Metrics for Data.Random.Distribution.Normal:normalTail from random-fu-0.2.6.2

analyze0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample699.0ms (23.9%)

Memory

24.7MiB live, 844.9MiB allocated

Samples

426.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 171.0ms

ival-add: 101.0ms (59.1% of total)

ival-mult: 62.0ms (36.3% of total)

ival-true: 6.0ms (3.5% of total)

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

Bogosity

preprocess34.0ms (1.2%)

Memory

5.0MiB live, 42.6MiB allocated

Algorithm

1×	egg-herbie

Rules

118×	`sub-neg`
108×	`unsub-neg`
72×	`associate-+l-`
64×	`distribute-rgt-in`
58×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	37
1	50	36
2	151	35
3	358	35
4	529	35
5	663	35
6	687	35
0	5	7
0	8	7
1	12	7
2	15	7
3	16	7
0	16	6

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

explain73.0ms (2.5%)

Memory

12.0MiB live, 98.4MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(+.f64 (*.f64 x x) y)`
-	-	`(+.f64 (+.f64 (*.f64 x x) y) y)`
-	-	`y`
-	-	`(*.f64 x x)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

20.0ms

512×

valid

Compiler

Compiled 56 to 24 computations (57.1% saved)

Precisions

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

ival-add: 4.0ms (46.9% of total)

ival-mult: 4.0ms (46.9% of total)

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

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

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)

Compiler

Compiled 9 to 5 computations (44.4% saved)

simplify5.0ms (0.2%)

Memory

4.4MiB live, 4.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	cost-diff	128	(+.f64 (*.f64 x x) y)

Rules

14×	`lower-+.f32`
10×	`lower-+.f64`
8×	`lower-fma.f64`
8×	`lower-fma.f32`
6×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	17
0	8	17
1	12	17
2	15	17
3	16	17
0	16	15

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize27.0ms (0.9%)

Memory

-19.9MiB live, 17.6MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	accuracy	100.0%	(+.f64 (*.f64 x x) y)

Samples

21.0ms

256×

valid

Compiler

Compiled 19 to 7 computations (63.2% saved)

Precisions

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

ival-add: 2.0ms (47.9% of total)

ival-mult: 2.0ms (47.9% of total)

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

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

series3.0ms (0.1%)

Memory

3.1MiB live, 3.1MiB allocated

Counts

3 → 60

Calls

Call 1

Inputs
#<alt (+.f64 (*.f64 x x) y)>
#<alt (+.f64 (+.f64 (*.f64 x x) y) y)>
#<alt (*.f64 x x)>

Outputs
#<alt y>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt y>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* 2 y)>
#<alt (+ (* 2 y) (pow x 2))>
#<alt (+ (* 2 y) (pow x 2))>
#<alt (+ (* 2 y) (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))>
#<alt (pow x 2)>
#<alt (+ (* 2 y) (pow x 2))>
#<alt (+ (* 2 y) (pow x 2))>
#<alt (+ (* 2 y) (pow x 2))>
#<alt (* 2 y)>
#<alt (* y (+ 2 (/ (pow x 2) y)))>
#<alt (* y (+ 2 (/ (pow x 2) y)))>
#<alt (* y (+ 2 (/ (pow x 2) y)))>
#<alt (* 2 y)>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

15 calls:

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

rewrite428.0ms (14.6%)

Memory

9.8MiB live, 324.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 306×	`lower-fma.f64`
7 306×	`lower-fma.f32`
4 782×	`lower-*.f32`
4 780×	`lower-*.f64`
2 300×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	37	15
2	316	15
3	4987	15
0	8103	13

Stop Event

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

Counts

3 → 251

Calls

Call 1

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

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

simplify206.0ms (7.1%)

Memory

-9.5MiB live, 266.5MiB allocated

Algorithm

1×	egg-herbie

Rules

4 558×	`lower-fma.f64`
4 558×	`lower-fma.f32`
3 232×	`lower-*.f64`
3 232×	`lower-*.f32`
1 326×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	282
1	80	282
2	193	282
3	655	282
4	1935	282
5	3634	282
6	6739	282
0	8124	246

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 57

Calls

Call 1

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

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

eval37.0ms (1.3%)

Memory: 27.0MiB live, 102.1MiB allocated
Compiler: Compiled 8 832 to 700 computations (92.1% saved)

prune38.0ms (1.3%)

Memory

-0.3MiB live, 82.0MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	304	4	308
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	305	4	309

Accuracy

100.0%

Counts

309 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 x x (+.f64 y y))
▶	57.3%	(+.f64 (*.f64 x x) y)
▶	53.4%	(*.f64 y #s(literal 2 binary64))
▶	49.4%	(*.f64 x x)

Compiler

Compiled 25 to 15 computations (40% saved)

simplify6.0ms (0.2%)

Memory

-29.3MiB live, 10.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 y y)
✓	cost-diff	0	(fma.f64 x x (+.f64 y y))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	128	(+.f64 (*.f64 x x) y)
✓	cost-diff	128	(*.f64 y #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 x x)

Rules

14×	`lower-+.f32`
10×	`lower-+.f64`
8×	`lower-fma.f32`
6×	`lower-fma.f64`
6×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	30
0	13	30
1	17	30
2	18	30
0	18	29

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize25.0ms (0.9%)

Memory

10.6MiB live, 49.6MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x x (+.f64 y y))
✓	accuracy	100.0%	(+.f64 y y)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (*.f64 x x) y)
✓	accuracy	100.0%	(*.f64 y #s(literal 2 binary64))
✓	accuracy	100.0%	(*.f64 x x)

Samples

15.0ms

256×

valid

Compiler

Compiled 33 to 10 computations (69.7% saved)

Precisions

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

ival-add: 3.0ms (43.3% of total)

ival-mult: 3.0ms (43.3% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Memory

4.5MiB live, 4.5MiB allocated

Counts

5 → 84

Calls

Call 1

Inputs
#<alt (*.f64 x x)>
#<alt (*.f64 y #s(literal 2 binary64))>
#<alt (+.f64 (*.f64 x x) y)>
#<alt (fma.f64 x x (+.f64 y y))>
#<alt (+.f64 y y)>

Outputs
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt y>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt y>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* 2 y)>
#<alt (+ (* 2 y) (pow x 2))>
#<alt (+ (* 2 y) (pow x 2))>
#<alt (+ (* 2 y) (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))>
#<alt (pow x 2)>
#<alt (+ (* 2 y) (pow x 2))>
#<alt (+ (* 2 y) (pow x 2))>
#<alt (+ (* 2 y) (pow x 2))>
#<alt (* 2 y)>
#<alt (* y (+ 2 (/ (pow x 2) y)))>
#<alt (* y (+ 2 (/ (pow x 2) y)))>
#<alt (* y (+ 2 (/ (pow x 2) y)))>
#<alt (* 2 y)>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>

Calls

21 calls:

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

rewrite65.0ms (2.2%)

Memory

-12.8MiB live, 78.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

398×	`lower-fma.f32`
396×	`lower-fma.f64`
192×	`lower-*.f32`
188×	`lower-*.f64`
144×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
0	13	20
1	47	20
0	428	19

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

5 → 124

Calls

Call 1

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

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

simplify257.0ms (8.8%)

Memory

-2.0MiB live, 312.9MiB allocated

Algorithm

1×	egg-herbie

Rules

4 558×	`lower-fma.f64`
4 558×	`lower-fma.f32`
3 232×	`lower-*.f64`
3 232×	`lower-*.f32`
1 326×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	354
1	80	354
2	193	354
3	649	354
4	1927	354
5	3639	354
6	6734	354
0	8117	318

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 81

Calls

Call 1

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

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

eval108.0ms (3.7%)

Memory: 12.0MiB live, 50.3MiB allocated
Compiler: Compiled 2 120 to 217 computations (89.8% saved)

prune18.0ms (0.6%)

Memory

1.2MiB live, 40.0MiB allocated

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	219	2	221
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	220	5	225

Accuracy

100.0%

Counts

225 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x x (+.f64 y y))
▶	57.3%	(fma.f64 x x y)
✓	57.3%	(+.f64 (*.f64 x x) y)
▶	53.4%	(+.f64 y y)
✓	49.4%	(*.f64 x x)

Compiler

Compiled 31 to 17 computations (45.2% saved)

simplify5.0ms (0.2%)

Memory

12.0MiB live, 12.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 x x y)
✓	cost-diff	0	(+.f64 y y)

Rules

6×	`lower-*.f64`
6×	`lower-*.f32`
6×	`lower-+.f32`
4×	`lower-+.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	7	10
1	10	10
2	11	10
0	11	10

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(+.f64 y y)
y
(fma.f64 x x y)
x
y

Outputs
(+.f64 y y)
y
(fma.f64 x x y)
x
y

localize16.0ms (0.6%)

Memory

3.7MiB live, 42.3MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x x y)
✓	accuracy	100.0%	(+.f64 y y)

Samples

11.0ms

256×

valid

Compiler

Compiled 13 to 7 computations (46.2% saved)

Precisions

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

ival-add: 3.0ms (56.1% of total)

ival-mult: 2.0ms (37.4% of total)

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

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

series0.0ms (0%)

Memory

1.3MiB live, 1.2MiB allocated

Counts

2 → 36

Calls

Call 1

Inputs
#<alt (+.f64 y y)>
#<alt (fma.f64 x x y)>

Outputs
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt y>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt y>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>

Calls

9 calls:

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

rewrite38.0ms (1.3%)

Memory

-14.4MiB live, 66.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

94×	`lower-fma.f32`
92×	`lower-*.f64`
92×	`lower-*.f32`
92×	`lower-fma.f64`
74×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
0	7	7
1	30	7
0	221	7

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

2 → 26

Calls

Call 1

Inputs
(+.f64 y y)
(fma.f64 x x y)

Outputs
(+.f64 y y)
(-.f64 (/.f64 (.f64 y y) #s(literal 0 binary64)) (/.f64 (.f64 y y) #s(literal 0 binary64)))
(/.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal 0 binary64) #s(literal 0 binary64))
(/.f64 (neg.f64 (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(/.f64 #s(literal 1 binary64) (+.f64 y y))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y))))
(*.f64 y #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) y)
(.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (+.f64 y y)) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(*.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) #s(literal 0 binary64)))
(+.f64 y (*.f64 x x))
(+.f64 (*.f64 x x) y)
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) y)) (/.f64 (.f64 y y) (-.f64 (.f64 x x) y)))
(fma.f64 x x y)
(fma.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)) y)
(/.f64 (fma.f64 y (.f64 y y) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (fma.f64 y (-.f64 y (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))))
(/.f64 (fma.f64 y (.f64 y y) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (fma.f64 y y (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y (*.f64 x x)))))
(/.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)) (-.f64 (*.f64 x x) y))
(/.f64 (neg.f64 (fma.f64 y (.f64 y y) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (fma.f64 y (-.f64 y (.f64 x x)) (.f64 x (.f64 x (.f64 x x))))))
(/.f64 (neg.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y))) (neg.f64 (-.f64 (*.f64 x x) y)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y (-.f64 y (.f64 x x)) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 y (.f64 y y) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 x x) y) (.f64 (fma.f64 x x y) (-.f64 (*.f64 x x) y))))
(/.f64 (-.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x)))) (-.f64 y (*.f64 x x)))
(.f64 (fma.f64 y (.f64 y y) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (fma.f64 y (-.f64 y (.f64 x x)) (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (.f64 (fma.f64 x x y) (-.f64 (.f64 x x) y)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) y)))

simplify240.0ms (8.2%)

Memory

-17.8MiB live, 321.7MiB allocated

Algorithm

1×	egg-herbie

Rules

3 894×	`lower-*.f64`
3 894×	`lower-*.f32`
3 312×	`lower-fma.f64`
3 312×	`lower-fma.f32`
2 140×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	138
1	50	138
2	112	138
3	379	138
4	1171	138
5	2511	138
6	4840	138
7	6269	138
0	8021	120

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 33

Calls

Call 1

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

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

eval18.0ms (0.6%)

Memory: -19.4MiB live, 18.7MiB allocated
Compiler: Compiled 505 to 64 computations (87.3% saved)

prune5.0ms (0.2%)

Memory

13.7MiB live, 13.7MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	0	0
Picked	0	2	2
Done	0	3	3
Total	59	5	64

Accuracy

100.0%

Counts

64 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x x (+.f64 y y))
✓	57.3%	(fma.f64 x x y)
✓	57.3%	(+.f64 (*.f64 x x) y)
✓	53.4%	(+.f64 y y)
✓	49.4%	(*.f64 x x)

Compiler

Compiled 64 to 27 computations (57.8% saved)

regimes14.0ms (0.5%)

Memory

-12.6MiB live, 26.3MiB allocated

Counts

7 → 1

Calls

Call 1

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

Outputs
(fma.f64 x x (+.f64 y y))

Calls

4 calls:

5.0ms	x
3.0ms	(+.f64 (+.f64 (*.f64 x x) y) y)
3.0ms	y
3.0ms	(*.f64 x x)

Results

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

Compiler

Compiled 20 to 12 computations (40% saved)

regimes10.0ms (0.3%)

Memory

31.1MiB live, 31.1MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
89.5%	2	`x`
74.2%	3	`y`
84.0%	2	`(+.f64 (+.f64 (*.f64 x x) y) y)`
89.5%	2	`(*.f64 x x)`

Compiler

Compiled 20 to 12 computations (40% saved)

regimes11.0ms (0.4%)

Memory

-31.5MiB live, 10.4MiB allocated

Counts

4 → 2

Calls

Call 1

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

Outputs
(+.f64 y y)
(fma.f64 x x y)

Calls

2 calls:

9.0ms	x
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
89.5%	2	`x`
89.5%	2	`(*.f64 x x)`

Compiler

Compiled 8 to 5 computations (37.5% saved)

regimes4.0ms (0.1%)

Memory

6.2MiB live, 6.2MiB allocated

Counts

3 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
88.1%	2	`x`
88.1%	2	`(*.f64 x x)`

Compiler

Compiled 8 to 5 computations (37.5% saved)

regimes5.0ms (0.2%)

Memory

14.3MiB live, 14.3MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(+.f64 y y)

Outputs
(+.f64 y y)

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
53.4%	1	`y`
53.4%	1	`(+.f64 (+.f64 (*.f64 x x) y) y)`
53.4%	1	`x`
53.4%	1	`(*.f64 x x)`

Compiler

Compiled 20 to 12 computations (40% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	9.807326691481363e-83	1.1177607331551905e-72

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	9.807326691481363e-83	1.1177607331551905e-72

Compiler

Compiled 12 to 10 computations (16.7% saved)

bsearch13.0ms (0.4%)

Memory

-13.7MiB live, 25.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	2.8981183430437604e-36	5.281115148715488e-27

Samples

7.0ms

144×

valid

Compiler

Compiled 102 to 73 computations (28.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-add: 1.0ms (64.5% of total)

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

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

simplify7.0ms (0.2%)

Memory

19.9MiB live, 19.9MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	48
1	15	48

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 x x (+.f64 y y))
(if (<=.f64 (.f64 x x) #s(literal 213598703592091/2135987035920910082395021706169552114602704522356652769947041607822219725780640550022962086936576 binary64)) (+.f64 y y) (+.f64 (.f64 x x) y))
(if (<=.f64 (*.f64 x x) #s(literal 213598703592091/2135987035920910082395021706169552114602704522356652769947041607822219725780640550022962086936576 binary64)) (+.f64 y y) (fma.f64 x x y))
(if (<=.f64 (.f64 x x) #s(literal 8622859660252327/2923003274661805836407369665432566039311865085952 binary64)) (+.f64 y y) (.f64 x x))
(+.f64 y y)

Outputs
(fma.f64 x x (+.f64 y y))
(if (<=.f64 (.f64 x x) #s(literal 213598703592091/2135987035920910082395021706169552114602704522356652769947041607822219725780640550022962086936576 binary64)) (+.f64 y y) (+.f64 (.f64 x x) y))
(if (<=.f64 (.f64 x x) #s(literal 213598703592091/2135987035920910082395021706169552114602704522356652769947041607822219725780640550022962086936576 binary64)) (+.f64 y y) (+.f64 y (.f64 x x)))
(if (<=.f64 (*.f64 x x) #s(literal 213598703592091/2135987035920910082395021706169552114602704522356652769947041607822219725780640550022962086936576 binary64)) (+.f64 y y) (fma.f64 x x y))
(if (<=.f64 (.f64 x x) #s(literal 8622859660252327/2923003274661805836407369665432566039311865085952 binary64)) (+.f64 y y) (.f64 x x))
(+.f64 y y)

soundness444.0ms (15.2%)

Memory

-10.7MiB live, 347.6MiB allocated

Rules

7 306×	`lower-fma.f64`
7 306×	`lower-fma.f32`
4 782×	`lower-*.f32`
4 780×	`lower-*.f64`
4 558×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	282
1	80	282
2	193	282
3	655	282
4	1935	282
5	3634	282
6	6739	282
0	8124	246
0	8	20
0	13	20
1	47	20
0	428	19
0	5	15
0	8	15
1	37	15
2	316	15
3	4987	15
0	8103	13

Stop Event

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

Compiler

Compiled 123 to 60 computations (51.2% saved)

preprocess57.0ms (1.9%)

Memory: -3.3MiB live, 194.4MiB allocated
Remove: (abs x)
Compiler: Compiled 152 to 56 computations (63.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	15	37
1	50	36
2	151	35
3	358	35
4	529	35
5	663	35
6	687	35
0	5	7
0	8	7
1	12	7
2	15	7
3	16	7
0	16	6

Iter	Nodes	Cost
0	15	37
1	50	36
2	151	35
3	358	35
4	529	35
5	663	35
6	687	35
0	5	7
0	8	7
1	12	7
2	15	7
3	16	7
0	16	6

analyze0.0ms (0%)

sample699.0ms (23.9%)

preprocess34.0ms (1.2%)

explain73.0ms (2.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.2%)

localize27.0ms (0.9%)

series3.0ms (0.1%)

rewrite428.0ms (14.6%)

simplify206.0ms (7.1%)

eval37.0ms (1.3%)

prune38.0ms (1.3%)

simplify6.0ms (0.2%)

localize25.0ms (0.9%)

series2.0ms (0.1%)

rewrite65.0ms (2.2%)

simplify257.0ms (8.8%)

eval108.0ms (3.7%)

prune18.0ms (0.6%)

simplify5.0ms (0.2%)

localize16.0ms (0.6%)

series0.0ms (0%)

rewrite38.0ms (1.3%)

simplify240.0ms (8.2%)

eval18.0ms (0.6%)

prune5.0ms (0.2%)

regimes14.0ms (0.5%)

regimes10.0ms (0.3%)

regimes11.0ms (0.4%)

regimes4.0ms (0.1%)

regimes5.0ms (0.2%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch13.0ms (0.4%)

simplify7.0ms (0.2%)

soundness444.0ms (15.2%)

preprocess57.0ms (1.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	15	37
1	50	36
2	151	35
3	358	35
4	529	35
5	663	35
6	687	35
0	5	7
0	8	7
1	12	7
2	15	7
3	16	7
0	16	6