Metrics for Numeric.Log:$clog1p from log-domain-0.10.2.1, A

analyze0.0ms (0%)

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 14 to 9 computations (35.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample999.0ms (23%)

Results

759.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 398.0ms

ival-mult: 280.0ms (70.3% of total)

ival-add: 105.0ms (26.4% of total)

const: 10.0ms (2.5% of total)

backward-pass: 3.0ms (0.8% of total)

Bogosity

preprocess91.0ms (2.1%)

Algorithm

2×	egg-herbie

Rules

1964×	`fnmadd-define`
1872×	`sum5-define`
1556×	`sum4-define`
1472×	`fmsub-define`
1444×	`fnmsub-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	52
1	81	46
2	286	42
3	1057	42
4	3491	42
5	6230	42
6	7472	42
7	7545	42
0	8	8
1	19	7
2	37	7
3	48	7
4	49	7
0	49	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(+ (+ (* x 2) (* x x)) (* y y))

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

Call 2

Inputs
(+ (+ (* x 2) (* x x)) (* y y))
(+ (+ (* (neg x) 2) (* (neg x) (neg x))) (* y y))
(+ (+ (* x 2) (* x x)) (* (neg y) (neg y)))
(neg (+ (+ (* (neg x) 2) (* (neg x) (neg x))) (* y y)))
(neg (+ (+ (* x 2) (* x x)) (* (neg y) (neg y))))
(+ (+ (* y 2) (* y y)) (* x x))

Outputs
(+ (+ (* x 2) (* x x)) (* y y))
(fma x (+ x 2) (square y))
(+ (+ (* (neg x) 2) (* (neg x) (neg x))) (* y y))
(fma x (+ x -2) (square y))
(+ (+ (* x 2) (* x x)) (* (neg y) (neg y)))
(fma x (+ x 2) (square y))
(neg (+ (+ (* (neg x) 2) (* (neg x) (neg x))) (* y y)))
(fnmsub x (+ x -2) (square y))
(neg (+ (+ (* x 2) (* x x)) (* (neg y) (neg y))))
(fnmsub x (+ x 2) (square y))
(+ (+ (* y 2) (* y y)) (* x x))
(fma y (+ 2 y) (square x))

Symmetry

(abs y)

explain89.0ms (2.1%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`x`
-	-	`(*.f64 x x)`
-	-	`(*.f64 y y)`
-	-	`(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))`
-	-	`(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))`
-	-	`(*.f64 x #s(literal 2 binary64))`
-	-	`#s(literal 2 binary64)`
-	-	`y`

Results

58.0ms

512×

valid

Compiler

Compiled 79 to 26 computations (67.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-mult: 13.0ms (67.6% of total)

ival-add: 5.0ms (26% of total)

const: 1.0ms (5.2% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) (.f64 y y))

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

30×	`fma-define`
28×	`fma-lowering-fma.f32`
28×	`+-lowering-+.f64`
28×	`+-lowering-+.f32`
28×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	17	20
2	33	20
3	47	20
4	54	20
0	54	20

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* x (+ x 2)) (* y y))
(* x (+ x 2))
x
(+ x 2)
2
(* y y)
y

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

localize33.0ms (0.8%)

Localize:

Found 4 expressions of interest:

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

Results

25.0ms

256×

valid

Compiler

Compiled 26 to 8 computations (69.2% saved)

Precisions

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

ival-mult: 4.0ms (57.5% of total)

ival-add: 3.0ms (43.1% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series3.0ms (0.1%)

Counts

4 → 60

Calls

Call 1

Inputs
#<alt (+ (* x (+ x 2)) (* y y))>
#<alt (* x (+ x 2))>
#<alt (+ x 2)>
#<alt (* y y)>

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

Calls

15 calls:

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

rewrite285.0ms (6.6%)

Algorithm

1×	batch-egg-rewrite

Rules

2574×	`-lowering-.f32`
2574×	`-lowering-.f64`
1952×	`sum5-define`
1950×	`fma-lowering-fma.f32`
1950×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	43	17
2	373	17
3	4650	17
0	8798	17

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 181

Calls

Call 1

Inputs
(+ (* x (+ x 2)) (* y y))
(* x (+ x 2))
(+ x 2)
(* y y)

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

simplify147.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

2330×	`-lowering-.f32`
2330×	`-lowering-.f64`
1684×	`fnmadd-define`
1592×	`times-frac`
972×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	324
1	104	277
2	303	241
3	1132	241
4	3912	241
0	8552	241

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

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

eval31.0ms (0.7%)

Compiler: Compiled 7240 to 643 computations (91.1% saved)

prune29.0ms (0.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	235	6	241
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	236	6	242

Accuracy

100.0%

Counts

242 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 y y (*.f64 x (+.f64 x #s(literal 2 binary64))))
	68.1%	(+.f64 (.f64 y y) (.f64 #s(literal 2 binary64) x))
▶	83.5%	(+.f64 (.f64 x x) (.f64 y y))
▶	52.1%	(*.f64 y y)
▶	54.7%	(*.f64 x (+.f64 #s(literal 2 binary64) x))
▶	39.0%	(*.f64 x x)

Compiler

Compiled 90 to 56 computations (37.8% saved)

simplify32.0ms (0.7%)

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 y y)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(+.f64 (.f64 x x) (.f64 y y))
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) x)
✓	cost-diff	0	(*.f64 x (+.f64 #s(literal 2 binary64) x))
✓	cost-diff	0	(*.f64 y y)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(+.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 x (+.f64 x #s(literal 2 binary64)))
✓	cost-diff	6272	(fma.f64 y y (*.f64 x (+.f64 x #s(literal 2 binary64))))

Rules

30×	`fma-define`
28×	`fma-lowering-fma.f32`
28×	`+-lowering-+.f64`
28×	`+-lowering-+.f32`
28×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	46
1	24	45
2	47	45
3	58	45
4	59	45
0	59	45

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* y y) (* x (+ x 2)))
y
(* x (+ x 2))
x
(+ x 2)
2
(* x x)
x
(* y y)
y
(* x (+ 2 x))
x
(+ 2 x)
2
(+ (* x x) (* y y))
(* x x)
x
(* y y)
y

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

localize89.0ms (2.1%)

Localize:

Found 10 expressions of interest:

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

Results

73.0ms

256×

valid

Compiler

Compiled 55 to 12 computations (78.2% saved)

Precisions

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

ival-mult: 14.0ms (59.7% of total)

ival-add: 5.0ms (21.3% of total)

compiled-spec: 4.0ms (17.1% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series2.0ms (0.1%)

Counts

8 → 120

Calls

Call 1

Inputs
#<alt (+ (* y y) (* x (+ x 2)))>
#<alt (* x (+ x 2))>
#<alt (+ x 2)>
#<alt (* x x)>
#<alt (* y y)>
#<alt (* x (+ 2 x))>
#<alt (+ 2 x)>
#<alt (+ (* x x) (* y y))>

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

Calls

30 calls:

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

rewrite332.0ms (7.7%)

Algorithm

1×	batch-egg-rewrite

Rules

4916×	`-lowering-.f32`
4916×	`-lowering-.f64`
4078×	`/-lowering-/.f32`
4078×	`/-lowering-/.f64`
1868×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	33
1	68	32
2	653	32
0	8561	32

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 484

Calls

Call 1

Inputs
(+ (* y y) (* x (+ x 2)))
(* x (+ x 2))
(+ x 2)
(* x x)
(* y y)
(* x (+ 2 x))
(+ 2 x)
(+ (* x x) (* y y))

Outputs
(+.f64 (.f64 y y) (.f64 x (+.f64 x #s(literal 2 binary64))))
(+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) (.f64 y y))
(+.f64 (.f64 x x) (+.f64 (.f64 y y) (*.f64 x #s(literal 2 binary64))))
(+.f64 (.f64 x x) (+.f64 (.f64 x #s(literal 2 binary64)) (*.f64 y y)))
(+.f64 (+.f64 (.f64 y y) (.f64 x x)) (*.f64 x #s(literal 2 binary64)))
(+.f64 (.f64 x #s(literal 2 binary64)) (+.f64 (.f64 y y) (*.f64 x x)))
(+.f64 (/.f64 (.f64 (.f64 y y) (.f64 y y)) (-.f64 (.f64 y y) (.f64 x (+.f64 x #s(literal 2 binary64))))) (neg.f64 (/.f64 (.f64 x (.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) (+.f64 x #s(literal 2 binary64)))) (-.f64 (.f64 y y) (.f64 x (+.f64 x #s(literal 2 binary64)))))))
(+.f64 (+.f64 (.f64 y y) (.f64 x #s(literal 2 binary64))) (*.f64 x x))
(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 y y)) (*.f64 x x))
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simplify191.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

2198×	`-lowering-.f32`
2198×	`-lowering-.f64`
2092×	`fma-define`
1576×	`fma-lowering-fma.f32`
1576×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	540
1	123	449
2	356	449
3	1278	449
4	3311	449
5	7337	449
0	8471	449

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

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

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

eval120.0ms (2.8%)

Compiler: Compiled 15649 to 1082 computations (93.1% saved)

prune68.0ms (1.6%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	637	3	640
Fresh	1	0	1
Picked	1	4	5
Done	0	0	0
Total	639	7	646

Accuracy

100.0%

Counts

646 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.1%	(fma.f64 y y (*.f64 x #s(literal 2 binary64)))
▶	68.1%	(+.f64 (.f64 y y) (.f64 x #s(literal 2 binary64)))
✓	83.5%	(+.f64 (.f64 x x) (.f64 y y))
✓	52.1%	(*.f64 y y)
✓	54.7%	(*.f64 x (+.f64 #s(literal 2 binary64) x))
✓	39.0%	(*.f64 x x)
▶	18.6%	(*.f64 x #s(literal 2 binary64))

Compiler

Compiled 48 to 31 computations (35.4% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x #s(literal 2 binary64))
✓	cost-diff	6272	(fma.f64 y y (*.f64 x #s(literal 2 binary64)))
✓	cost-diff	0	(*.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(*.f64 y y)
✓	cost-diff	0	(+.f64 (.f64 y y) (.f64 x #s(literal 2 binary64)))
✓	cost-diff	0	(*.f64 x #s(literal 2 binary64))

Rules

6×	`fma-lowering-fma.f32`
6×	`fma-define`
6×	`-lowering-.f32`
6×	`-lowering-.f64`
6×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	31
1	10	29
2	12	29
0	12	29

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* x 2)
x
2
(+ (* y y) (* x 2))
(* y y)
y
(* x 2)
x
2
(+ (* y y) (* x 2))
y
(* x 2)
x
2

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

localize50.0ms (1.1%)

Localize:

Found 6 expressions of interest:

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

Results

37.0ms

256×

valid

Compiler

Compiled 36 to 8 computations (77.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-mult: 6.0ms (49.4% of total)

compiled-spec: 3.0ms (24.7% of total)

ival-add: 2.0ms (16.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series3.0ms (0.1%)

Counts

4 → 72

Calls

Call 1

Inputs
#<alt (* x 2)>
#<alt (+ (* y y) (* x 2))>
#<alt (* y y)>
#<alt (+ (* y y) (* x 2))>

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

Calls

18 calls:

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

rewrite278.0ms (6.4%)

Algorithm

1×	batch-egg-rewrite

Rules

2464×	`-lowering-.f32`
2464×	`-lowering-.f64`
2180×	`/-lowering-/.f32`
2180×	`/-lowering-/.f64`
1716×	`sum5-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	17
1	24	15
2	206	15
3	2351	15
0	8470	15

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 247

Calls

Call 1

Inputs
(* x 2)
(+ (* y y) (* x 2))
(* y y)
(+ (* y y) (* x 2))

Outputs
(exp.f64 (log.f64 (*.f64 x #s(literal 2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)))
(pow.f64 (*.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
(*.f64 x #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) x)
(*.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1 binary64)) #s(literal 2 binary64))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 #s(literal 2 binary64))))
(*.f64 (exp.f64 (log.f64 #s(literal 2 binary64))) (exp.f64 (log.f64 x)))
(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 y y))
(+.f64 (.f64 y y) (.f64 x #s(literal 2 binary64)))
(+.f64 (/.f64 (.f64 y (.f64 y (.f64 y y))) (+.f64 (.f64 y y) (.f64 x #s(literal -2 binary64)))) (neg.f64 (/.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (+.f64 (.f64 y y) (*.f64 x #s(literal -2 binary64))))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 2 binary64)) (*.f64 y y)))) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 y (.f64 y (.f64 y y))) (+.f64 (.f64 y y) (.f64 x #s(literal -2 binary64)))) (/.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (+.f64 (.f64 y y) (*.f64 x #s(literal -2 binary64)))))
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(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 y y))) #s(literal 1 binary64)) #s(literal -1 binary64))
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(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y y) (.f64 x #s(literal -2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 x (.f64 x #s(literal 4 binary64))))) #s(literal -1 binary64)))
(.f64 (-.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (.f64 y (.f64 y (.f64 y y)))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x #s(literal 2 binary64)) (.f64 y y))))
(.f64 (/.f64 (-.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 x (.f64 x #s(literal 4 binary64)))) (-.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 x (.f64 x #s(literal 4 binary64))))) (+.f64 (.f64 x #s(literal 2 binary64)) (*.f64 y y)))
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(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (.f64 (.f64 y y) (+.f64 (.f64 y y) (.f64 x #s(literal -2 binary64))))) (+.f64 (.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) (.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 512 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (-.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 x (.f64 x #s(literal 4 binary64))) (.f64 (.f64 y y) (+.f64 (.f64 y y) (.f64 x #s(literal -2 binary64))))) (-.f64 (.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 64 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y))) (.f64 (.f64 x (.f64 x x)) #s(literal -8 binary64)))))

simplify185.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

2194×	`/-lowering-/.f32`
2194×	`/-lowering-/.f64`
1946×	`-lowering-.f32`
1946×	`-lowering-.f64`
1074×	`distribute-frac-neg2`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	324
1	56	270
2	147	270
3	480	270
4	1527	270
5	4016	270
0	8192	270

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

Calls

Call 1

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

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

eval41.0ms (0.9%)

Compiler: Compiled 13730 to 429 computations (96.9% saved)

prune24.0ms (0.6%)

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	361	0	361
Fresh	0	0	0
Picked	0	3	3
Done	0	4	4
Total	361	7	368

Accuracy

100.0%

Counts

368 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	68.1%	(fma.f64 y y (*.f64 x #s(literal 2 binary64)))
✓	68.1%	(+.f64 (.f64 y y) (.f64 x #s(literal 2 binary64)))
✓	83.5%	(+.f64 (.f64 x x) (.f64 y y))
✓	52.1%	(*.f64 y y)
✓	54.7%	(*.f64 x (+.f64 #s(literal 2 binary64) x))
✓	39.0%	(*.f64 x x)
✓	18.6%	(*.f64 x #s(literal 2 binary64))

Compiler

Compiled 119 to 50 computations (58% saved)

regimes21.0ms (0.5%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

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

Compiler

Compiled 33 to 21 computations (36.4% saved)

regimes64.0ms (1.5%)

Counts

10 → 1

Calls

Call 1

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

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

Calls

5 calls:

48.0ms	(*.f64 y y)
4.0ms	y
4.0ms	(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))
4.0ms	x
4.0ms	(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))

Results

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

Compiler

Compiled 33 to 21 computations (36.4% saved)

regimes15.0ms (0.3%)

Counts

7 → 2

Calls

Call 1

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

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

Calls

3 calls:

8.0ms	(*.f64 y y)
3.0ms	y
3.0ms	x

Results

Accuracy	Segments	Branch
99.1%	3	`x`
98.0%	2	`y`
98.0%	2	`(*.f64 y y)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes8.0ms (0.2%)

Counts

4 → 2

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
75.8%	3	`x`
84.4%	2	`y`
84.4%	2	`(*.f64 y y)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes6.0ms (0.1%)

Counts

3 → 3

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
75.8%	3	`x`
73.6%	3	`y`
71.3%	3	`(*.f64 y y)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes3.0ms (0.1%)

Counts

2 → 3

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
44.0%	2	`y`
53.8%	3	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
18.6%	1	`y`
18.6%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch15.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	6.207492198262537e-202	9.31629925573837e-196

Results

9.0ms

144×

valid

Compiler

Compiled 162 to 111 computations (31.5% saved)

Precisions

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

ival-mult: 2.0ms (54.8% of total)

ival-add: 1.0ms (27.4% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch12.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	5.911763934614433e-15	8.643445517318313e-13

Results

7.0ms

112×

valid

Compiler

Compiled 102 to 75 computations (26.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-mult: 2.0ms (68.1% of total)

ival-add: 1.0ms (34.1% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch35.0ms (0.8%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
23.0ms	7.812051619316976e+73	1.7920371636487829e+90
9.0ms	-6.858508449526914e+33	-1.699085081558665e+33

Results

25.0ms

256×

valid

Compiler

Compiled 210 to 140 computations (33.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-mult: 10.0ms (77% of total)

ival-add: 2.0ms (15.4% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch29.0ms (0.7%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	0.09202542499932496	157.78635160028125
13.0ms	-1.888514230138014e-9	-4.094592613041885e-14

Results

17.0ms

256×

valid

Compiler

Compiled 210 to 156 computations (25.7% saved)

Precisions

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

ival-mult: 6.0ms (65% of total)

ival-add: 3.0ms (32.5% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`if-if-or-not_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	82
1	42	82

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 y y (*.f64 x (+.f64 x #s(literal 2 binary64))))
(+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) (.f64 y y))
(if (<=.f64 (.f64 y y) #s(literal 3878192997493585/5386379163185534471414773640069251753523547958090930032126239644742381726000210761844394533148250574056430560108726494938131898624188215155842882325147525990354149039235527268548263688073546462485804289777440129024 binary64)) (.f64 x (+.f64 #s(literal 2 binary64) x)) (+.f64 (.f64 x x) (.f64 y y)))
(if (<=.f64 (.f64 y y) #s(literal 2574915281713591/39614081257132168796771975168 binary64)) (.f64 x (+.f64 #s(literal 2 binary64) x)) (*.f64 y y))
(if (<=.f64 x #s(literal -3100000000000000004221441750859776 binary64)) (.f64 x x) (if (<=.f64 x #s(literal 249999999999999981634945294120299730877200803799866971815661604945090576384 binary64)) (.f64 y y) (*.f64 x x)))
(if (<=.f64 x #s(literal -279564095785883/151115727451828646838272 binary64)) (.f64 x x) (if (<=.f64 x #s(literal 2 binary64)) (.f64 x #s(literal 2 binary64)) (*.f64 x x)))
(*.f64 x #s(literal 2 binary64))

Outputs
(fma.f64 y y (*.f64 x (+.f64 x #s(literal 2 binary64))))
(+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) (.f64 y y))
(if (<=.f64 (.f64 y y) #s(literal 3878192997493585/5386379163185534471414773640069251753523547958090930032126239644742381726000210761844394533148250574056430560108726494938131898624188215155842882325147525990354149039235527268548263688073546462485804289777440129024 binary64)) (.f64 x (+.f64 #s(literal 2 binary64) x)) (+.f64 (.f64 x x) (.f64 y y)))
(if (<=.f64 (.f64 y y) #s(literal 3878192997493585/5386379163185534471414773640069251753523547958090930032126239644742381726000210761844394533148250574056430560108726494938131898624188215155842882325147525990354149039235527268548263688073546462485804289777440129024 binary64)) (.f64 x (+.f64 x #s(literal 2 binary64))) (+.f64 (.f64 y y) (.f64 x x)))
(if (<=.f64 (.f64 y y) #s(literal 2574915281713591/39614081257132168796771975168 binary64)) (.f64 x (+.f64 #s(literal 2 binary64) x)) (*.f64 y y))
(if (<=.f64 (.f64 y y) #s(literal 2574915281713591/39614081257132168796771975168 binary64)) (.f64 x (+.f64 x #s(literal 2 binary64))) (*.f64 y y))
(if (<=.f64 x #s(literal -3100000000000000004221441750859776 binary64)) (.f64 x x) (if (<=.f64 x #s(literal 249999999999999981634945294120299730877200803799866971815661604945090576384 binary64)) (.f64 y y) (*.f64 x x)))
(if (<=.f64 x #s(literal -279564095785883/151115727451828646838272 binary64)) (.f64 x x) (if (<=.f64 x #s(literal 2 binary64)) (.f64 x #s(literal 2 binary64)) (*.f64 x x)))
(*.f64 x #s(literal 2 binary64))

soundness929.0ms (21.4%)

Rules

2574×	`-lowering-.f32`
2574×	`-lowering-.f64`
2330×	`-lowering-.f32`
2330×	`-lowering-.f64`
2198×	`-lowering-.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	8
1	19	7
2	37	7
3	48	7
4	49	7
0	49	7
0	37	540
1	123	449
2	356	449
3	1278	449
4	3311	449
5	7337	449
0	8471	449
0	7	17
1	43	17
2	373	17
3	4650	17
0	8798	17
0	31	324
1	104	277
2	303	241
3	1132	241
4	3912	241
0	8552	241

Stop Event

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

Compiler

Compiled 286 to 156 computations (45.5% saved)

preprocess50.0ms (1.1%)

Remove: (abs y)
Compiler: Compiled 268 to 112 computations (58.2% saved)

analyze0.0ms (0%)

sample999.0ms (23%)

preprocess91.0ms (2.1%)

explain89.0ms (2.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0.2%)

localize33.0ms (0.8%)

series3.0ms (0.1%)

rewrite285.0ms (6.6%)

simplify147.0ms (3.4%)

eval31.0ms (0.7%)

prune29.0ms (0.7%)

simplify32.0ms (0.7%)

localize89.0ms (2.1%)

series2.0ms (0.1%)

rewrite332.0ms (7.7%)

simplify191.0ms (4.4%)

eval120.0ms (2.8%)

prune68.0ms (1.6%)

simplify5.0ms (0.1%)

localize50.0ms (1.1%)

series3.0ms (0.1%)

rewrite278.0ms (6.4%)

simplify185.0ms (4.3%)

eval41.0ms (0.9%)

prune24.0ms (0.6%)

regimes21.0ms (0.5%)

regimes64.0ms (1.5%)

regimes15.0ms (0.3%)

regimes8.0ms (0.2%)

regimes6.0ms (0.1%)

regimes3.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch15.0ms (0.3%)

bsearch12.0ms (0.3%)

bsearch35.0ms (0.8%)

bsearch29.0ms (0.7%)

simplify10.0ms (0.2%)

soundness929.0ms (21.4%)

preprocess50.0ms (1.1%)

end0.0ms (0%)

Profiling