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

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)

sample611.0ms (22%)

Results

439.0ms

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 236.0ms

ival-add: 116.0ms (49.2% of total)

ival-mult: 110.0ms (46.6% of total)

const: 7.0ms (3% of total)

backward-pass: 3.0ms (1.3% of total)

Bogosity

preprocess56.0ms (2%)

Algorithm

2×	egg-herbie

Rules

844×	`sum5-define`
752×	`fnmadd-define`
752×	`sum4-define`
716×	`fmsub-define`
690×	`fnmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	34
1	62	33
2	187	32
3	640	30
4	1788	30
5	2819	30
6	3238	30
7	3312	30
0	5	5
1	12	5
2	17	5
3	20	5
4	21	5
0	21	5

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

Outputs
(+ (+ (* x x) y) y)
(sum3 (square x) y y)
(+ (+ (* (neg x) (neg x)) y) y)
(sum3 (square x) y y)
(+ (+ (* x x) (neg y)) (neg y))
(fma y -2 (square x))
(neg (+ (+ (* (neg x) (neg x)) y) y))
(fnmsub y 2 (square x))
(neg (+ (+ (* x x) (neg y)) (neg y)))
(fnmsub y -2 (square x))
(+ (+ (* y y) x) x)
(sum3 x x (square y))

Symmetry

(abs x)

explain70.0ms (2.5%)

FPErrors

Click to see full error table

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

Results

40.0ms

512×

valid

Compiler

Compiled 49 to 17 computations (65.3% saved)

Precisions

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

ival-mult: 13.0ms (69.1% of total)

ival-add: 5.0ms (26.6% of total)

const: 0.0ms (0% 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 (+.f64 (*.f64 x x) y) y)
▶	100.0%	(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))

Compiler

Compiled 18 to 11 computations (38.9% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

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

Rules

14×	`+-lowering-+.f64`
14×	`+-lowering-+.f32`
10×	`fma-define`
8×	`fma-lowering-fma.f32`
8×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	28
1	18	26
2	22	26
3	23	26
0	23	26

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize53.0ms (1.9%)

Localize:

Found 6 expressions of interest:

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

Results

21.0ms

256×

valid

Compiler

Compiled 36 to 9 computations (75% saved)

Precisions

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

ival-add: 4.0ms (50.6% of total)

ival-mult: 4.0ms (50.6% of total)

const: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Counts

5 → 96

Calls

Call 1

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

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

Calls

24 calls:

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

rewrite303.0ms (10.9%)

Algorithm

1×	batch-egg-rewrite

Rules

4020×	`-lowering-.f32`
4020×	`-lowering-.f64`
2944×	`/-lowering-/.f32`
2944×	`/-lowering-/.f64`
1414×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	52	19
2	511	19
0	8388	19

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 421

Calls

Call 1

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

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

simplify192.0ms (6.9%)

Algorithm

1×	egg-herbie

Rules

2330×	`fnmadd-define`
2012×	`fnmsub-define`
1894×	`-lowering-.f32`
1894×	`-lowering-.f64`
1878×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	426
1	85	351
2	221	351
3	736	351
4	2474	351
5	5878	351
0	8169	351

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

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

eval55.0ms (2%)

Compiler: Compiled 15304 to 822 computations (94.6% saved)

prune43.0ms (1.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	531	4	535
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	531	6	537

Accuracy

100.0%

Counts

537 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	45.5%	(+.f64 (/.f64 (-.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x)))) (-.f64 y (*.f64 x x))) y)
✓	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	100.0%	(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))
▶	57.9%	(+.f64 (*.f64 x x) y)
▶	51.9%	(+.f64 y y)
▶	50.0%	(*.f64 x x)

Compiler

Compiled 56 to 31 computations (44.6% saved)

simplify191.0ms (6.9%)

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 y y)
✓	cost-diff	0	(-.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x))))
✓	cost-diff	768	(/.f64 (-.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x)))) (-.f64 y (*.f64 x x)))
✓	cost-diff	768	(+.f64 (/.f64 (-.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x)))) (-.f64 y (*.f64 x x))) y)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(+.f64 (*.f64 x x) y)
✓	cost-diff	0	(+.f64 y y)
✓	cost-diff	0	(*.f64 x x)

Rules

2794×	`sum3-define`
1890×	`fma-lowering-fma.f32`
1890×	`fma-lowering-fma.f64`
1800×	`fnmsub-define`
1722×	`fmsub-define`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	12	60
1	38	54
2	81	54
3	181	48
4	414	47
5	1256	46
6	4281	46
0	8110	46

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize52.0ms (1.9%)

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(.f64 x (.f64 x (*.f64 x x)))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	92.9%	(-.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x))))
✓	accuracy	49.8%	(/.f64 (-.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x)))) (-.f64 y (*.f64 x x)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (*.f64 x x) y)
✓	accuracy	100.0%	(+.f64 y y)
✓	accuracy	100.0%	(*.f64 x x)

Results

34.0ms

256×

valid

Compiler

Compiled 93 to 13 computations (86% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-mult: 7.0ms (46.4% of total)

ival-add: 4.0ms (26.5% of total)

ival-sub: 2.0ms (13.3% of total)

ival-div: 2.0ms (13.3% of total)

const: 0.0ms (0% of total)

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

series31.0ms (1.1%)

Counts

9 → 156

Calls

Call 1

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

Outputs
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt (* 2 y)>
#<alt y>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt y>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (pow x 2)>
#<alt (- (* 2 y) (* -1 (pow x 2)))>
#<alt (- (* 2 y) (* -1 (pow x 2)))>
#<alt (- (* 2 y) (* -1 (pow x 2)))>
#<alt (* 2 y)>
#<alt (* y (+ 2 (/ (pow x 2) y)))>
#<alt (* y (- (+ 2 (* -1 (/ (+ (* -1 (pow x 4)) (pow x 4)) (pow y 2)))) (* -1 (/ (pow x 2) y))))>
#<alt (* y (- (+ 2 (* -1 (/ (+ (* -1 (pow x 4)) (pow x 4)) (pow y 2)))) (* -1 (/ (pow x 2) y))))>
#<alt (* 2 y)>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))>
#<alt (* 2 y)>
#<alt (+ (* 2 y) (pow x 2))>
#<alt (+ (* 2 y) (pow x 2))>
#<alt (+ (* 2 y) (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (* -1 (/ (pow y 2) (pow x 4))) (+ (* 2 (/ y (pow x 2))) (/ (pow y 2) (pow x 4))))))>
#<alt (* (pow x 2) (+ 1 (+ (* -1 (/ (pow y 2) (pow x 4))) (+ (* 2 (/ y (pow x 2))) (/ (pow y 2) (pow x 4))))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (* -1 (/ (pow y 2) (pow x 4))) (+ (* 2 (/ y (pow x 2))) (/ (pow y 2) (pow x 4))))))>
#<alt (* (pow x 2) (+ 1 (+ (* -1 (/ (pow y 2) (pow x 4))) (+ (* 2 (/ y (pow x 2))) (/ (pow y 2) (pow x 4))))))>
#<alt (pow x 2)>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt y>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt (* y (+ 1 (/ (pow x 2) y)))>
#<alt y>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt (* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))>
#<alt y>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (+ y (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ y (pow x 2))))>
#<alt (* -1 (pow x 4))>
#<alt (- (pow y 2) (pow x 4))>
#<alt (- (pow y 2) (pow x 4))>
#<alt (- (pow y 2) (pow x 4))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (* -1 (/ (pow x 4) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1 (* -1 (/ (pow x 4) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1 (* -1 (/ (pow x 4) (pow y 2)))))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (* -1 (/ (pow x 4) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1 (* -1 (/ (pow x 4) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1 (* -1 (/ (pow x 4) (pow y 2)))))>
#<alt (pow y 2)>
#<alt (+ (* -1 (pow x 4)) (pow y 2))>
#<alt (+ (* -1 (pow x 4)) (pow y 2))>
#<alt (+ (* -1 (pow x 4)) (pow y 2))>
#<alt (* -1 (pow x 4))>
#<alt (* (pow x 4) (- (/ (pow y 2) (pow x 4)) 1))>
#<alt (* (pow x 4) (- (/ (pow y 2) (pow x 4)) 1))>
#<alt (* (pow x 4) (- (/ (pow y 2) (pow x 4)) 1))>
#<alt (* -1 (pow x 4))>
#<alt (* (pow x 4) (- (/ (pow y 2) (pow x 4)) 1))>
#<alt (* (pow x 4) (- (/ (pow y 2) (pow x 4)) 1))>
#<alt (* (pow x 4) (- (/ (pow y 2) (pow x 4)) 1))>
#<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 (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>

Calls

39 calls:

Time	Variable		Point	Expression
21.0ms	x	@	inf	(+ (/ (- (* y y) (* x (* x (* x x)))) (- y (* x x))) y)
2.0ms	y	@	0	(+ (/ (- (* y y) (* x (* x (* x x)))) (- y (* x x))) y)
1.0ms	y	@	inf	(/ (- (* y y) (* x (* x (* x x)))) (- y (* x x)))
1.0ms	x	@	0	(+ (/ (- (* y y) (* x (* x (* x x)))) (- y (* x x))) y)
1.0ms	y	@	inf	(+ (/ (- (* y y) (* x (* x (* x x)))) (- y (* x x))) y)

rewrite81.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

452×	`-lowering-.f32`
452×	`-lowering-.f64`
390×	`/-lowering-/.f32`
390×	`/-lowering-/.f64`
246×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	46
1	104	33
0	931	33

Stop Event

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

Counts

9 → 151

Calls

Call 1

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

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

simplify219.0ms (7.9%)

Algorithm

1×	egg-herbie

Rules

2022×	`-lowering-.f32`
2022×	`-lowering-.f64`
1906×	`--lowering--.f32`
1906×	`--lowering--.f64`
1434×	`unsub-neg`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	711
1	175	585
2	533	585
3	2248	585
4	7484	585
0	8428	585

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

Calls

Call 1

Inputs
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
(* 2 y)
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(pow x 2)
(- (* 2 y) (* -1 (pow x 2)))
(- (* 2 y) (* -1 (pow x 2)))
(- (* 2 y) (* -1 (pow x 2)))
(* 2 y)
(* y (+ 2 (/ (pow x 2) y)))
(* y (- (+ 2 (* -1 (/ (+ (* -1 (pow x 4)) (pow x 4)) (pow y 2)))) (* -1 (/ (pow x 2) y))))
(* y (- (+ 2 (* -1 (/ (+ (* -1 (pow x 4)) (pow x 4)) (pow y 2)))) (* -1 (/ (pow x 2) y))))
(* 2 y)
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 2)))
(* 2 y)
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(+ (* 2 y) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* -1 (/ (pow y 2) (pow x 4))) (+ (* 2 (/ y (pow x 2))) (/ (pow y 2) (pow x 4))))))
(* (pow x 2) (+ 1 (+ (* -1 (/ (pow y 2) (pow x 4))) (+ (* 2 (/ y (pow x 2))) (/ (pow y 2) (pow x 4))))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ y (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* -1 (/ (pow y 2) (pow x 4))) (+ (* 2 (/ y (pow x 2))) (/ (pow y 2) (pow x 4))))))
(* (pow x 2) (+ 1 (+ (* -1 (/ (pow y 2) (pow x 4))) (+ (* 2 (/ y (pow x 2))) (/ (pow y 2) (pow x 4))))))
(pow x 2)
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
y
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (/ (pow x 2) y)))
y
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
(* -1 (* y (- (* -1 (/ (pow x 2) y)) 1)))
y
(+ y (pow x 2))
(+ y (pow x 2))
(+ y (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* (pow x 2) (+ 1 (/ y (pow x 2))))
(* -1 (pow x 4))
(- (pow y 2) (pow x 4))
(- (pow y 2) (pow x 4))
(- (pow y 2) (pow x 4))
(pow y 2)
(* (pow y 2) (+ 1 (* -1 (/ (pow x 4) (pow y 2)))))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 4) (pow y 2)))))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 4) (pow y 2)))))
(pow y 2)
(* (pow y 2) (+ 1 (* -1 (/ (pow x 4) (pow y 2)))))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 4) (pow y 2)))))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 4) (pow y 2)))))
(pow y 2)
(+ (* -1 (pow x 4)) (pow y 2))
(+ (* -1 (pow x 4)) (pow y 2))
(+ (* -1 (pow x 4)) (pow y 2))
(* -1 (pow x 4))
(* (pow x 4) (- (/ (pow y 2) (pow x 4)) 1))
(* (pow x 4) (- (/ (pow y 2) (pow x 4)) 1))
(* (pow x 4) (- (/ (pow y 2) (pow x 4)) 1))
(* -1 (pow x 4))
(* (pow x 4) (- (/ (pow y 2) (pow x 4)) 1))
(* (pow x 4) (- (/ (pow y 2) (pow x 4)) 1))
(* (pow x 4) (- (/ (pow y 2) (pow x 4)) 1))
(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)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)

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

eval35.0ms (1.3%)

Compiler: Compiled 6809 to 436 computations (93.6% saved)

prune25.0ms (0.9%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	354	1	355
Fresh	0	0	0
Picked	0	4	4
Done	0	2	2
Total	354	7	361

Accuracy

100.0%

Counts

361 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	45.5%	(+.f64 (/.f64 (-.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x)))) (-.f64 y (*.f64 x x))) y)
✓	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	100.0%	(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))
✓	57.9%	(+.f64 (*.f64 x x) y)
✓	51.9%	(+.f64 y y)
✓	50.0%	(*.f64 x x)
▶	11.0%	y

Compiler

Compiled 59 to 33 computations (44.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
y

Outputs
y

localize26.0ms (0.9%)

Results

11.0ms

256×

valid

Compiler

Compiled 4 to 3 computations (25% saved)

Precisions

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

const: 0.0ms (0% of total)

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

series0.0ms (0%)

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

rewrite10.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
0	0	0

Stop Event

1×	saturated
1×	saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune4.0ms (0.2%)

Pruning

7 alts after pruning (0 fresh and 7 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	6	6
Total	7	7

Accuracy

100.0%

Counts

7 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	45.5%	(+.f64 (/.f64 (-.f64 (.f64 y y) (.f64 x (.f64 x (.f64 x x)))) (-.f64 y (*.f64 x x))) y)
✓	100.0%	(+.f64 (+.f64 (*.f64 x x) y) y)
✓	100.0%	(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))
✓	57.9%	(+.f64 (*.f64 x x) y)
✓	51.9%	(+.f64 y y)
✓	50.0%	(*.f64 x x)
✓	11.0%	y

Compiler

Compiled 106 to 49 computations (53.8% saved)

regimes13.0ms (0.5%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 20 to 12 computations (40% saved)

regimes7.0ms (0.2%)

Counts

4 → 2

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
90.9%	2	`x`
69.9%	3	`y`
90.9%	2	`(*.f64 x x)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes4.0ms (0.1%)

Counts

3 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
89.8%	2	`x`
89.8%	2	`(*.f64 x x)`

Compiler

Compiled 8 to 5 computations (37.5% saved)

regimes6.0ms (0.2%)

Counts

2 → 2

Calls

Call 1

Inputs
y
(*.f64 x x)

Outputs
y
(*.f64 x x)

Calls

3 calls:

3.0ms	x
2.0ms	y
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
50.0%	1	`y`
55.4%	2	`x`
55.4%	2	`(*.f64 x x)`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes3.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
y

Outputs
y

Calls

2 calls:

1.0ms	x
1.0ms	y

Results

Accuracy	Segments	Branch
11.0%	1	`y`
11.0%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch9.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
8.0ms	3.070192068223197e-89	6.730328280477576e-86

Results

4.0ms

128×

valid

Compiler

Compiled 110 to 73 computations (33.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-add: 1.0ms (69.7% of total)

const: 0.0ms (0% of total)

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

bsearch12.0ms (0.4%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	3.070192068223197e-89	6.730328280477576e-86

Results

8.0ms

128×

valid

Compiler

Compiled 94 to 65 computations (30.9% saved)

Precisions

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

ival-add: 1.0ms (66.7% of total)

const: 0.0ms (0% of total)

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

bsearch8.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
7.0ms	2.8407890409703527e-139	4.681816072668503e-137

Results

4.0ms

112×

valid

Compiler

Compiled 70 to 51 computations (27.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

ival-add: 1.0ms (78.9% of total)

const: 0.0ms (0% of total)

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

simplify10.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	44
1	20	44

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))
(if (<=.f64 (.f64 x x) #s(literal 8958978968711217/139984046386112763159840142535527767382602843577165595931249318810236991948760059086304843329475444736 binary64)) (+.f64 y y) (+.f64 (.f64 x x) y))
(if (<=.f64 (.f64 x x) #s(literal 5039425669900059/139984046386112763159840142535527767382602843577165595931249318810236991948760059086304843329475444736 binary64)) (+.f64 y y) (.f64 x x))
(if (<=.f64 (.f64 x x) #s(literal 3888264299683353/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096 binary64)) y (.f64 x x))
y

Outputs
(+.f64 (.f64 x x) (.f64 y #s(literal 2 binary64)))
(if (<=.f64 (.f64 x x) #s(literal 8958978968711217/139984046386112763159840142535527767382602843577165595931249318810236991948760059086304843329475444736 binary64)) (+.f64 y y) (+.f64 (.f64 x x) y))
(if (<=.f64 (.f64 x x) #s(literal 5039425669900059/139984046386112763159840142535527767382602843577165595931249318810236991948760059086304843329475444736 binary64)) (+.f64 y y) (.f64 x x))
(if (<=.f64 (.f64 x x) #s(literal 3888264299683353/13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096 binary64)) y (.f64 x x))
y

soundness580.0ms (20.9%)

Rules

2330×	`fnmadd-define`
2022×	`-lowering-.f32`
2022×	`-lowering-.f64`
2012×	`fnmsub-define`
1906×	`--lowering--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	711
1	175	585
2	533	585
3	2248	585
4	7484	585
0	8428	585
0	27	426
1	85	351
2	221	351
3	736	351
4	2474	351
5	5878	351
0	8169	351
0	5	5
1	12	5
2	17	5
3	20	5
4	21	5
0	21	5

Stop Event

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

Compiler

Compiled 120 to 63 computations (47.5% saved)

preprocess41.0ms (1.5%)

Remove: (abs x)
Compiler: Compiled 164 to 78 computations (52.4% saved)

analyze0.0ms (0%)

sample611.0ms (22%)

preprocess56.0ms (2%)

explain70.0ms (2.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.2%)

localize53.0ms (1.9%)

series4.0ms (0.1%)

rewrite303.0ms (10.9%)

simplify192.0ms (6.9%)

eval55.0ms (2%)

prune43.0ms (1.5%)

simplify191.0ms (6.9%)

localize52.0ms (1.9%)

series31.0ms (1.1%)

rewrite81.0ms (2.9%)

simplify219.0ms (7.9%)

eval35.0ms (1.3%)

prune25.0ms (0.9%)

simplify4.0ms (0.1%)

localize26.0ms (0.9%)

series0.0ms (0%)

rewrite10.0ms (0.4%)

simplify9.0ms (0.3%)

eval0.0ms (0%)

prune4.0ms (0.2%)

regimes13.0ms (0.5%)

regimes7.0ms (0.2%)

regimes4.0ms (0.1%)

regimes6.0ms (0.2%)

regimes3.0ms (0.1%)

bsearch9.0ms (0.3%)

bsearch12.0ms (0.4%)

bsearch8.0ms (0.3%)

simplify10.0ms (0.4%)

soundness580.0ms (20.9%)

preprocess41.0ms (1.5%)

end0.0ms (0%)

Profiling