify65.0ms (1%)

Memory

4.6MiB live, 98.9MiB allocated; 17ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 #s(literal 2 binary64) y x)
cost-diff	0	(*.f64 (fma.f64 #s(literal 2 binary64) y x) x)
cost-diff	0	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))
cost-diff	0	(+.f64 y x)
cost-diff	0	(*.f64 (+.f64 y x) (+.f64 y x))
cost-diff	0	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	87
0	23	87
1	60	78
2	184	69
3	522	69
4	922	69
5	1221	69
6	1722	69
7	2372	69
8	2720	69
9	2972	69
10	3058	69
0	3058	69

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(*.f64 y y)
y
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
(*.f64 (+.f64 y x) (+.f64 y x))
(+.f64 y x)
y
x
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))
(*.f64 (fma.f64 #s(literal 2 binary64) y x) x)
(fma.f64 #s(literal 2 binary64) y x)
#s(literal 2 binary64)
y
x

Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(*.f64 y y)
y
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
(*.f64 (+.f64 y x) (+.f64 y x))
(+.f64 y x)
y
x
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 y #s(literal 2 binary64) x) x))
(*.f64 (fma.f64 #s(literal 2 binary64) y x) x)
(*.f64 (fma.f64 y #s(literal 2 binary64) x) x)
(fma.f64 #s(literal 2 binary64) y x)
(fma.f64 y #s(literal 2 binary64) x)
#s(literal 2 binary64)
y
x

localize42.0ms (0.6%)

Memory

3.1MiB live, 93.9MiB allocated; 9ms collecting garbage

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 #s(literal 2 binary64) y x)
accuracy	0.0	(*.f64 (fma.f64 #s(literal 2 binary64) y x) x)
accuracy	27.06258435716946	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))
accuracy	0.0	(+.f64 y x)
accuracy	0.0	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
accuracy	0.006191259768442017	(*.f64 (+.f64 y x) (+.f64 y x))
accuracy	0.0	(*.f64 y y)
accuracy	27.997409706795	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Samples

25.0ms

256×

valid

Compiler

Compiled 72 to 16 computations (77.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-mult: 12.0ms (73% of total)

ival-add: 4.0ms (24.3% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series7.0ms (0.1%)

Memory

16.6MiB live, 16.6MiB allocated; 0ms collecting garbage

Counts

8 → 29

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(*.f64 y y)
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
(*.f64 (+.f64 y x) (+.f64 y x))
(+.f64 y x)
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))
(*.f64 (fma.f64 #s(literal 2 binary64) y x) x)
(fma.f64 #s(literal 2 binary64) y x)

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

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	y	@	-inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ y x) (+ y x)) (+ y x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 y) x) x) (+ (* 2 y) x))
1.0ms	y	@	inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ y x) (+ y x)) (+ y x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 y) x) x) (+ (* 2 y) x))
1.0ms	x	@	-inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ y x) (+ y x)) (+ y x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 y) x) x) (+ (* 2 y) x))
1.0ms	x	@	inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ y x) (+ y x)) (+ y x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 y) x) x) (+ (* 2 y) x))
1.0ms	x	@	0	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ y x) (+ y x)) (+ y x) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ (* 2 y) x) x) (+ (* 2 y) x))

simplify235.0ms (3.4%)

Memory

4.2MiB live, 253.8MiB allocated; 53ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	254
1	268	246
2	896	234
3	3729	234
0	8273	217

Stop Event

1×	iter limit
1×	node limit

Counts

29 → 27

Calls

Call 1

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

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

rewrite285.0ms (4.2%)

Memory

-17.5MiB live, 262.7MiB allocated; 40ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	81
0	23	77
1	108	68
2	956	68
0	8843	65

Stop Event

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

Counts

8 → 445

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(*.f64 y y)
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
(*.f64 (+.f64 y x) (+.f64 y x))
(+.f64 y x)
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))
(*.f64 (fma.f64 #s(literal 2 binary64) y x) x)
(fma.f64 #s(literal 2 binary64) y x)

Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
(*.f64 (neg.f64 (neg.f64 (neg.f64 y))) (neg.f64 (neg.f64 (neg.f64 y))))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)))
(*.f64 (neg.f64 (neg.f64 y)) (neg.f64 (neg.f64 y)))
(*.f64 (neg.f64 y) (neg.f64 y))
(*.f64 y y)
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 y)) #s(literal 2 binary64))
(pow.f64 (neg.f64 y) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 y) y))
(sqrt.f64 (pow.f64 y #s(literal 4 binary64)))
(fabs.f64 (*.f64 (neg.f64 y) y))
(fabs.f64 (*.f64 y y))
(exp.f64 (*.f64 (log.f64 (neg.f64 y)) #s(literal 2 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))))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (pow.f64 (+.f64 y x) #s(literal 2 binary64)))
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eval88.0ms (1.3%)

Memory: 42.6MiB live, 226.4MiB allocated; 29ms collecting garbage
Compiler: Compiled 21 586 to 1 874 computations (91.3% saved)

prune106.0ms (1.5%)

Memory

-58.4MiB live, 104.0MiB allocated; 17ms collecting garbage

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	547	1	548
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	547	4	551

Accuracy

100.0%

Counts

551 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	57.7%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))
✓	100.0%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
✓	56.3%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
▶	57.5%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Compiler

Compiled 75 to 47 computations (37.3% saved)

simplify68.0ms (1%)

Memory

27.3MiB live, 112.2MiB allocated; 12ms collecting garbage

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) (* (* x 2) y)) (* y y)) (*.f64 x x))

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	21
0	12	21
1	35	19
2	124	19
3	327	19
4	628	19
5	962	15
6	1286	15
7	1844	15
8	2492	15
9	2783	15
10	3037	15
11	3055	15
0	3055	15

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(*.f64 x x)
x

Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(*.f64 x x)
x

localize39.0ms (0.6%)

Memory

17.6MiB live, 71.6MiB allocated; 18ms collecting garbage

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0.0	(*.f64 x x)
accuracy	27.23089285757499	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Samples

33.0ms

256×

valid

Compiler

Compiled 19 to 11 computations (42.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-mult: 21.0ms (77.6% of total)

ival-add: 6.0ms (22.2% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

4.5MiB live, 4.5MiB allocated; 0ms collecting garbage

Counts

2 → 12

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(*.f64 x x)

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

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x))
0.0ms	x	@	-inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x))
0.0ms	x	@	0	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x))
0.0ms	y	@	-inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x))
0.0ms	y	@	inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* x x))

simplify173.0ms (2.5%)

Memory

-12.4MiB live, 265.0MiB allocated; 36ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	142
1	172	132
2	641	124
3	3245	116
0	8105	108

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 12

Calls

Call 1

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

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

rewrite168.0ms (2.5%)

Memory

-12.9MiB live, 175.7MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
0	12	20
1	62	18
2	565	18
0	9262	16

Stop Event

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

Counts

2 → 15

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
(*.f64 x x)

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

eval3.0ms (0%)

Memory: 5.7MiB live, 5.7MiB allocated; 0ms collecting garbage
Compiler: Compiled 488 to 84 computations (82.8% saved)

prune3.0ms (0%)

Memory

6.5MiB live, 6.5MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	24	4	28

Accuracy

100.0%

Counts

28 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	57.7%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))
✓	100.0%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
✓	56.3%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
✓	57.5%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Compiler

Compiled 163 to 71 computations (56.4% saved)

regimes6.0ms (0.1%)

Memory

15.7MiB live, 15.7MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (fma.f64 #s(literal 2 binary64) y x) x))
(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))

Calls

3 calls:

2.0ms	x
2.0ms	y
2.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Results

Accuracy	Segments	Branch
100.0%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`
100.0%	1	`x`
100.0%	1	`y`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes4.0ms (0.1%)

Memory

12.3MiB live, 12.3MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Calls

3 calls:

1.0ms	y
1.0ms	x
1.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Results

Accuracy	Segments	Branch
65.5%	4	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`
89.4%	2	`x`
90.5%	2	`y`

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes23.0ms (0.3%)

Memory

-36.1MiB live, 10.7MiB allocated; 3ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Outputs
#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Calls

3 calls:

21.0ms	y
1.0ms	x
1.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))

Results

Accuracy	Segments	Branch
57.5%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`
57.5%	1	`x`
57.5%	1	`y`

Compiler

Compiled 15 to 13 computations (13.3% saved)

bsearch14.0ms (0.2%)

Memory

17.0MiB live, 17.0MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	2.833488236757449e-28	1.5919211171843444e-24

Samples

7.0ms

128×

valid

Compiler

Compiled 288 to 206 computations (28.5% saved)

Precisions

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

ival-mult: 3.0ms (68.2% of total)

ival-add: 1.0ms (22.7% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

simplify126.0ms (1.8%)

Memory

-26.3MiB live, 87.5MiB allocated; 52ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	19	76
1	42	68
2	130	68
3	338	68
4	661	68
5	1019	52
6	1497	52
7	3848	52
8	6120	52

Stop Event

1×	node limit

Calls

Call 1

Inputs

#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))

(if (<=.f64 y #s(literal 8920298079412249/2787593149816327892691964784081045188247552 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y)))

#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

Outputs

#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))

(if (<=.f64 y #s(literal 8920298079412249/2787593149816327892691964784081045188247552 binary64)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x)) #s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y)))

#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 x x))

derivations323.0ms (4.7%)

Memory

-3.0MiB live, 331.5MiB allocated; 28ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	254
1	268	246
2	896	234
3	3729	234
0	8273	217
0	56	177
1	194	169
2	746	157
3	3571	149
0	8118	140

Stop Event

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

Compiler

Compiled 76 to 19 computations (75% saved)

preprocess36.0ms (0.5%)

Memory: 8.4MiB live, 54.8MiB allocated; 5ms collecting garbage
Remove: (sort x y)
Compiler: Compiled 246 to 98 computations (60.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze0.0ms (0%)

sample4.0s (58.6%)

explain194.0ms (2.8%)

preprocess168.0ms (2.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify59.0ms (0.9%)

localize83.0ms (1.2%)

series7.0ms (0.1%)

simplify174.0ms (2.6%)

rewrite273.0ms (4%)

eval45.0ms (0.7%)

prune6.0ms (0.1%)

simplify65.0ms (1%)

localize42.0ms (0.6%)

series7.0ms (0.1%)

simplify235.0ms (3.4%)

rewrite285.0ms (4.2%)

eval88.0ms (1.3%)

prune106.0ms (1.5%)

simplify68.0ms (1%)

localize39.0ms (0.6%)

series2.0ms (0%)

simplify173.0ms (2.5%)

rewrite168.0ms (2.5%)

eval3.0ms (0%)

prune3.0ms (0%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

regimes23.0ms (0.3%)

bsearch14.0ms (0.2%)

simplify126.0ms (1.8%)

derivations323.0ms (4.7%)

preprocess36.0ms (0.5%)

end0.0ms (0%)

Profiling