Metrics for Numeric.Log:$cexpm1 from log-domain-0.10.2.1, B

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 10 to 6 computations (40% 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)

sample670.0ms (11%)

Results

473.0ms	8254×	0	valid
0.0ms	2×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 222.0ms

ival-add: 107.0ms (48.2% of total)

ival-mult: 105.0ms (47.3% of total)

const: 7.0ms (3.2% of total)

backward-pass: 3.0ms (1.4% of total)

Bogosity

preprocess95.0ms (1.6%)

Algorithm

2×	egg-herbie

Rules

1960×	`sum5-define`
1780×	`fnmadd-define`
1536×	`sum4-define`
1368×	`fmsub-define`
1344×	`fnmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	44
1	69	37
2	218	36
3	841	36
4	3279	36
5	6343	36
6	6948	36
7	6964	36
0	5	6
1	12	6
2	26	6
3	39	6
4	50	6
5	67	6
6	93	6
7	115	6
8	122	6
9	123	6
0	123	6

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

Outputs
(+ (+ (* x y) x) y)
(+.f64 x (*.f64 y (+.f64 x #s(literal 1 binary64))))

Call 2

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

Outputs
(+ (+ (* x y) x) y)
(+ x (fma x y y))
(+ (+ (* (neg x) y) (neg x)) y)
(+ y (fnmsub x y x))
(+ (+ (* x (neg y)) x) (neg y))
(+ x (fnmsub x y y))
(neg (+ (+ (* (neg x) y) (neg x)) y))
(+ x (fmsub x y y))
(neg (+ (+ (* x (neg y)) x) (neg y)))
(+ y (fmsub x y x))
(+ (+ (* y x) y) x)
(+ x (fma x y y))

Symmetry

(sort x y)

explain73.0ms (1.2%)

FPErrors

Click to see full error table

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

Results

43.0ms

512×

valid

Compiler

Compiled 49 to 17 computations (65.3% saved)

Precisions

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

ival-mult: 6.0ms (51% of total)

ival-add: 5.0ms (42.5% of total)

const: 1.0ms (8.5% of total)

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

eval0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 x (*.f64 y (+.f64 x #s(literal 1 binary64))))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	(*.f64 y (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	(+.f64 x (*.f64 y (+.f64 x #s(literal 1 binary64))))

Rules

92×	`fma-define`
76×	`fma-lowering-fma.f32`
76×	`fma-lowering-fma.f64`
48×	`-lowering-.f32`
48×	`-lowering-.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	17	16
2	37	16
3	66	16
4	95	16
5	110	16
6	117	16
7	118	16
0	118	16

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ x (* y (+ x 1)))
x
(* y (+ x 1))
y
(+ x 1)
1

Outputs
(+ x (* y (+ x 1)))
(+.f64 y (*.f64 x (+.f64 y #s(literal 1 binary64))))
x
(* y (+ x 1))
(*.f64 y (+.f64 x #s(literal 1 binary64)))
y
(+ x 1)
(+.f64 x #s(literal 1 binary64))
1
#s(literal 1 binary64)

localize29.0ms (0.5%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x (*.f64 y (+.f64 x #s(literal 1 binary64))))
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 y (+.f64 x #s(literal 1 binary64)))

Results

22.0ms

256×

valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-add: 4.0ms (64.2% of total)

ival-mult: 2.0ms (32.1% of total)

const: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Counts

3 → 60

Calls

Call 1

Inputs
#<alt (+ x (* y (+ x 1)))>
#<alt (* y (+ x 1))>
#<alt (+ x 1)>

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

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	(+ x (* y (+ x 1)))
0.0ms	x	@	inf	(+ x (* y (+ x 1)))
0.0ms	x	@	-inf	(+ x (* y (+ x 1)))
0.0ms	y	@	inf	(+ x (* y (+ x 1)))
0.0ms	x	@	0	(+ x (* y (+ x 1)))

rewrite3.1s (51.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2468×	`-lowering-.f32`
2468×	`-lowering-.f64`
1844×	`fma-lowering-fma.f32`
1844×	`fma-lowering-fma.f64`
1736×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	40	13
2	367	13
3	4440	13
0	8167	13

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 177

Calls

Call 1

Inputs
(+ x (* y (+ x 1)))
(* y (+ x 1))
(+ x 1)

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

simplify273.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

2004×	`fmsub-define`
1956×	`fnmsub-define`
1788×	`fmm-def`
1602×	`sum4-define`
1562×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	290
1	147	249
2	447	247
3	1430	247
4	4275	247
0	8035	247

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

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

eval28.0ms (0.5%)

Compiler: Compiled 5692 to 613 computations (89.2% saved)

prune28.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	232	5	237
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	232	6	238

Accuracy

100.0%

Counts

238 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 x (*.f64 y (+.f64 x #s(literal 1 binary64))))
▶	60.9%	(+.f64 x (*.f64 y x))
▶	76.8%	(+.f64 x y)
▶	63.5%	(*.f64 y (+.f64 x #s(literal 1 binary64)))
▶	41.0%	y
▶	38.5%	x

Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 y x)
✓	cost-diff	(+.f64 x (*.f64 y x))
✓	cost-diff	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	(*.f64 y (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	(+.f64 x y)

Rules

76×	`fma-define`
44×	`-lowering-.f32`
44×	`-lowering-.f64`
40×	`fma-lowering-fma.f32`
40×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	22	26
2	34	26
3	58	26
4	83	26
5	88	26
6	89	26
0	89	26

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ x y)
x
y
x
y
(* y (+ x 1))
y
(+ x 1)
x
1
(+ x (* y x))
x
(* y x)
y

Outputs
(+ x y)
(+.f64 x y)
x
y
x
y
(* y (+ x 1))
(*.f64 y (+.f64 x #s(literal 1 binary64)))
y
(+ x 1)
(+.f64 x #s(literal 1 binary64))
x
1
#s(literal 1 binary64)
(+ x (* y x))
(*.f64 x (+.f64 y #s(literal 1 binary64)))
x
(* y x)
(*.f64 x y)
y

localize71.0ms (1.2%)

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x (*.f64 y x))
✓	accuracy	100.0%	(*.f64 y x)
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 y (+.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(+.f64 x y)

Results

62.0ms

256×

valid

Compiler

Compiled 31 to 9 computations (71% saved)

Precisions

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

ival-add: 4.0ms (47.7% of total)

ival-mult: 4.0ms (47.7% of total)

const: 0.0ms (0% of total)

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

series16.0ms (0.3%)

Counts

5 → 108

Calls

Call 1

Inputs
#<alt (+ x y)>
#<alt (* y (+ x 1))>
#<alt (+ x 1)>
#<alt (+ x (* y x))>
#<alt (* y x)>

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

Calls

27 calls:

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

rewrite270.0ms (4.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3686×	`-lowering-.f32`
3686×	`-lowering-.f64`
1898×	`/-lowering-/.f32`
1898×	`/-lowering-/.f64`
1554×	`sum5-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	55	17
2	432	17
3	4568	17
0	8464	17

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 263

Calls

Call 1

Inputs
(+ x y)
(* y (+ x 1))
(+ x 1)
(+ x (* y x))
(* y x)

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

simplify187.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

2112×	`fnmadd-define`
1694×	`fmsub-define`
1680×	`fnmsub-define`
1658×	`fma-lowering-fma.f32`
1658×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	386
1	152	344
2	379	344
3	1004	344
4	3711	344
5	6153	344
6	7919	344
0	8063	344

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

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

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

eval39.0ms (0.6%)

Compiler: Compiled 6917 to 741 computations (89.3% saved)

prune50.0ms (0.8%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	370	1	371
Fresh	0	0	0
Picked	0	5	5
Done	0	1	1
Total	370	7	377

Accuracy

100.0%

Counts

377 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 x (*.f64 y (+.f64 x #s(literal 1 binary64))))
✓	60.9%	(+.f64 x (*.f64 y x))
✓	76.8%	(+.f64 x y)
✓	63.5%	(*.f64 y (+.f64 x #s(literal 1 binary64)))
▶	24.9%	(*.f64 y x)
✓	41.0%	y
✓	38.5%	x

Compiler

Compiled 39 to 25 computations (35.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 1 expressions of interest:

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

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	5
1	4	5
0	4	5

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* y x)
y
x

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

localize20.0ms (0.3%)

Localize:

Found 1 expressions of interest:

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

Results

15.0ms

256×

valid

Compiler

Compiled 8 to 4 computations (50% saved)

Precisions

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

ival-mult: 4.0ms (83.6% of total)

const: 0.0ms (0% of total)

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

series0.0ms (0%)

Counts

1 → 24

Calls

Call 1

Inputs
#<alt (* y x)>

Outputs
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>

Calls

6 calls:

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

rewrite10.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	3
1	4	3
0	4	3

Stop Event

1×	iter limit
1×	saturated

Counts

1 → 2

Calls

Call 1

Inputs
(* y x)

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`-lowering-.f32`
4×	`-lowering-.f64`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	72
1	4	72
0	4	72

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

Calls

Call 1

Inputs
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)

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

eval2.0ms (0%)

Compiler: Compiled 80 to 4 computations (95% saved)

prune3.0ms (0.1%)

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	26	7	33

Accuracy

100.0%

Counts

33 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(+.f64 x (*.f64 y (+.f64 x #s(literal 1 binary64))))
✓	60.9%	(+.f64 x (*.f64 y x))
✓	76.8%	(+.f64 x y)
✓	63.5%	(*.f64 y (+.f64 x #s(literal 1 binary64)))
✓	24.9%	(*.f64 y x)
✓	41.0%	y
✓	38.5%	x

Compiler

Compiled 73 to 37 computations (49.3% saved)

regimes10.0ms (0.2%)

Counts

8 → 1

Calls

Call 1

Inputs
x
y
(*.f64 y x)
(+.f64 x y)
(*.f64 y (+.f64 x #s(literal 1 binary64)))
(+.f64 x (*.f64 y x))
(+.f64 x (*.f64 y (+.f64 x #s(literal 1 binary64))))
(+.f64 (+.f64 (*.f64 x y) x) y)

Outputs
(+.f64 x (*.f64 y (+.f64 x #s(literal 1 binary64))))

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 9 computations (40% saved)

regimes8.0ms (0.1%)

Counts

6 → 3

Calls

Call 1

Inputs
x
y
(*.f64 y x)
(+.f64 x y)
(*.f64 y (+.f64 x #s(literal 1 binary64)))
(+.f64 x (*.f64 y x))

Outputs
(+.f64 x (*.f64 y x))
(+.f64 x y)
(*.f64 y (+.f64 x #s(literal 1 binary64)))

Calls

2 calls:

5.0ms	y
3.0ms	x

Results

Accuracy	Segments	Branch
99.7%	3	`x`
100.0%	3	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0.1%)

Counts

5 → 3

Calls

Call 1

Inputs
x
y
(*.f64 y x)
(+.f64 x y)
(*.f64 y (+.f64 x #s(literal 1 binary64)))

Outputs
(*.f64 y x)
(+.f64 x y)
(*.f64 y (+.f64 x #s(literal 1 binary64)))

Calls

2 calls:

2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
83.1%	2	`x`
99.0%	3	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0.1%)

Counts

4 → 2

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
82.4%	2	`x`
82.3%	2	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes4.0ms (0.1%)

Counts

3 → 3

Calls

Call 1

Inputs
x
y
(*.f64 y x)

Outputs
x
y
(*.f64 y x)

Calls

2 calls:

2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
73.1%	3	`y`
74.3%	3	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0.1%)

Counts

2 → 2

Calls

Call 1

Inputs
x
y

Outputs
x
y

Calls

2 calls:

3.0ms	x
2.0ms	y

Results

Accuracy	Segments	Branch
67.6%	2	`y`
68.7%	2	`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
x

Outputs
x

Calls

2 calls:

1.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
38.5%	1	`y`
38.5%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch30.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
14.0ms	7.479150510854698e-19	1.3006196055838482e-8
14.0ms	-1.888514230138014e-9	-3.3817087381316616e-19

Results

18.0ms

320×

valid

Compiler

Compiled 294 to 199 computations (32.3% saved)

Precisions

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

ival-add: 4.0ms (58.5% of total)

ival-mult: 3.0ms (43.9% of total)

const: 0.0ms (0% of total)

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

bsearch30.0ms (0.5%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
13.0ms	7.479150510854698e-19	1.3006196055838482e-8
14.0ms	-8.659064450509498e+20	-0.16046285271706487

Results

17.0ms

336×

valid

Compiler

Compiled 286 to 197 computations (31.1% saved)

Precisions

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

ival-add: 3.0ms (45.5% of total)

ival-mult: 3.0ms (45.5% of total)

const: 0.0ms (0% of total)

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

bsearch17.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	7.688799603718667e-8	157.78635160028125

Results

7.0ms

144×

valid

Compiler

Compiled 122 to 81 computations (33.6% saved)

Precisions

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

ival-add: 1.0ms (34.8% of total)

ival-mult: 1.0ms (34.8% of total)

const: 0.0ms (0% of total)

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

bsearch21.0ms (0.3%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
12.0ms	7.688799603718667e-8	157.78635160028125
8.0ms	-8.09005446415144e-95	-1.4671482088741793e-95

Results

12.0ms

240×

valid

Compiler

Compiled 152 to 108 computations (28.9% saved)

Precisions

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

ival-add: 2.0ms (42.3% of total)

ival-mult: 2.0ms (42.3% 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	-8.09005446415144e-95	-1.4671482088741793e-95

Results

8.0ms

96×

valid

Compiler

Compiled 62 to 45 computations (27.4% saved)

Precisions

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

ival-mult: 4.0ms (82.1% of total)

ival-add: 1.0ms (20.5% of total)

const: 0.0ms (0% of total)

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
4×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	77
1	36	77

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 x (*.f64 y (+.f64 x #s(literal 1 binary64))))
(if (<=.f64 y #s(literal -7833839311102797/4835703278458516698824704 binary64)) (+.f64 x (.f64 y x)) (if (<=.f64 y #s(literal 3929008913747545/302231454903657293676544 binary64)) (+.f64 x y) (.f64 y (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 y #s(literal -1080000000000000000 binary64)) (.f64 y x) (if (<=.f64 y #s(literal 3929008913747545/302231454903657293676544 binary64)) (+.f64 x y) (.f64 y (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 x #s(literal 155 binary64)) (+.f64 x y) (*.f64 y x))
(if (<=.f64 x #s(literal -6012269011901013/75153362648762663292463379097258784876021841565066235862633311089030688803667470190838367948312598497021919232 binary64)) x (if (<=.f64 x #s(literal 1 binary64)) y (*.f64 y x)))
(if (<=.f64 x #s(literal -6012269011901013/75153362648762663292463379097258784876021841565066235862633311089030688803667470190838367948312598497021919232 binary64)) x y)
x

Outputs
(+.f64 x (*.f64 y (+.f64 x #s(literal 1 binary64))))
(if (<=.f64 y #s(literal -7833839311102797/4835703278458516698824704 binary64)) (+.f64 x (.f64 y x)) (if (<=.f64 y #s(literal 3929008913747545/302231454903657293676544 binary64)) (+.f64 x y) (.f64 y (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 y #s(literal -7833839311102797/4835703278458516698824704 binary64)) (+.f64 x (.f64 x y)) (if (<=.f64 y #s(literal 3929008913747545/302231454903657293676544 binary64)) (+.f64 x y) (.f64 y (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 y #s(literal -1080000000000000000 binary64)) (.f64 y x) (if (<=.f64 y #s(literal 3929008913747545/302231454903657293676544 binary64)) (+.f64 x y) (.f64 y (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 y #s(literal -1080000000000000000 binary64)) (.f64 x y) (if (<=.f64 y #s(literal 3929008913747545/302231454903657293676544 binary64)) (+.f64 x y) (.f64 y (+.f64 x #s(literal 1 binary64)))))
(if (<=.f64 x #s(literal 155 binary64)) (+.f64 x y) (*.f64 y x))
(if (<=.f64 x #s(literal 155 binary64)) (+.f64 x y) (*.f64 x y))
(if (<=.f64 x #s(literal -6012269011901013/75153362648762663292463379097258784876021841565066235862633311089030688803667470190838367948312598497021919232 binary64)) x (if (<=.f64 x #s(literal 1 binary64)) y (*.f64 y x)))
(if (<=.f64 x #s(literal -6012269011901013/75153362648762663292463379097258784876021841565066235862633311089030688803667470190838367948312598497021919232 binary64)) x (if (<=.f64 x #s(literal 1 binary64)) y (*.f64 x y)))
(if (<=.f64 x #s(literal -6012269011901013/75153362648762663292463379097258784876021841565066235862633311089030688803667470190838367948312598497021919232 binary64)) x y)
x

soundness880.0ms (14.4%)

Rules

2112×	`fnmadd-define`
2004×	`fmsub-define`
1956×	`fnmsub-define`
1788×	`fmm-def`
1694×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	290
1	147	249
2	447	247
3	1430	247
4	4275	247
0	8035	247
0	44	386
1	152	344
2	379	344
3	1004	344
4	3711	344
5	6153	344
6	7919	344
0	8063	344
0	5	6
1	12	6
2	26	6
3	39	6
4	50	6
5	67	6
6	93	6
7	115	6
8	122	6
9	123	6
0	123	6

Stop Event

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

Compiler

Compiled 301 to 174 computations (42.2% saved)

preprocess48.0ms (0.8%)

Compiler: Compiled 212 to 88 computations (58.5% saved)

analyze0.0ms (0%)

sample670.0ms (11%)

preprocess95.0ms (1.6%)

explain73.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.1%)

localize29.0ms (0.5%)

series3.0ms (0.1%)

rewrite3.1s (51.1%)

simplify273.0ms (4.5%)

eval28.0ms (0.5%)

prune28.0ms (0.5%)

simplify7.0ms (0.1%)

localize71.0ms (1.2%)

series16.0ms (0.3%)

rewrite270.0ms (4.4%)

simplify187.0ms (3.1%)

eval39.0ms (0.6%)

prune50.0ms (0.8%)

simplify4.0ms (0.1%)

localize20.0ms (0.3%)

series0.0ms (0%)

rewrite10.0ms (0.2%)

simplify9.0ms (0.1%)

eval2.0ms (0%)

prune3.0ms (0.1%)

regimes10.0ms (0.2%)

regimes8.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

regimes5.0ms (0.1%)

regimes3.0ms (0%)

bsearch30.0ms (0.5%)

bsearch30.0ms (0.5%)

bsearch17.0ms (0.3%)

bsearch21.0ms (0.3%)

bsearch12.0ms (0.2%)

simplify8.0ms (0.1%)

soundness880.0ms (14.4%)

preprocess48.0ms (0.8%)

end0.0ms (0%)

Profiling