Metrics for Examples.Basics.ProofTests:f4 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 15 to 11 computations (26.7% saved)

sample857.0ms (21.5%)

Memory

23.2MiB live, 1 049.4MiB allocated

Samples

592.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 402.0ms

ival-mult: 305.0ms (75.9% of total)

ival-add: 82.0ms (20.4% of total)

ival-true: 6.0ms (1.5% of total)

exact: 5.0ms (1.2% of total)

ival-assert: 3.0ms (0.7% of total)

Bogosity

explain179.0ms (4.5%)

Memory

-10.5MiB live, 117.3MiB allocated

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))`
9	-	-	`(+.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	66
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	overflow	38
`+.f64`	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`	nan-rescue	9	0
↳	`(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))`	overflow	79
↳	`(*.f64 x x)`	overflow	66
↳	`(.f64 (.f64 x #s(literal 2 binary64)) y)`	overflow	38
↳	`(*.f64 y y)`	overflow	71

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	10
2	6

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

32.0ms

512×

valid

Compiler

Compiled 134 to 40 computations (70.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 12.0ms (69.5% of total)

ival-add: 4.0ms (23.2% of total)

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

exact: 0.0ms (0% of total)

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

preprocess163.0ms (4.1%)

Memory

4.1MiB live, 76.6MiB allocated

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

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	93.8%	(+.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)

simplify67.0ms (1.7%)

Memory

2.6MiB live, 44.6MiB allocated

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)

localize44.0ms (1.1%)

Memory

0.8MiB live, 37.1MiB allocated

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	1.1953125000000002	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
accuracy	2.9960854933208236	(+.f64 (.f64 x x) (.f64 (*.f64 x #s(literal 2 binary64)) y))

Samples

37.0ms

256×

valid

Compiler

Compiled 80 to 20 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 8.0ms (72.9% of total)

ival-add: 2.0ms (18.2% of total)

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

exact: 0.0ms (0% of total)

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

series38.0ms (1%)

Memory

-29.1MiB live, 8.9MiB allocated

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
31.0ms	y	@	-inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (+ (* x x) (* (* x 2) y)) (* x x) (* (* x 2) y) (* x 2))
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))

simplify179.0ms (4.5%)

Memory

15.7MiB live, 179.7MiB allocated

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)))

rewrite187.0ms (4.7%)

Memory

-21.8MiB live, 220.2MiB allocated

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

eval66.0ms (1.6%)

Memory: 10.8MiB live, 86.7MiB allocated
Compiler: Compiled 8 056 to 793 computations (90.2% saved)

prune4.0ms (0.1%)

Memory

12.1MiB live, 12.1MiB allocated

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
▶	100.0%	(fma.f64 y (fma.f64 #s(literal 2 binary64) x y) (*.f64 x x))
▶	100.0%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
▶	60.1%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Compiler

Compiled 47 to 29 computations (38.3% saved)

simplify61.0ms (1.5%)

Memory

-0.3MiB live, 38.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 #s(literal 2 binary64) x y)
cost-diff	2	(fma.f64 y (fma.f64 #s(literal 2 binary64) x y) (*.f64 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	73
0	25	63
1	68	63
2	203	59
3	554	59
4	958	59
5	1290	59
6	1790	59
7	2438	59
8	2783	59
9	3035	59
10	3121	59
0	3121	59

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

localize89.0ms (2.2%)

Memory

9.1MiB live, 51.4MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 y (fma.f64 #s(literal 2 binary64) x y) (*.f64 x x))
accuracy	0.0	(fma.f64 #s(literal 2 binary64) x y)
accuracy	0.0	(*.f64 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	0.00390625	(*.f64 (+.f64 y x) (+.f64 y x))
accuracy	0.0	(*.f64 y y)
accuracy	25.545015070389333	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Samples

80.0ms

256×

valid

Compiler

Compiled 139 to 35 computations (74.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 71.0ms

ival-mult: 65.0ms (91.2% of total)

ival-add: 5.0ms (7% of total)

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

exact: 0.0ms (0% of total)

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

series10.0ms (0.3%)

Memory

-19.7MiB live, 12.8MiB allocated

Counts

8 → 25

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

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

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	y	@	-inf	((+ (+ (* x x) (* (* x 2) y)) (* y y)) (* y y) (+ (+ (* x x) (* (* x 2) y)) (* y y)) (* (+ y x) (+ y x)) (+ y x) (+ (* y (+ (* 2 x) y)) (* x x)) (+ (* 2 x) y) (* x 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) (+ (* y (+ (* 2 x) y)) (* x x)) (+ (* 2 x) y) (* x 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) (+ (* y (+ (* 2 x) y)) (* x x)) (+ (* 2 x) y) (* x 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) (+ (* y (+ (* 2 x) y)) (* x x)) (+ (* 2 x) y) (* x 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) (+ (* y (+ (* 2 x) y)) (* x x)) (+ (* 2 x) y) (* x x))

simplify200.0ms (5%)

Memory

17.1MiB live, 187.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	222
1	247	212
2	791	204
3	3435	204
0	8194	188

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 23

Calls

Call 1

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

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

rewrite163.0ms (4.1%)

Memory

8.7MiB live, 239.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	67
0	25	55
1	126	55
2	1101	55
0	8639	55

Stop Event

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

Counts

8 → 523

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)
(fma.f64 y (fma.f64 #s(literal 2 binary64) x y) (*.f64 x x))
(fma.f64 #s(literal 2 binary64) x y)
(*.f64 x 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)))
(*.f64 (exp.f64 (log.f64 (+.f64 y x))) (exp.f64 (log.f64 (+.f64 y x))))
(*.f64 (+.f64 y x) (+.f64 y x))
(pow.f64 (exp.f64 (log.f64 (+.f64 y x))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 y x) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (+.f64 y x) #s(literal 2 binary64))
(/.f64 (-.f64 (pow.f64 (.f64 (+.f64 y x) y) #s(literal 2 binary64)) (.f64 (.f64 (neg.f64 x) (+.f64 y x)) (.f64 (neg.f64 x) (+.f64 y x)))) (fma.f64 (+.f64 y x) y (*.f64 (neg.f64 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 (+.f64 y x) x) (.f64 (+.f64 y x) y)))
(/.f64 (-.f64 (pow.f64 (.f64 (+.f64 y x) y) #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 x) (+.f64 y x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (+.f64 y x) y) #s(literal 2 binary64)) (fma.f64 (.f64 (neg.f64 x) (+.f64 y x)) (.f64 (neg.f64 x) (+.f64 y x)) (.f64 (.f64 (+.f64 y x) y) (.f64 (neg.f64 x) (+.f64 y x))))))
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(/.f64 (fma.f64 (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (fma.f64 #s(literal -2 binary64) x y) y)) (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (fma.f64 #s(literal -2 binary64) x y) y)) (pow.f64 y #s(literal 3 binary64)))) (.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (fma.f64 #s(literal -2 binary64) x y) y)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (fma.f64 #s(literal -2 binary64) x y) y))))
(/.f64 (-.f64 (.f64 y y) (.f64 #s(literal 4 binary64) (*.f64 x x))) (fma.f64 #s(literal -2 binary64) x y))
(/.f64 (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 y) y))) (neg.f64 (-.f64 (*.f64 #s(literal -2 binary64) x) y)))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (fma.f64 y y (-.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (.f64 (.f64 y #s(literal 2 binary64)) x)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (fma.f64 #s(literal -2 binary64) x y) y))))
(/.f64 (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (neg.f64 y) y)) (-.f64 (*.f64 #s(literal -2 binary64) x) y))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 y y (-.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (.f64 (.f64 y #s(literal 2 binary64)) x))))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (fma.f64 #s(literal -2 binary64) x y) y)))
(fma.f64 (pow.f64 (+.f64 y x) #s(literal 1/2 binary64)) (pow.f64 (+.f64 y x) #s(literal 1/2 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (+.f64 y x))
(fma.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)) (*.f64 #s(literal -2 binary64) x))
(fma.f64 (sqrt.f64 (neg.f64 (neg.f64 x))) (sqrt.f64 (neg.f64 (neg.f64 x))) (+.f64 y x))
(fma.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)) (+.f64 y x))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (+.f64 y x))
(fma.f64 (sqrt.f64 (neg.f64 (neg.f64 y))) (sqrt.f64 (neg.f64 (neg.f64 y))) (*.f64 #s(literal -2 binary64) x))
(fma.f64 (sqrt.f64 (neg.f64 y)) (sqrt.f64 (neg.f64 y)) (*.f64 #s(literal -2 binary64) x))
(fma.f64 (sqrt.f64 y) (sqrt.f64 y) (*.f64 #s(literal -2 binary64) x))
(fma.f64 (sqrt.f64 (+.f64 y x)) (sqrt.f64 (+.f64 y x)) x)
(fma.f64 #s(literal -2 binary64) x y)
(fma.f64 (neg.f64 x) #s(literal 2 binary64) y)
(fma.f64 #s(literal 2 binary64) (neg.f64 x) y)
(fma.f64 #s(literal 2 binary64) x y)
(fma.f64 x #s(literal -2 binary64) y)
(fma.f64 x #s(literal 2 binary64) y)
(-.f64 (/.f64 (.f64 y y) (fma.f64 #s(literal -2 binary64) x y)) (/.f64 (.f64 #s(literal 4 binary64) (*.f64 x x)) (fma.f64 #s(literal -2 binary64) x y)))
(-.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -2 binary64) x) y)) (/.f64 (.f64 y y) (-.f64 (*.f64 #s(literal -2 binary64) x) y)))
(-.f64 y (*.f64 #s(literal -2 binary64) x))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (-.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (.f64 (.f64 y #s(literal 2 binary64)) x)))) (/.f64 (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 3 binary64)) (fma.f64 y y (-.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (.f64 (*.f64 y #s(literal 2 binary64)) x)))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 3 binary64)) (fma.f64 y y (-.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (.f64 (.f64 y #s(literal 2 binary64)) x)))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y (-.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (.f64 (*.f64 y #s(literal 2 binary64)) x)))))
(+.f64 (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (fma.f64 #s(literal -2 binary64) x y) y))) (/.f64 (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (fma.f64 #s(literal -2 binary64) x y) y))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 3 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 (fma.f64 #s(literal -2 binary64) x y) y))) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 #s(literal 4 binary64) (.f64 x x) (*.f64 (fma.f64 #s(literal -2 binary64) x y) y))))
(+.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -2 binary64) x) y)) (/.f64 (.f64 (neg.f64 (neg.f64 y)) (neg.f64 y)) (-.f64 (*.f64 #s(literal -2 binary64) x) y)))
(+.f64 (/.f64 (.f64 #s(literal 4 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -2 binary64) x) y)) (/.f64 (.f64 (neg.f64 y) y) (-.f64 (*.f64 #s(literal -2 binary64) x) y)))
(+.f64 (*.f64 #s(literal -2 binary64) x) y)
(+.f64 (+.f64 y x) x)
(+.f64 y (*.f64 #s(literal -2 binary64) x))
(+.f64 x (+.f64 y x))
(*.f64 (neg.f64 (neg.f64 (neg.f64 x))) (neg.f64 (neg.f64 (neg.f64 x))))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.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 (neg.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))))

eval84.0ms (2.1%)

Memory: -17.2MiB live, 147.7MiB allocated
Compiler: Compiled 22 367 to 1 903 computations (91.5% saved)

prune38.0ms (1%)

Memory

-18.0MiB live, 28.3MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	621	1	622
Fresh	0	0	0
Picked	1	2	3
Done	0	0	0
Total	622	3	625

Accuracy

100.0%

Counts

625 → 3

Alt Table

Click to see full alt table

Status

Accuracy

Program

▶

55.5%

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

✓

100.0%

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

✓

60.1%

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

Compiler

Compiled 52 to 33 computations (36.5% saved)

simplify6.0ms (0.2%)

Memory

7.7MiB live, 7.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	32
0	13	32
1	26	32
2	64	32
3	107	32
4	142	32
5	156	32
6	170	32
7	172	32
0	172	30

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize24.0ms (0.6%)

Memory

5.4MiB live, 42.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 y #s(approx (+ (* 2 x) y) (.f64 #s(literal 2 binary64) x)) (.f64 x x))
accuracy	0.0	(*.f64 x x)
accuracy	0.0	(*.f64 #s(literal 2 binary64) x)
accuracy	33.75715232086045	#s(approx (+ (* 2 x) y) (*.f64 #s(literal 2 binary64) x))

Samples

18.0ms

256×

valid

Compiler

Compiled 59 to 20 computations (66.1% saved)

Precisions

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

ival-mult: 5.0ms (65.7% of total)

ival-add: 2.0ms (26.3% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

4.9MiB live, 4.9MiB allocated

Counts

4 → 19

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((+ (* y (+ (* 2 x) y)) (* x x)) (+ (* 2 x) y) (* 2 x) (* x x))
1.0ms	x	@	-inf	((+ (* y (+ (* 2 x) y)) (* x x)) (+ (* 2 x) y) (* 2 x) (* x x))
0.0ms	x	@	0	((+ (* y (+ (* 2 x) y)) (* x x)) (+ (* 2 x) y) (* 2 x) (* x x))
0.0ms	y	@	inf	((+ (* y (+ (* 2 x) y)) (* x x)) (+ (* 2 x) y) (* 2 x) (* x x))
0.0ms	y	@	-inf	((+ (* y (+ (* 2 x) y)) (* x x)) (+ (* 2 x) y) (* 2 x) (* x x))

simplify290.0ms (7.3%)

Memory

1.2MiB live, 224.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	186
1	211	176
2	726	168
3	3398	160
0	8176	150

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 18

Calls

Call 1

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

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

rewrite156.0ms (3.9%)

Memory

-7.6MiB live, 158.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
0	13	29
1	52	29
2	404	29
0	4854	27

Stop Event

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

Counts

4 → 247

Calls

Call 1

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

Outputs
(.f64 (/.f64 (-.f64 (pow.f64 (.f64 #s(approx (+ (* 2 x) y) (.f64 #s(literal -2 binary64) x)) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 (.f64 #s(approx (+ (* 2 x) y) (.f64 #s(literal -2 binary64) x)) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (.f64 x x) (fma.f64 #s(approx (+ (* 2 x) y) (.f64 #s(literal -2 binary64) x)) y (.f64 x x)) (pow.f64 (.f64 #s(approx (+ ( 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (.f64 #s(approx (+ (* 2 x) y) (.f64 #s(literal -2 binary64) x)) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 (.f64 #s(approx (+ (* 2 x) y) (.f64 #s(literal -2 binary64) x)) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 #s(approx (+ ( 2 x) y) (.f64 #s(literal -2 binary64) x)) y (.f64 x x)))
(.f64 (/.f64 (-.f64 (pow.f64 (.f64 #s(approx (+ (* 2 x) y) (.f64 #s(literal -2 binary64) x)) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 (.f64 #s(approx (+ (* 2 x) y) (.f64 #s(literal -2 binary64) x)) y) #s(literal 4 binary64)) (pow.f64 (fma.f64 #s(approx (+ ( 2 x) y) (.f64 #s(literal -2 binary64) x)) (.f64 y (.f64 (neg.f64 x) x)) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64)))) (fma.f64 (.f64 x x) (fma.f64 #s(approx (+ (* 2 x) y) (.f64 #s(literal -2 binary64) x)) y (.f64 x x)) (pow.f64 (.f64 #s(approx (+ ( 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (.f64 #s(approx (+ (* 2 x) y) (.f64 #s(literal -2 binary64) x)) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 x x (.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (.f64 #s(literal -2 binary64) x)))) #s(literal 3 binary64)) (pow.f64 (.f64 #s(approx (+ (* 2 x) y) (.f64 #s(literal -2 binary64) x)) y) #s(literal 6 binary64)))) (fma.f64 (fma.f64 #s(approx (+ ( 2 x) y) (.f64 #s(literal -2 binary64) x)) (.f64 y (.f64 (neg.f64 x) x)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (fma.f64 #s(approx (+ ( 2 x) y) (.f64 #s(literal -2 binary64) x)) (.f64 y (.f64 (neg.f64 x) x)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (.f64 #s(approx (+ (* 2 x) y) (.f64 #s(literal -2 binary64) x)) y) #s(literal 2 binary64))) (pow.f64 (.f64 #s(approx (+ (* 2 x) y) (*.f64 #s(literal -2 binary64) x)) y) #s(literal 4 binary64))))
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(.f64 (fma.f64 #s(approx (+ ( 2 x) y) (.f64 #s(literal -2 binary64) x)) y (.f64 x x)) (/.f64 (fma.f64 #s(approx (+ (* 2 x) y) (.f64 #s(literal -2 binary64) x)) y (.f64 (neg.f64 x) x)) (fma.f64 #s(approx (+ (* 2 x) y) (.f64 #s(literal -2 binary64) x)) y (.f64 (neg.f64 x) x))))
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(.f64 (.f64 #s(literal -2 binary64) x) (*.f64 x x))
(.f64 (.f64 #s(literal -2 binary64) x) x)
(.f64 (.f64 #s(literal -2 binary64) x) #s(literal 2 binary64))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 4 binary64)))
(*.f64 (neg.f64 x) #s(literal 2 binary64))
(.f64 (.f64 x x) #s(literal 4 binary64))
(.f64 (.f64 x x) (*.f64 #s(literal -2 binary64) x))
(.f64 (.f64 x x) #s(literal 2 binary64))
(*.f64 x #s(literal -2 binary64))
(*.f64 x #s(literal 4 binary64))
(.f64 x (.f64 #s(literal -2 binary64) x))
(*.f64 x #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 #s(literal -2 binary64) x))
(*.f64 #s(literal 2 binary64) (neg.f64 x))
(.f64 #s(literal 2 binary64) (.f64 x x))
(*.f64 #s(literal 2 binary64) x)
(pow.f64 (exp.f64 (log.f64 (*.f64 #s(literal -2 binary64) x))) #s(literal 3 binary64))
(pow.f64 (*.f64 #s(literal -2 binary64) x) #s(literal 9 binary64))
(pow.f64 (*.f64 #s(literal -2 binary64) x) #s(literal 3/2 binary64))
(pow.f64 (*.f64 #s(literal -2 binary64) x) #s(literal 4 binary64))
(pow.f64 (*.f64 #s(literal -2 binary64) x) #s(literal 6 binary64))
(pow.f64 (*.f64 #s(literal -2 binary64) x) #s(literal 3 binary64))
(pow.f64 (*.f64 #s(literal -2 binary64) x) #s(literal 2 binary64))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (.f64 #s(literal 0 binary64) (.f64 #s(literal -2 binary64) x)) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (*.f64 #s(literal -2 binary64) x)) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (*.f64 #s(literal 0 binary64) x) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) x) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (.f64 #s(literal 2 binary64) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (.f64 x (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (.f64 (.f64 #s(literal -2 binary64) x) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (.f64 #s(literal 0 binary64) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 0 binary64)) (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (fabs.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (fabs.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 3 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x))
(neg.f64 (.f64 #s(literal 4 binary64) (.f64 (neg.f64 x) x)))
(neg.f64 (.f64 (.f64 (neg.f64 x) x) #s(literal 4 binary64)))
(neg.f64 (*.f64 #s(literal -2 binary64) x))
(fma.f64 (.f64 #s(literal 4 binary64) (neg.f64 x)) (neg.f64 x) (.f64 #s(literal -2 binary64) x))
(fma.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64)) (*.f64 #s(literal -2 binary64) x))
(fma.f64 (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) (*.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 (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 3/4 binary64)) (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 3/4 binary64)) (*.f64 #s(literal -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)
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 x x))
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)) (*.f64 #s(literal -2 binary64) x))
(fma.f64 (pow.f64 #s(literal 2 binary64) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)) (*.f64 #s(literal -2 binary64) x))
(fma.f64 #s(literal 64 binary64) (pow.f64 x #s(literal 6 binary64)) (*.f64 #s(literal -2 binary64) x))
(fma.f64 #s(literal 512 binary64) (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 3 binary64)) (*.f64 #s(literal -2 binary64) x))
(fma.f64 (pow.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 3 binary64)) #s(literal 512 binary64) (*.f64 #s(literal -2 binary64) x))
(fma.f64 #s(literal -2 binary64) x (*.f64 #s(literal -2 binary64) x))
(fma.f64 #s(literal 4 binary64) (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x))
(fma.f64 #s(literal 4 binary64) (.f64 x x) (.f64 #s(literal -2 binary64) x))
(fma.f64 #s(literal 4 binary64) x (*.f64 #s(literal -2 binary64) x))
(fma.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)) (*.f64 #s(literal -2 binary64) x))
(fma.f64 #s(literal 8 binary64) (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 8 binary64) (*.f64 #s(literal -2 binary64) x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 16 binary64) (*.f64 #s(literal -2 binary64) x))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 64 binary64) (*.f64 #s(literal -2 binary64) x))
(fma.f64 (.f64 #s(literal -2 binary64) x) #s(literal 4 binary64) (.f64 #s(literal -2 binary64) x))
(fma.f64 (.f64 #s(literal -2 binary64) x) #s(literal 8 binary64) (.f64 #s(literal -2 binary64) x))
(fma.f64 (.f64 #s(literal -2 binary64) x) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal -2 binary64) x))
(fma.f64 (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x) (*.f64 #s(literal -2 binary64) x))
(fma.f64 (.f64 #s(literal -2 binary64) x) (.f64 x x) (*.f64 #s(literal -2 binary64) x))
(fma.f64 (.f64 #s(literal -2 binary64) x) x (.f64 #s(literal -2 binary64) x))
(fma.f64 (.f64 #s(literal -2 binary64) x) #s(literal 2 binary64) (.f64 #s(literal -2 binary64) x))
(fma.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 4 binary64)) (.f64 #s(literal -2 binary64) x))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 x x))
(fma.f64 (neg.f64 x) #s(literal 2 binary64) (*.f64 #s(literal -2 binary64) x))
(fma.f64 (.f64 x x) #s(literal 4 binary64) (.f64 #s(literal -2 binary64) x))
(fma.f64 (.f64 x x) (.f64 #s(literal -2 binary64) x) (*.f64 #s(literal -2 binary64) x))
(fma.f64 (.f64 x x) #s(literal 2 binary64) (.f64 #s(literal -2 binary64) x))
(fma.f64 x #s(literal -2 binary64) (*.f64 #s(literal -2 binary64) x))
(fma.f64 x #s(literal 4 binary64) (*.f64 #s(literal -2 binary64) x))
(fma.f64 x (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x))
(fma.f64 x x (*.f64 x x))
(fma.f64 x #s(literal 2 binary64) (*.f64 #s(literal -2 binary64) x))
(fma.f64 #s(literal 2 binary64) (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x))
(fma.f64 #s(literal 2 binary64) (neg.f64 x) (*.f64 #s(literal -2 binary64) x))
(fma.f64 #s(literal 2 binary64) (.f64 x x) (.f64 #s(literal -2 binary64) x))
(fma.f64 #s(literal 2 binary64) x (*.f64 #s(literal -2 binary64) x))
(sqrt.f64 (*.f64 #s(literal -2 binary64) x))
(-.f64 (/.f64 (.f64 x x) #s(literal 0 binary64)) (/.f64 (.f64 x x) #s(literal 0 binary64)))
(-.f64 (.f64 #s(literal -2 binary64) x) (.f64 (neg.f64 x) (*.f64 #s(literal -2 binary64) x)))
(-.f64 (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x))
(fabs.f64 (*.f64 #s(literal -2 binary64) x))
(hypot.f64 (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)))
(hypot.f64 (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 3/4 binary64)))
(hypot.f64 (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)) (.f64 #s(literal -2 binary64) x))
(hypot.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)))
(hypot.f64 (pow.f64 x #s(literal 1/2 binary64)) (sqrt.f64 (neg.f64 x)))
(hypot.f64 (pow.f64 x #s(literal 1/2 binary64)) (sqrt.f64 x))
(hypot.f64 (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 3/4 binary64)) (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)))
(hypot.f64 (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 3/4 binary64)) (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 3/4 binary64)))
(hypot.f64 (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 3/4 binary64)) (.f64 #s(literal -2 binary64) x))
(hypot.f64 (sqrt.f64 (neg.f64 x)) (pow.f64 x #s(literal 1/2 binary64)))
(hypot.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)))
(hypot.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 x))
(hypot.f64 (sqrt.f64 x) (pow.f64 x #s(literal 1/2 binary64)))
(hypot.f64 (sqrt.f64 x) (sqrt.f64 (neg.f64 x)))
(hypot.f64 (sqrt.f64 x) (sqrt.f64 x))
(hypot.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(hypot.f64 (exp.f64 (log.f64 x)) (neg.f64 x))
(hypot.f64 (exp.f64 (log.f64 x)) x)
(hypot.f64 (.f64 #s(literal -2 binary64) x) (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 1 binary64)))
(hypot.f64 (.f64 #s(literal -2 binary64) x) (pow.f64 (.f64 #s(literal -2 binary64) x) #s(literal 3/4 binary64)))
(hypot.f64 (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x))
(hypot.f64 (neg.f64 x) (exp.f64 (log.f64 x)))
(hypot.f64 (neg.f64 x) (neg.f64 x))
(hypot.f64 (neg.f64 x) x)
(hypot.f64 x (exp.f64 (log.f64 x)))
(hypot.f64 x (neg.f64 x))
(hypot.f64 x x)
(exp.f64 (fma.f64 (log.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 3 binary64) (.f64 (log.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 3 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 3 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 #s(literal -2 binary64) x)) #s(literal 3 binary64)) #s(literal 3 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 3/2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 3 binary64)))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))))
(+.f64 (cosh.f64 (.f64 (log.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 3 binary64))) (sinh.f64 (.f64 (log.f64 (.f64 #s(literal -2 binary64) x)) #s(literal 3 binary64))))
(+.f64 (.f64 #s(literal -2 binary64) x) (.f64 #s(literal -2 binary64) x))
(+.f64 (neg.f64 x) (neg.f64 x))
(+.f64 (.f64 x x) (.f64 x x))
(+.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))))

eval48.0ms (1.2%)

Memory: 0.9MiB live, 82.5MiB allocated
Compiler: Compiled 8 251 to 834 computations (89.9% saved)

prune4.0ms (0.1%)

Memory

20.5MiB live, 20.5MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	261	1	262
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	262	3	265

Accuracy

100.0%

Counts

265 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.5%	(fma.f64 y #s(approx (+ (* 2 x) y) (+.f64 x x)) (*.f64 x x))
✓	100.0%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
✓	60.1%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Compiler

Compiled 52 to 32 computations (38.5% saved)

simplify26.0ms (0.7%)

Memory

-20.3MiB live, 19.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	31
0	13	31
1	26	31
2	64	31
3	107	31
4	142	31
5	156	31
6	170	31
7	172	31
0	172	29

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize21.0ms (0.5%)

Memory

25.0MiB live, 25.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 y #s(approx (+ (* 2 x) y) (+.f64 x x)) (*.f64 x x))
accuracy	0.0	(+.f64 x x)
accuracy	0.0	(*.f64 x x)
accuracy	33.75715232086045	#s(approx (+ (* 2 x) y) (+.f64 x x))

Samples

15.0ms

256×

valid

Compiler

Compiled 57 to 20 computations (64.9% saved)

Precisions

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

ival-mult: 5.0ms (60.4% of total)

ival-add: 3.0ms (36.3% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

3.6MiB live, 3.6MiB allocated

Counts

4 → 19

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((+ (* y (+ (* 2 x) y)) (* x x)) (+ (* 2 x) y) (+ x x) (* x x))
1.0ms	x	@	-inf	((+ (* y (+ (* 2 x) y)) (* x x)) (+ (* 2 x) y) (+ x x) (* x x))
0.0ms	x	@	0	((+ (* y (+ (* 2 x) y)) (* x x)) (+ (* 2 x) y) (+ x x) (* x x))
0.0ms	y	@	inf	((+ (* y (+ (* 2 x) y)) (* x x)) (+ (* 2 x) y) (+ x x) (* x x))
0.0ms	y	@	-inf	((+ (* y (+ (* 2 x) y)) (* x x)) (+ (* 2 x) y) (+ x x) (* x x))

simplify181.0ms (4.5%)

Memory

10.1MiB live, 163.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	186
1	211	176
2	726	168
3	3398	160
0	8176	150

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 18

Calls

Call 1

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

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

rewrite53.0ms (1.3%)

Memory

-10.4MiB live, 27.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
0	13	29
1	59	29
0	552	27

Stop Event

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

Counts

4 → 76

Calls

Call 1

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

Outputs
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 #s(approx (+ ( 2 x) y) (.f64 x #s(literal 2 binary64))) y) #s(literal 2 binary64))) (-.f64 (.f64 x x) (.f64 #s(approx (+ ( 2 x) y) (*.f64 x #s(literal 2 binary64))) y)))
(/.f64 (-.f64 (pow.f64 (.f64 #s(approx (+ ( 2 x) y) (.f64 x #s(literal 2 binary64))) y) #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 x) x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 #s(approx (+ ( 2 x) y) (.f64 x #s(literal 2 binary64))) y) #s(literal 2 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (.f64 #s(approx (+ ( 2 x) y) (.f64 x #s(literal 2 binary64))) y) (.f64 (neg.f64 x) x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(approx (+ ( 2 x) y) (.f64 x #s(literal 2 binary64))) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (fma.f64 #s(approx (+ ( 2 x) y) (.f64 x #s(literal 2 binary64))) y (.f64 (neg.f64 x) x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 #s(approx (+ ( 2 x) y) (.f64 x #s(literal 2 binary64))) y) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 x x) (.f64 #s(approx (+ (* 2 x) y) (.f64 x #s(literal 2 binary64))) y)) (pow.f64 (.f64 #s(approx (+ (* 2 x) y) (*.f64 x #s(literal 2 binary64))) y) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(approx (+ ( 2 x) y) (.f64 x #s(literal 2 binary64))) y) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(approx (+ ( 2 x) y) (.f64 x #s(literal 2 binary64))) y (.f64 (neg.f64 x) x)))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 #s(approx (+ ( 2 x) y) (.f64 x #s(literal 2 binary64))) y) #s(literal 3 binary64))) (+.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (pow.f64 (.f64 #s(approx (+ (* 2 x) y) (.f64 x #s(literal 2 binary64))) y) #s(literal 2 binary64)) (.f64 #s(approx (+ (* 2 x) y) (.f64 x #s(literal 2 binary64))) (.f64 y (*.f64 x x))))))
(/.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 #s(approx (+ ( 2 x) y) (.f64 x #s(literal 2 binary64))) y) #s(literal 3 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) (.f64 #s(approx (+ (* 2 x) y) (.f64 x #s(literal 2 binary64))) y)) (pow.f64 (.f64 #s(approx (+ (* 2 x) y) (*.f64 x #s(literal 2 binary64))) y) #s(literal 2 binary64))))
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) (.f64 #s(approx (+ ( 2 x) y) (*.f64 x #s(literal 2 binary64))) y))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (.f64 #s(approx (+ ( 2 x) y) (*.f64 x #s(literal 2 binary64))) y))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (.f64 #s(approx (+ ( 2 x) y) (*.f64 x #s(literal 2 binary64))) y))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (.f64 #s(approx (+ ( 2 x) y) (*.f64 x #s(literal 2 binary64))) y))
(fma.f64 (neg.f64 x) (neg.f64 x) (.f64 #s(approx (+ ( 2 x) y) (*.f64 x #s(literal 2 binary64))) y))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (.f64 #s(approx (+ ( 2 x) y) (*.f64 x #s(literal 2 binary64))) y))
(fma.f64 #s(approx (+ (* 2 x) y) (.f64 x #s(literal 2 binary64))) y (.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 #s(approx (+ (* 2 x) y) (.f64 x #s(literal 2 binary64))) y (.f64 x x))
(fma.f64 x x (.f64 #s(approx (+ ( 2 x) y) (*.f64 x #s(literal 2 binary64))) y))
(fma.f64 y #s(approx (+ (* 2 x) y) (.f64 x #s(literal 2 binary64))) (.f64 (neg.f64 (neg.f64 x)) x))
(fma.f64 y #s(approx (+ (* 2 x) y) (.f64 x #s(literal 2 binary64))) (.f64 x x))
(-.f64 (/.f64 (pow.f64 (.f64 #s(approx (+ ( 2 x) y) (.f64 x #s(literal 2 binary64))) y) #s(literal 2 binary64)) (fma.f64 #s(approx (+ ( 2 x) y) (.f64 x #s(literal 2 binary64))) y (.f64 (neg.f64 x) x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 #s(approx (+ (* 2 x) y) (.f64 x #s(literal 2 binary64))) y (.f64 (neg.f64 x) x))))
(-.f64 (.f64 #s(approx (+ ( 2 x) y) (.f64 x #s(literal 2 binary64))) y) (.f64 (neg.f64 (neg.f64 x)) (neg.f64 x)))
(-.f64 (.f64 #s(approx (+ ( 2 x) y) (.f64 x #s(literal 2 binary64))) y) (.f64 (neg.f64 (fabs.f64 x)) (fabs.f64 x)))
(-.f64 (.f64 #s(approx (+ ( 2 x) y) (.f64 x #s(literal 2 binary64))) y) (.f64 (neg.f64 x) x))
(-.f64 (.f64 x x) (.f64 (neg.f64 #s(approx (+ (* 2 x) y) (*.f64 x #s(literal 2 binary64)))) y))
(-.f64 (.f64 x x) (.f64 (neg.f64 y) #s(approx (+ (* 2 x) y) (*.f64 x #s(literal 2 binary64)))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(approx (+ ( 2 x) y) (.f64 x #s(literal 2 binary64))) y) #s(literal 3 binary64)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) (.f64 #s(approx (+ (* 2 x) y) (.f64 x #s(literal 2 binary64))) y)) (pow.f64 (.f64 #s(approx (+ (* 2 x) y) (.f64 x #s(literal 2 binary64))) y) #s(literal 2 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (.f64 x x) (-.f64 (.f64 x x) (.f64 #s(approx (+ (* 2 x) y) (.f64 x #s(literal 2 binary64))) y)) (pow.f64 (.f64 #s(approx (+ (* 2 x) y) (*.f64 x #s(literal 2 binary64))) y) #s(literal 2 binary64)))))
(+.f64 (.f64 #s(approx (+ ( 2 x) y) (.f64 x #s(literal 2 binary64))) y) (.f64 (neg.f64 (neg.f64 x)) x))
(+.f64 (.f64 #s(approx (+ ( 2 x) y) (.f64 x #s(literal 2 binary64))) y) (.f64 x x))
(+.f64 (.f64 x x) (.f64 #s(approx (+ (* 2 x) y) (*.f64 x #s(literal 2 binary64))) y))
#s(approx (+ (* 2 x) y) (*.f64 x #s(literal 2 binary64)))
(.f64 (.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64)) x)
(.f64 (.f64 (*.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64))
(.f64 (pow.f64 (.f64 x #s(literal 2 binary64)) #s(literal 3/2 binary64)) (pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 3/2 binary64)))
(.f64 (neg.f64 (.f64 x #s(literal 2 binary64))) (neg.f64 (*.f64 x #s(literal 2 binary64))))
(.f64 (fabs.f64 (.f64 x #s(literal 2 binary64))) (fabs.f64 (*.f64 x #s(literal 2 binary64))))
(.f64 #s(literal 4 binary64) (.f64 x x))
(*.f64 #s(literal 8 binary64) (pow.f64 x #s(literal 3 binary64)))
(*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 8 binary64))
(.f64 (.f64 x x) #s(literal 4 binary64))
(.f64 (.f64 x #s(literal 2 binary64)) (*.f64 x #s(literal 2 binary64)))
(.f64 x (.f64 #s(literal 2 binary64) (*.f64 x #s(literal 2 binary64))))
(*.f64 x #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 x (*.f64 x #s(literal 2 binary64))))
(*.f64 #s(literal 2 binary64) x)
(pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 3 binary64))
(pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (.f64 #s(literal 0 binary64) (.f64 x #s(literal 2 binary64))) #s(literal 0 binary64))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (*.f64 x #s(literal 2 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (.f64 (.f64 x #s(literal 2 binary64)) (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x x #s(literal 0 binary64)))
(/.f64 (neg.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (.f64 #s(literal 0 binary64) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (*.f64 #s(literal 0 binary64) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 0 binary64)) (*.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)))
(/.f64 (.f64 (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 (fma.f64 x x #s(literal 0 binary64)) (fma.f64 x x #s(literal 0 binary64))))
(/.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (pow.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 3 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x #s(literal 0 binary64)))
(fma.f64 (.f64 x #s(literal 2 binary64)) x (.f64 (*.f64 x #s(literal 2 binary64)) x))
(fma.f64 x (.f64 x #s(literal 2 binary64)) (.f64 x (*.f64 x #s(literal 2 binary64))))
(-.f64 (/.f64 (.f64 x x) #s(literal 0 binary64)) (/.f64 (.f64 x x) #s(literal 0 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 2 binary64))) #s(literal 3 binary64)))
(+.f64 (.f64 x (.f64 x #s(literal 2 binary64))) (.f64 x (.f64 x #s(literal 2 binary64))))
(+.f64 (.f64 (.f64 x #s(literal 2 binary64)) x) (.f64 (.f64 x #s(literal 2 binary64)) x))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 0 binary64))))
(+.f64 x x)
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 x x)
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval86.0ms (2.2%)

Memory: -17.4MiB live, 52.3MiB allocated
Compiler: Compiled 1 945 to 297 computations (84.7% saved)

prune7.0ms (0.2%)

Memory

-26.7MiB live, 8.7MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	91	3	94

Accuracy

100.0%

Counts

94 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	55.5%	(fma.f64 y #s(approx (+ (* 2 x) y) (+.f64 x x)) (*.f64 x x))
✓	100.0%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 (+.f64 y x) (+.f64 y x)))
✓	60.1%	#s(approx (+ (+ (* x x) (* (* x 2) y)) (* y y)) (*.f64 y y))

Compiler

Compiled 140 to 62 computations (55.7% saved)

regimes7.0ms (0.2%)

Memory

16.8MiB live, 16.8MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes6.0ms (0.2%)

Memory

17.5MiB live, 17.5MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 13 computations (13.3% saved)

regimes6.0ms (0.2%)

Memory

-18.7MiB live, 15.0MiB allocated

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 y y))

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

Calls

3 calls:

4.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))
1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
60.1%	1	`x`
60.1%	1	`y`
60.1%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 (.f64 x #s(literal 2 binary64)) y)) (.f64 y y))`

Compiler

Compiled 15 to 13 computations (13.3% saved)

simplify53.0ms (1.3%)

Memory

5.5MiB live, 42.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	17	47
1	40	43
2	128	43
3	336	43
4	660	43
5	1018	35
6	1502	35
7	3705	35
8	6002	35

Stop Event

1×	node limit

Calls

Call 1

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

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

soundness396.0ms (9.9%)

Memory

-2.9MiB live, 213.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	177
1	194	169
2	746	157
3	3571	149
0	8118	140
0	9	33
0	15	33
1	65	29
2	568	29
0	9286	26

Stop Event

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

Compiler

Compiled 79 to 36 computations (54.4% saved)

preprocess177.0ms (4.4%)

Memory: -7.1MiB live, 66.1MiB allocated
Compiler: Compiled 164 to 84 computations (48.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze0.0ms (0%)

sample857.0ms (21.5%)

explain179.0ms (4.5%)

preprocess163.0ms (4.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify67.0ms (1.7%)

localize44.0ms (1.1%)

series38.0ms (1%)

simplify179.0ms (4.5%)

rewrite187.0ms (4.7%)

eval66.0ms (1.6%)

prune4.0ms (0.1%)

simplify61.0ms (1.5%)

localize89.0ms (2.2%)

series10.0ms (0.3%)

simplify200.0ms (5%)

rewrite163.0ms (4.1%)

eval84.0ms (2.1%)

prune38.0ms (1%)

simplify6.0ms (0.2%)

localize24.0ms (0.6%)

series3.0ms (0.1%)

simplify290.0ms (7.3%)

rewrite156.0ms (3.9%)

eval48.0ms (1.2%)

prune4.0ms (0.1%)

simplify26.0ms (0.7%)

localize21.0ms (0.5%)

series3.0ms (0.1%)

simplify181.0ms (4.5%)

rewrite53.0ms (1.3%)

eval86.0ms (2.2%)

prune7.0ms (0.2%)

regimes7.0ms (0.2%)

regimes6.0ms (0.2%)

regimes6.0ms (0.2%)

simplify53.0ms (1.3%)

soundness396.0ms (9.9%)

preprocess177.0ms (4.4%)

end0.0ms (0%)

Profiling