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)

sample863.0ms (12.4%)

Results

658.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 283.0ms

ival-mult: 181.0ms (64% of total)

ival-add: 87.0ms (30.8% of total)

const: 12.0ms (4.2% of total)

backward-pass: 3.0ms (1.1% of total)

Bogosity

preprocess93.0ms (1.3%)

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 (1.3%)

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

57.0ms

512×

valid

Compiler

Compiled 79 to 26 computations (67.1% saved)

Precisions

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

ival-mult: 11.0ms (52.9% of total)

ival-add: 9.0ms (43.3% of total)

const: 1.0ms (4.8% 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 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))
▶	100.0%	(+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) (.f64 y y))

Compiler

Compiled 24 to 15 computations (37.5% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	42
1	25	42
2	40	42
3	50	42
4	51	42
0	51	42

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

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

localize64.0ms (0.9%)

Localize:

Found 8 expressions of interest:

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

Results

51.0ms

256×

valid

Compiler

Compiled 56 to 12 computations (78.6% saved)

Precisions

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

ival-add: 8.0ms (51.4% of total)

ival-mult: 7.0ms (45% of total)

const: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Counts

8 → 120

Calls

Call 1

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

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

30 calls:

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

rewrite358.0ms (5.1%)

Algorithm

1×	batch-egg-rewrite

Rules

5494×	`-lowering-.f32`
5494×	`-lowering-.f64`
3454×	`/-lowering-/.f32`
3454×	`/-lowering-/.f64`
1840×	`frac-times`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	77	34
2	580	34
0	8545	34

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 323

Calls

Call 1

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

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

simplify192.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

2220×	`-lowering-.f32`
2220×	`-lowering-.f64`
1312×	`fma-define`
1212×	`sum4-define`
1036×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	654
1	129	560
2	381	488
3	1457	488
4	3911	488
5	7123	488
0	8200	488

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

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

eval59.0ms (0.8%)

Compiler: Compiled 11763 to 688 computations (94.2% saved)

prune44.0ms (0.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	456	5	461
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	456	7	463

Accuracy

100.0%

Counts

463 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))
▶	60.7%	(+.f64 (.f64 y y) (.f64 #s(literal 2 binary64) x))
✓	100.0%	(+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) (.f64 y y))
▶	80.6%	(+.f64 (.f64 x x) (.f64 y y))
▶	42.5%	(*.f64 y y)
▶	65.8%	(*.f64 x (+.f64 #s(literal 2 binary64) x))
▶	47.8%	(*.f64 x x)

Compiler

Compiled 94 to 59 computations (37.2% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

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

Rules

16×	`fma-lowering-fma.f32`
16×	`fma-define`
16×	`+-lowering-+.f64`
16×	`+-lowering-+.f32`
16×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	41
1	21	40
2	27	40
3	28	40
0	28	40

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize82.0ms (1.2%)

Localize:

Found 10 expressions of interest:

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

Results

62.0ms

256×

valid

Compiler

Compiled 52 to 11 computations (78.8% saved)

Precisions

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

ival-mult: 7.0ms (62.4% of total)

ival-add: 4.0ms (35.6% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0%)

Counts

7 → 108

Calls

Call 1

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

Outputs
#<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))))>
#<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 (* 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 (* 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)>

Calls

27 calls:

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

rewrite359.0ms (5.2%)

Algorithm

1×	batch-egg-rewrite

Rules

4552×	`-lowering-.f32`
4552×	`-lowering-.f64`
1908×	`/-lowering-/.f32`
1908×	`/-lowering-/.f64`
1860×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	26
1	58	25
2	477	25
3	5510	25
0	8611	25

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 268

Calls

Call 1

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

Outputs
(+.f64 (.f64 x x) (.f64 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))) (neg.f64 (/.f64 (.f64 y (.f64 y (.f64 y y))) (-.f64 (.f64 x x) (.f64 y y)))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (*.f64 y y)))) #s(literal -1 binary64)))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) (.f64 y y))) (/.f64 (.f64 y (.f64 y (.f64 y y))) (-.f64 (.f64 x x) (.f64 y y))))
(-.f64 (/.f64 (.f64 y (.f64 y (.f64 y y))) (-.f64 (.f64 y y) (.f64 x x))) (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 y y) (.f64 x x))))
(fma.f64 x x (*.f64 y y))
(fma.f64 y y (*.f64 x x))
(neg.f64 (/.f64 (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 y (.f64 y (.f64 y (.f64 y (.f64 y y)))))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (-.f64 (.f64 y y) (*.f64 x x)))))))
(neg.f64 (/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y (.f64 y y)))) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) (.f64 y y)))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 y (.f64 y (.f64 y (.f64 y (.f64 y y))))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (-.f64 (.f64 y y) (*.f64 x x))))))
(neg.f64 (/.f64 (.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) (.f64 y y)))) (-.f64 (.f64 x x) (*.f64 y y))))
(/.f64 (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 y (.f64 y (.f64 y (.f64 y (.f64 y y)))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 y y) (-.f64 (.f64 y y) (*.f64 x x)))))
(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 y (.f64 y (.f64 y y)))) (-.f64 (.f64 x x) (.f64 y y)))
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(.f64 (/.f64 (+.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 (.f64 x x) #s(literal -4 binary64))) (+.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 (.f64 x x) #s(literal -4 binary64)))) (+.f64 (.f64 y y) (*.f64 x #s(literal 2 binary64))))
(.f64 (/.f64 (+.f64 (.f64 y (.f64 y (.f64 y (.f64 y (.f64 y y))))) (.f64 x (.f64 (.f64 x x) #s(literal 8 binary64)))) (+.f64 (.f64 (.f64 y y) (.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 y (.f64 y (.f64 y (.f64 y (.f64 y y))))))) (.f64 (.f64 x (-.f64 (.f64 x #s(literal 4 binary64)) (.f64 (.f64 y y) #s(literal 2 binary64)))) (.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 (-.f64 (.f64 x #s(literal 2 binary64)) (.f64 y y)) (-.f64 (.f64 x #s(literal 2 binary64)) (.f64 y y))))))) (+.f64 (.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 y (.f64 y (.f64 y y)))) (.f64 (.f64 x (-.f64 (.f64 x #s(literal 4 binary64)) (.f64 (.f64 y y) #s(literal 2 binary64)))) (-.f64 (.f64 x (-.f64 (.f64 x #s(literal 4 binary64)) (.f64 (.f64 y y) #s(literal 2 binary64)))) (.f64 y (.f64 y (.f64 y y)))))))
(.f64 (/.f64 (+.f64 (.f64 y (.f64 y (.f64 y (.f64 y (.f64 y y))))) (.f64 x (.f64 (.f64 x x) #s(literal 8 binary64)))) (.f64 (+.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 (.f64 y y) (+.f64 (.f64 y y) (.f64 x #s(literal -2 binary64))))) (+.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 (.f64 x #s(literal -2 binary64)) (-.f64 (.f64 x #s(literal 2 binary64)) (.f64 y y)))))) (+.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 (.f64 x #s(literal -2 binary64)) (-.f64 (.f64 x #s(literal 2 binary64)) (.f64 y y)))))
(.f64 (/.f64 (+.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 (.f64 x x) #s(literal -4 binary64))) (+.f64 (.f64 y (.f64 y (.f64 y (.f64 y (.f64 y y))))) (.f64 (.f64 x (.f64 x x)) #s(literal -8 binary64)))) (+.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 (.f64 x #s(literal 2 binary64)) (+.f64 (.f64 y y) (*.f64 x #s(literal 2 binary64))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 y y) (.f64 x #s(literal -2 binary64))) (-.f64 (.f64 (.f64 y y) (.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 y (.f64 y (.f64 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 (.f64 y y))) (.f64 y (.f64 y (.f64 y y)))) (.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (+.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 (*.f64 x x) #s(literal 4 binary64)))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 y y) (.f64 x #s(literal -2 binary64))) (-.f64 (.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 y (.f64 y (.f64 y y)))) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 16 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 (*.f64 x x) #s(literal 4 binary64)))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 (.f64 x 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 (.f64 y (.f64 y (.f64 y y))))) (.f64 y (.f64 y y))) (.f64 (.f64 y (.f64 y (.f64 y (.f64 y (.f64 y y))))) (.f64 y (.f64 y y)))) (.f64 #s(literal 512 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x x)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 y y) (.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 y (.f64 y (.f64 y (.f64 y (.f64 y y))))))) (.f64 (.f64 x (.f64 (.f64 x x) #s(literal 8 binary64))) (-.f64 (.f64 x (.f64 (.f64 x x) #s(literal 8 binary64))) (.f64 y (.f64 y (.f64 y (.f64 y (.f64 y y))))))))))
(.f64 (pow.f64 (/.f64 (+.f64 (.f64 (.f64 x x) #s(literal 4 binary64)) (.f64 (.f64 y y) (+.f64 (.f64 y y) (.f64 x #s(literal -2 binary64))))) (-.f64 (.f64 (.f64 y y) (.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 y (.f64 y (.f64 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 y (.f64 y (.f64 y (.f64 y (.f64 y y))))) (.f64 (.f64 x (.f64 x x)) #s(literal -8 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)

simplify263.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

2282×	`-lowering-.f32`
2282×	`-lowering-.f64`
1684×	`/-lowering-/.f32`
1684×	`/-lowering-/.f64`
1478×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	462
1	108	373
2	288	373
3	997	373
4	2952	373
5	5890	373
0	8191	373

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

Inputs
(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))))
(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))))
(* 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)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)

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

eval73.0ms (1%)

Compiler: Compiled 9872 to 810 computations (91.8% saved)

prune78.0ms (1.1%)

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	440	2	442
Fresh	0	0	0
Picked	0	5	5
Done	1	1	2
Total	441	8	449

Accuracy

100.0%

Counts

449 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	60.7%	(+.f64 (.f64 y y) (.f64 #s(literal 2 binary64) x))
✓	100.0%	(+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) (.f64 y y))
✓	80.6%	(+.f64 (.f64 x x) (.f64 y y))
▶	65.8%	(+.f64 (.f64 x x) (.f64 x #s(literal 2 binary64)))
✓	42.5%	(*.f64 y y)
✓	65.8%	(*.f64 x (+.f64 #s(literal 2 binary64) x))
✓	47.8%	(*.f64 x x)
▶	20.5%	(*.f64 x #s(literal 2 binary64))

Compiler

Compiled 60 to 39 computations (35% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

10×	`-lowering-.f32`
10×	`-lowering-.f64`
8×	`+-lowering-+.f64`
8×	`+-lowering-+.f32`
6×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	17
1	11	17
2	16	17
0	16	17

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize64.0ms (0.9%)

Localize:

Found 4 expressions of interest:

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

Results

56.0ms

256×

valid

Compiler

Compiled 23 to 7 computations (69.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-mult: 36.0ms (96.2% of total)

ival-add: 1.0ms (2.7% of total)

const: 0.0ms (0% of total)

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

series1.0ms (0%)

Counts

3 → 36

Calls

Call 1

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

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 (* 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 (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

9 calls:

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

rewrite3.0s (43.5%)

Algorithm

1×	batch-egg-rewrite

Rules

2540×	`-lowering-.f32`
2540×	`-lowering-.f64`
1774×	`/-lowering-/.f32`
1774×	`/-lowering-/.f64`
1716×	`sum5-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	10
1	25	10
2	214	10
3	2510	10
0	8378	10

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 147

Calls

Call 1

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

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

simplify214.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

3800×	`-lowering-.f32`
3800×	`-lowering-.f64`
1670×	`cube-prod`
1570×	`times-frac`
1320×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	126
1	31	112
2	67	112
3	132	112
4	191	112
5	310	112
6	2124	112
7	3200	112
8	4448	112
9	6385	112
10	6968	112
11	7765	112
0	8086	112

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

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)
(* 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))))
(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
(* 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)
(* 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))
(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)

eval24.0ms (0.3%)

Compiler: Compiled 5278 to 464 computations (91.2% saved)

prune23.0ms (0.3%)

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	0	0
Picked	0	2	2
Done	0	6	6
Total	202	8	210

Accuracy

100.0%

Counts

210 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	60.7%	(+.f64 (.f64 y y) (.f64 #s(literal 2 binary64) x))
✓	100.0%	(+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) (.f64 y y))
✓	80.6%	(+.f64 (.f64 x x) (.f64 y y))
✓	65.8%	(+.f64 (.f64 x x) (.f64 x #s(literal 2 binary64)))
✓	42.5%	(*.f64 y y)
✓	65.8%	(*.f64 x (+.f64 #s(literal 2 binary64) x))
✓	47.8%	(*.f64 x x)
✓	20.5%	(*.f64 x #s(literal 2 binary64))

Compiler

Compiled 117 to 56 computations (52.1% saved)

regimes18.0ms (0.3%)

Counts

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

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

Calls

5 calls:

4.0ms	(+.f64 (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x)) (*.f64 y y))
4.0ms	(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 x x))
3.0ms	x
3.0ms	y
3.0ms	(*.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)

regimes11.0ms (0.2%)

Counts

7 → 3

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

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

Calls

3 calls:

4.0ms	(*.f64 y y)
3.0ms	x
3.0ms	y

Results

Accuracy	Segments	Branch
98.6%	3	`x`
95.6%	2	`y`
95.6%	2	`(*.f64 y y)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes9.0ms (0.1%)

Counts

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
95.6%	2	`y`
95.6%	2	`(*.f64 y y)`
80.6%	1	`x`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes5.0ms (0.1%)

Counts

5 → 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 x #s(literal 2 binary64)))

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
85.1%	2	`y`
85.1%	2	`(*.f64 y y)`

Compiler

Compiled 8 to 5 computations (37.5% 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	y
2.0ms	x
2.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
75.2%	3	`x`
70.4%	4	`y`
67.1%	2	`(*.f64 y y)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes5.0ms (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:

3.0ms	x
2.0ms	y

Results

Accuracy	Segments	Branch
51.0%	3	`y`
64.7%	3	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

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:

1.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
20.5%	1	`y`
20.5%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch26.0ms (0.4%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
9.0ms	2.5790093095457586e-6	2.3532829152611087e-5
15.0ms	-12164640.99733025	-0.42956106875083344

Results

16.0ms

240×

valid

Compiler

Compiled 318 to 207 computations (34.9% saved)

Precisions

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

ival-mult: 6.0ms (71.5% of total)

ival-add: 2.0ms (23.8% of total)

const: 0.0ms (0% of total)

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

bsearch32.0ms (0.5%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
31.0ms	3.491087244856546e-120	5.55876992827026e-119

Results

28.0ms

96×

valid

Compiler

Compiled 114 to 78 computations (31.6% saved)

Precisions

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

ival-add: 1.0ms (42.1% of total)

ival-mult: 1.0ms (42.1% of total)

const: 0.0ms (0% of total)

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

bsearch12.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	6.597557057020878e+163	1.3109711488756988e+165

Results

7.0ms

112×

valid

Compiler

Compiled 102 to 75 computations (26.5% saved)

Precisions

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

ival-add: 2.0ms (52.6% of total)

ival-mult: 2.0ms (52.6% of total)

const: 0.0ms (0% of total)

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

bsearch29.0ms (0.4%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
9.0ms	9903583212471992000.0	8.479884857632283e+19
16.0ms	-3.611826757415754e+28	-68114254987267500.0

Results

18.0ms

256×

valid

Compiler

Compiled 210 to 140 computations (33.3% saved)

Precisions

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

ival-mult: 5.0ms (61.2% of total)

ival-add: 2.0ms (24.5% of total)

const: 0.0ms (0% of total)

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

bsearch58.0ms (0.8%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	2.3532829152611087e-5	8.195740538832473
42.0ms	-0.42956106875083344	-1.2321904213548747e-8

Results

46.0ms

288×

valid

Compiler

Compiled 234 to 174 computations (25.6% saved)

Precisions

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

ival-mult: 6.0ms (65.6% of total)

ival-add: 3.0ms (32.8% of total)

const: 0.0ms (0% of total)

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	97
1	54	97

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) (.f64 y y))
(if (<=.f64 x #s(literal -2 binary64)) (+.f64 (.f64 x x) (.f64 y y)) (if (<=.f64 x #s(literal 6788401819125115/295147905179352825856 binary64)) (+.f64 (.f64 y y) (.f64 #s(literal 2 binary64) x)) (+.f64 (.f64 x x) (.f64 y y))))
(if (<=.f64 (.f64 y y) #s(literal 1362822608054263/90854840536950861318665475986000566794205170085914757535186274897579911014174740415773881339220445695095315200783272241691825203576832 binary64)) (.f64 x (+.f64 #s(literal 2 binary64) x)) (+.f64 (.f64 x x) (.f64 y y)))
(if (<=.f64 (.f64 y y) #s(literal 300000000000000000535004984576375509543690927680904178132104583310388508543369860686140612397852888299630691108662934706931422938094885870361259549757690342218399744 binary64)) (.f64 x (+.f64 #s(literal 2 binary64) x)) (*.f64 y y))
(if (<=.f64 x #s(literal -124999999999999997902848 binary64)) (.f64 x x) (if (<=.f64 x #s(literal 14000000000000000000 binary64)) (.f64 y y) (*.f64 x x)))
(if (<=.f64 x #s(literal -7566047373982433/18014398509481984 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
(+.f64 (.f64 x (+.f64 x #s(literal 2 binary64))) (.f64 y y))
(if (<=.f64 x #s(literal -2 binary64)) (+.f64 (.f64 x x) (.f64 y y)) (if (<=.f64 x #s(literal 6788401819125115/295147905179352825856 binary64)) (+.f64 (.f64 y y) (.f64 #s(literal 2 binary64) x)) (+.f64 (.f64 x x) (.f64 y y))))
(if (<=.f64 x #s(literal -2 binary64)) (+.f64 (.f64 y y) (.f64 x x)) (if (<=.f64 x #s(literal 6788401819125115/295147905179352825856 binary64)) (+.f64 (.f64 y y) (.f64 x #s(literal 2 binary64))) (+.f64 (.f64 y y) (.f64 x x))))
(if (<=.f64 (.f64 y y) #s(literal 1362822608054263/90854840536950861318665475986000566794205170085914757535186274897579911014174740415773881339220445695095315200783272241691825203576832 binary64)) (.f64 x (+.f64 #s(literal 2 binary64) x)) (+.f64 (.f64 x x) (.f64 y y)))
(if (<=.f64 (.f64 y y) #s(literal 1362822608054263/90854840536950861318665475986000566794205170085914757535186274897579911014174740415773881339220445695095315200783272241691825203576832 binary64)) (.f64 x (+.f64 x #s(literal 2 binary64))) (+.f64 (.f64 y y) (.f64 x x)))
(if (<=.f64 (.f64 y y) #s(literal 300000000000000000535004984576375509543690927680904178132104583310388508543369860686140612397852888299630691108662934706931422938094885870361259549757690342218399744 binary64)) (.f64 x (+.f64 #s(literal 2 binary64) x)) (*.f64 y y))
(if (<=.f64 (.f64 y y) #s(literal 300000000000000000535004984576375509543690927680904178132104583310388508543369860686140612397852888299630691108662934706931422938094885870361259549757690342218399744 binary64)) (.f64 x (+.f64 x #s(literal 2 binary64))) (*.f64 y y))
(if (<=.f64 x #s(literal -124999999999999997902848 binary64)) (.f64 x x) (if (<=.f64 x #s(literal 14000000000000000000 binary64)) (.f64 y y) (*.f64 x x)))
(if (<=.f64 x #s(literal -7566047373982433/18014398509481984 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))

soundness691.0ms (9.9%)

Rules

2282×	`-lowering-.f32`
2282×	`-lowering-.f64`
2220×	`-lowering-.f32`
2220×	`-lowering-.f64`
1684×	`/-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	40	654
1	129	560
2	381	488
3	1457	488
4	3911	488
5	7123	488
0	8200	488
0	34	462
1	108	373
2	288	373
3	997	373
4	2952	373
5	5890	373
0	8191	373

Stop Event

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

Compiler

Compiled 319 to 170 computations (46.7% saved)

preprocess48.0ms (0.7%)

Remove: (abs y)
Compiler: Compiled 314 to 128 computations (59.2% saved)

analyze0.0ms (0%)

sample863.0ms (12.4%)

preprocess93.0ms (1.3%)

explain89.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify12.0ms (0.2%)

localize64.0ms (0.9%)

series6.0ms (0.1%)

rewrite358.0ms (5.1%)

simplify192.0ms (2.8%)

eval59.0ms (0.8%)

prune44.0ms (0.6%)

simplify5.0ms (0.1%)

localize82.0ms (1.2%)

series2.0ms (0%)

rewrite359.0ms (5.2%)

simplify263.0ms (3.8%)

eval73.0ms (1%)

prune78.0ms (1.1%)

simplify12.0ms (0.2%)

localize64.0ms (0.9%)

series1.0ms (0%)

rewrite3.0s (43.5%)

simplify214.0ms (3.1%)

eval24.0ms (0.3%)

prune23.0ms (0.3%)

regimes18.0ms (0.3%)

regimes11.0ms (0.2%)

regimes9.0ms (0.1%)

regimes5.0ms (0.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes3.0ms (0%)

bsearch26.0ms (0.4%)

bsearch32.0ms (0.5%)

bsearch12.0ms (0.2%)

bsearch29.0ms (0.4%)

bsearch58.0ms (0.8%)

simplify9.0ms (0.1%)

soundness691.0ms (9.9%)

preprocess48.0ms (0.7%)

end0.0ms (0%)

Profiling