Metrics for Data.Number.Erf:$cinvnormcdf from erf-2.0.0.0, B

analyze52.0ms (0.6%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
62.5%	62.4%	37.5%	0.1%	0%	0%	0%	5
68.8%	68.7%	31.2%	0.1%	0%	0%	0%	6
78.1%	78%	21.9%	0.1%	0%	0%	0%	7
82.8%	82.7%	17.2%	0.1%	0%	0%	0%	8
88.3%	88.2%	11.7%	0.1%	0%	0%	0%	9
91%	90.9%	9%	0.1%	0%	0%	0%	10
93.9%	93.9%	6%	0.1%	0%	0%	0%	11
95.4%	95.3%	4.6%	0.1%	0%	0%	0%	12

Compiler

Compiled 14 to 10 computations (28.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-div: 28.0ms (78.7% of total)

ival-mult: 3.0ms (8.4% of total)

ival-sub: 2.0ms (5.6% of total)

ival-add: 2.0ms (5.6% of total)

const: 1.0ms (2.8% of total)

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

sample903.0ms (9.7%)

Results

658.0ms	8254×	0	valid
0.0ms	1×	3	valid
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 399.0ms

ival-div: 177.0ms (44.4% of total)

ival-sub: 83.0ms (20.8% of total)

ival-mult: 77.0ms (19.3% of total)

ival-add: 45.0ms (11.3% of total)

const: 14.0ms (3.5% of total)

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

Bogosity

preprocess121.0ms (1.3%)

Algorithm

2×	egg-herbie

Rules

1168×	`fnmadd-define`
848×	`fnmsub-define`
820×	`fmsub-define`
732×	`fnmadd-define`
714×	`fma-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	74
1	65	66
2	138	62
3	302	60
4	849	60
5	2164	60
6	3360	60
7	3876	60
8	3910	60
9	3950	60
10	3966	60
0	9	11
1	17	10
2	29	10
3	47	10
4	96	10
5	209	10
6	507	10
7	796	10
8	1252	10
9	1830	10
10	2285	10
11	2341	10
12	2590	10
13	2697	10
14	2705	10
0	2705	10

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

Outputs
(- x (/ y (+ 1 (/ (* x y) 2))))
(+ x (/ y (fnmsub x (* y 1/2) 1)))
(- (neg x) (/ y (+ 1 (/ (* (neg x) y) 2))))
(- (/ y (fnmsub x (* y -1/2) 1)) x)
(- x (/ (neg y) (+ 1 (/ (* x (neg y)) 2))))
(+ x (/ y (fnmsub x (* y 1/2) -1)))
(neg (- (neg x) (/ y (+ 1 (/ (* (neg x) y) 2)))))
(+ x (/ y (fnmsub x (* y 1/2) -1)))
(neg (- x (/ (neg y) (+ 1 (/ (* x (neg y)) 2)))))
(- (/ y (fnmsub x (* y -1/2) 1)) x)
(- y (/ x (+ 1 (/ (* y x) 2))))
(+ y (/ x (fnmsub x (* y 1/2) 1)))

explain104.0ms (1.1%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
29	-	-	`(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))`
0	-	-	`x`
0	-	-	`#s(literal 2 binary64)`
0	-	-	`y`
0	-	-	`(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))`
0	-	-	`(*.f64 x y)`
0	-	-	`(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))`
0	-	-	`(/.f64 (*.f64 x y) #s(literal 2 binary64))`
0	-	-	`#s(literal 1 binary64)`

Results

67.0ms

512×

valid

Compiler

Compiled 97 to 29 computations (70.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-mult: 14.0ms (37.3% of total)

ival-sub: 10.0ms (26.6% of total)

ival-div: 9.0ms (24% of total)

ival-add: 3.0ms (8% of total)

const: 1.0ms (2.7% of total)

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

eval18.0ms (0.2%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))

Compiler

Compiled 13 to 9 computations (30.8% saved)

simplify61.0ms (0.7%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(/.f64 (*.f64 x y) #s(literal 2 binary64))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))
✓	cost-diff	(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))
✓	cost-diff	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))

Rules

732×	`fnmadd-define`
558×	`fmsub-define`
540×	`fnmsub-define`
484×	`fmm-def`
444×	`sum3-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	39
1	17	36
2	29	36
3	47	36
4	96	36
5	209	36
6	507	36
7	796	36
8	1252	36
9	1830	36
10	2285	36
11	2341	36
12	2590	36
13	2697	36
14	2705	36
0	2705	36

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize41.0ms (0.4%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x y)
✓	accuracy	100.0%	(/.f64 (*.f64 x y) #s(literal 2 binary64))
✓	accuracy	100.0%	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
✓	accuracy	89.4%	(/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))

Results

27.0ms

256×

valid

Compiler

Compiled 42 to 10 computations (76.2% saved)

Precisions

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

ival-div: 7.0ms (56.8% of total)

ival-mult: 2.0ms (16.2% of total)

ival-sub: 1.0ms (8.1% of total)

ival-add: 1.0ms (8.1% of total)

const: 0.0ms (0% of total)

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

series11.0ms (0.1%)

Counts

5 → 120

Calls

Call 1

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

Outputs
#<alt (* -1 y)>
#<alt (- (* x (+ 1 (* 1/2 (pow y 2)))) y)>
#<alt (- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)>
#<alt (- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)>
#<alt x>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))>
#<alt x>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* y (- (* 1/2 (* x y)) 1)))>
#<alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))>
#<alt (- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt y>
#<alt (* y (+ 1 (* -1/2 (* x y))))>
#<alt (* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))>
#<alt (* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))>
#<alt (- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))>
#<alt y>
#<alt (+ y (* -1/2 (* x (pow y 2))))>
#<alt (+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))>
#<alt (+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))>
#<alt (/ 2 x)>
#<alt (/ (- 2 (* 4 (/ 1 (* x y)))) x)>
#<alt (/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)>
#<alt (/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)>
#<alt (/ 2 x)>
#<alt (* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))>
#<alt 1>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* x (+ (* 1/2 y) (/ 1 x)))>
#<alt (* x (+ (* 1/2 y) (/ 1 x)))>
#<alt (* x (+ (* 1/2 y) (/ 1 x)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* x (- (* -1/2 y) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1/2 y) (/ 1 x))))>
#<alt (* -1 (* x (- (* -1/2 y) (/ 1 x))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (+ 1 (* 1/2 (* x y)))>
#<alt (* 1/2 (* x y))>
#<alt (* y (+ (* 1/2 x) (/ 1 y)))>
#<alt (* y (+ (* 1/2 x) (/ 1 y)))>
#<alt (* y (+ (* 1/2 x) (/ 1 y)))>
#<alt (* 1/2 (* x y))>
#<alt (* -1 (* y (- (* -1/2 x) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1/2 x) (/ 1 y))))>
#<alt (* -1 (* y (- (* -1/2 x) (/ 1 y))))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* 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

30 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(+ 1 (/ (* x y) 2))
1.0ms	y	@	inf	(- x (/ y (+ 1 (/ (* x y) 2))))
0.0ms	x	@	inf	(- x (/ y (+ 1 (/ (* x y) 2))))
0.0ms	y	@	-inf	(- x (/ y (+ 1 (/ (* x y) 2))))
0.0ms	x	@	0	(- x (/ y (+ 1 (/ (* x y) 2))))

rewrite470.0ms (5.1%)

Algorithm

1×	batch-egg-rewrite

Rules

4140×	`-lowering-.f32`
4140×	`-lowering-.f64`
2970×	`/-lowering-/.f32`
2970×	`/-lowering-/.f64`
1742×	`sum5-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	35
1	58	32
2	518	32
3	7497	32
0	8368	32

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 224

Calls

Call 1

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

Outputs
(+.f64 x (/.f64 y (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
(+.f64 (/.f64 y (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) x)
(+.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x x) (.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))))))) (neg.f64 (/.f64 (/.f64 (/.f64 (.f64 y y) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (/.f64 (.f64 (-.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) y)) (+.f64 (.f64 x x) (.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))))))))
(+.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))))) (neg.f64 (/.f64 (/.f64 y (/.f64 (.f64 (-.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) y)) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))))))
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
(-.f64 #s(literal 0 binary64) (-.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) x))
(-.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x x) (.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))))))) (/.f64 (/.f64 (/.f64 (.f64 y y) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (/.f64 (.f64 (-.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) y)) (+.f64 (.f64 x x) (.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))))))
(-.f64 (/.f64 (.f64 x x) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))))) (/.f64 (/.f64 y (/.f64 (.f64 (-.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) y)) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))))))
(-.f64 (+.f64 x #s(literal 0 binary64)) (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
(fma.f64 y (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) x)
(fma.f64 (-.f64 #s(literal 0 binary64) y) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) x)
(fma.f64 #s(literal -1 binary64) (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) x)
(neg.f64 (/.f64 (-.f64 (.f64 x (.f64 x x)) (/.f64 (/.f64 (.f64 y y) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (/.f64 (.f64 (-.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) y))) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) (.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (+.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))))))))
(neg.f64 (/.f64 (+.f64 (.f64 x x) (/.f64 (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (/.f64 (-.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) y))) (+.f64 (/.f64 y (-.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) x))))
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(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64)))) (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64))))))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) (/.f64 #s(literal -4 binary64) (.f64 x y)))) (-.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) (/.f64 #s(literal -4 binary64) (.f64 x y)))) (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) (/.f64 #s(literal -4 binary64) (.f64 x y)))) (neg.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
(/.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64))))) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64))))))
(/.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64))))) (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64)))))))
(/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) (/.f64 #s(literal 4 binary64) (.f64 x y)))) (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))
(/.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) (/.f64 #s(literal 4 binary64) (.f64 x y)))) (.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64))) (.f64 (.f64 (.f64 (.f64 x y) (.f64 x (.f64 y (.f64 x y)))) (.f64 (.f64 x y) (.f64 x (.f64 y (.f64 x y))))) #s(literal 1/64 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64))) (-.f64 (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64))) #s(literal 1 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x y) (.f64 x (.f64 y (.f64 x y)))) (.f64 (.f64 x y) (.f64 x (.f64 y (.f64 x y))))) #s(literal 1/64 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64))))))
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(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (.f64 (/.f64 (/.f64 (.f64 x y) (/.f64 #s(literal 4 binary64) (.f64 x y))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (/.f64 (/.f64 (.f64 x y) (/.f64 #s(literal 4 binary64) (.f64 x y))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))))) (+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (/.f64 (/.f64 (.f64 x y) (/.f64 #s(literal 4 binary64) (.f64 x y))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64)))) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64)))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) (/.f64 #s(literal -4 binary64) (.f64 x y)))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64))) (.f64 (.f64 (.f64 (.f64 x y) (.f64 x (.f64 y (.f64 x y)))) (.f64 (.f64 x y) (.f64 x (.f64 y (.f64 x y))))) #s(literal 1/64 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64))) (-.f64 (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64))) #s(literal 1 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x y) (.f64 x (.f64 y (.f64 x y)))) (.f64 (.f64 x y) (.f64 x (.f64 y (.f64 x y))))) #s(literal 1/64 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64)))))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (.f64 x y) (.f64 x (.f64 y (.f64 x y)))) (.f64 (.f64 x y) (.f64 x (.f64 y (.f64 x y))))) #s(literal 1/64 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 x y) (/.f64 #s(literal 4 binary64) (.f64 x y))) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) (/.f64 #s(literal 4 binary64) (*.f64 x y)))))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x (.f64 y (.f64 x y))) (.f64 x (.f64 y (.f64 x y)))) #s(literal 1/16 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) (/.f64 #s(literal 4 binary64) (.f64 x y)))))
(pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64))))) #s(literal 1 binary64)))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) (/.f64 #s(literal -4 binary64) (.f64 x y)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) (/.f64 #s(literal -4 binary64) (.f64 x y)))) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) #s(literal 1 binary64)))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))
(.f64 (+.f64 #s(literal -1 binary64) (neg.f64 (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64)))))))
(.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) (/.f64 #s(literal 4 binary64) (.f64 x y)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) (/.f64 #s(literal -4 binary64) (.f64 x y)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64)))))
(.f64 (+.f64 (/.f64 (.f64 x y) (/.f64 #s(literal 4 binary64) (.f64 x y))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal -1 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) (/.f64 #s(literal -4 binary64) (.f64 x y)))) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) (/.f64 #s(literal -4 binary64) (.f64 x y))))) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64))) (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64))))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64))) (-.f64 (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64))) #s(literal 1 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64))) (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64)))))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x y) (-.f64 (.f64 #s(literal 1/4 binary64) (*.f64 x y)) #s(literal 1/2 binary64)))))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) (/.f64 #s(literal -4 binary64) (.f64 x y)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 y (.f64 y y)) #s(literal 8 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x y) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x y)) #s(literal 1/2 binary64)))))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 2 binary64) (.f64 x y))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 x y) #s(literal -2 binary64)))
(neg.f64 (/.f64 (*.f64 x y) #s(literal -2 binary64)))
(/.f64 x (/.f64 #s(literal 2 binary64) y))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (*.f64 x y)))
(/.f64 (*.f64 x y) #s(literal 2 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 x y)) #s(literal -2 binary64))
(/.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x y)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x y)))
(pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal -1 binary64))
(*.f64 x (/.f64 y #s(literal 2 binary64)))
(.f64 x (.f64 (/.f64 y #s(literal 2 binary64)) #s(literal 1 binary64)))
(*.f64 y (/.f64 x #s(literal 2 binary64)))
(.f64 y (.f64 (/.f64 x #s(literal 2 binary64)) #s(literal 1 binary64)))
(.f64 y (.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64)))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 x y) #s(literal 2 binary64)))
(.f64 (.f64 x y) #s(literal 1/2 binary64))
(.f64 (/.f64 (.f64 x y) #s(literal 2 binary64)) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 x y)) #s(literal -1/2 binary64))
(.f64 (-.f64 #s(literal 0 binary64) y) (.f64 x #s(literal -1/2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) y) (/.f64 x #s(literal -2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 x y))
(.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x y)) #s(literal -1 binary64)))
(*.f64 (/.f64 y #s(literal 2 binary64)) x)
(.f64 #s(literal -1 binary64) (/.f64 (.f64 x y) #s(literal -2 binary64)))
(.f64 #s(literal -1/2 binary64) (-.f64 #s(literal 0 binary64) (.f64 x y)))
(*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 y #s(literal -2 binary64)))
(.f64 (-.f64 #s(literal 0 binary64) x) (.f64 y #s(literal -1/2 binary64)))
(*.f64 (/.f64 x #s(literal 2 binary64)) y)
(.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (.f64 x y)) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (*.f64 x y)) #s(literal -1/2 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x y)))
(neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x y)))
(*.f64 x y)
(*.f64 y x)
(*.f64 y (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(.f64 #s(literal 1 binary64) (.f64 x y))
(.f64 (.f64 x y) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) y) (-.f64 #s(literal 0 binary64) x))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x y)))
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) y))
(*.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) y)

simplify292.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

3952×	`-lowering-.f32`
3952×	`-lowering-.f64`
1762×	`/-lowering-/.f32`
1762×	`/-lowering-/.f64`
1656×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	231	1040
1	826	982
2	2365	947
3	7863	947
0	8125	947

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

Calls

Call 1

Inputs
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(/ 2 x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/ 2 x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(* 1/2 (* x y))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 x)))
(* x (+ (* 1/2 y) (/ 1 x)))
(* 1/2 (* x y))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
1
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(+ 1 (* 1/2 (* x y)))
(* 1/2 (* x y))
(* y (+ (* 1/2 x) (/ 1 y)))
(* y (+ (* 1/2 x) (/ 1 y)))
(* y (+ (* 1/2 x) (/ 1 y)))
(* 1/2 (* x y))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* 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
(* -1 y)
(-.f64 #s(literal 0 binary64) y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 y y)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 y y) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/4 binary64) (*.f64 y x)))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
(-.f64 (.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 y y) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/4 binary64) (.f64 y x))))) (.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 x (.f64 x #s(literal 1/8 binary64)))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 4 binary64) (.f64 y (.f64 x x))) x)))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(.f64 x (-.f64 (+.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 4 binary64) (.f64 y (.f64 x x))) x)) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (/.f64 #s(literal 8 binary64) (.f64 y (.f64 y (pow.f64 x #s(literal 4 binary64))))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))) (/.f64 (/.f64 #s(literal 4 binary64) (.f64 y (.f64 x x))) x)))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(+.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x)))) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 x (.f64 y y)))) (*.f64 x x)))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 y y)))) y)
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 y y) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/4 binary64) (*.f64 y x)))))) y)
(- x (* 2 (/ 1 x)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(+.f64 x (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(+.f64 x (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 x (.f64 y y)))) x)) x))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(+.f64 x (+.f64 (/.f64 #s(literal 16 binary64) (.f64 y (.f64 y (.f64 y (pow.f64 x #s(literal 4 binary64)))))) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 x (*.f64 y y)))) x)) x)))
(- x (* 2 (/ 1 x)))
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(+.f64 x (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(+.f64 x (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 #s(literal -8 binary64) (.f64 x (.f64 y y)))) x)) x))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(-.f64 (-.f64 x (/.f64 #s(literal 2 binary64) x)) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal -16 binary64) (.f64 y (pow.f64 x #s(literal 4 binary64))))) y) (/.f64 #s(literal -4 binary64) (.f64 x x))) y))
y
(* y (+ 1 (* -1/2 (* x y))))
(.f64 y (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 y #s(literal -1/2 binary64)))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(+.f64 y (.f64 x (.f64 (.f64 y y) (+.f64 (.f64 #s(literal 1/4 binary64) (*.f64 y x)) #s(literal -1/2 binary64)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(.f64 y (+.f64 #s(literal 1 binary64) (.f64 y (+.f64 (.f64 y (+.f64 (.f64 (.f64 #s(literal -1/8 binary64) (.f64 y (.f64 x x))) x) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) (.f64 x #s(literal -1/2 binary64))))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 x (.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(+.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 x (.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x) (/.f64 (/.f64 #s(literal -16 binary64) (.f64 y (pow.f64 x #s(literal 4 binary64)))) (.f64 y y)))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 x (.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal -16 binary64) (.f64 y (pow.f64 x #s(literal 4 binary64))))) y) (/.f64 #s(literal -4 binary64) (.f64 x x))) y))
y
(+ y (* -1/2 (* x (pow y 2))))
(.f64 y (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 y #s(literal -1/2 binary64)))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+.f64 y (.f64 x (.f64 (.f64 y y) (+.f64 (.f64 #s(literal 1/4 binary64) (*.f64 y x)) #s(literal -1/2 binary64)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(+.f64 y (.f64 x (+.f64 (.f64 x (.f64 (.f64 x (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64))) (.f64 (.f64 y y) (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 y x)) #s(literal -1/2 binary64))))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 x (.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 x (.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x) (+.f64 #s(literal 2 binary64) (/.f64 #s(literal -16 binary64) (.f64 (.f64 x (.f64 y (.f64 y y))) (*.f64 x x))))) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 x (.f64 y y))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 y y)) (/.f64 #s(literal -16 binary64) (.f64 x (.f64 y (.f64 y y))))) x) (/.f64 #s(literal -4 binary64) y)) x)) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (.f64 y (.f64 x #s(literal 1/2 binary64))))
(+ 1 (* 1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (.f64 y (.f64 x #s(literal 1/2 binary64))))
(+ 1 (* 1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (.f64 y (.f64 x #s(literal 1/2 binary64))))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* x (+ (* 1/2 y) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (.f64 y (.f64 x #s(literal 1/2 binary64))))
(* x (+ (* 1/2 y) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (.f64 y (.f64 x #s(literal 1/2 binary64))))
(* x (+ (* 1/2 y) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (.f64 y (.f64 x #s(literal 1/2 binary64))))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (.f64 x (*.f64 y #s(literal -1/2 binary64)))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (.f64 x (*.f64 y #s(literal -1/2 binary64)))))
(* -1 (* x (- (* -1/2 y) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (.f64 x (*.f64 y #s(literal -1/2 binary64)))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (.f64 y (.f64 x #s(literal 1/2 binary64))))
(+ 1 (* 1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (.f64 y (.f64 x #s(literal 1/2 binary64))))
(+ 1 (* 1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (.f64 y (.f64 x #s(literal 1/2 binary64))))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* y (+ (* 1/2 x) (/ 1 y)))
(+.f64 #s(literal 1 binary64) (.f64 y (.f64 x #s(literal 1/2 binary64))))
(* y (+ (* 1/2 x) (/ 1 y)))
(+.f64 #s(literal 1 binary64) (.f64 y (.f64 x #s(literal 1/2 binary64))))
(* y (+ (* 1/2 x) (/ 1 y)))
(+.f64 #s(literal 1 binary64) (.f64 y (.f64 x #s(literal 1/2 binary64))))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (.f64 x (*.f64 y #s(literal -1/2 binary64)))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (.f64 x (*.f64 y #s(literal -1/2 binary64)))))
(* -1 (* y (- (* -1/2 x) (/ 1 y))))
(+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (.f64 x (*.f64 y #s(literal -1/2 binary64)))))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 binary64)))
(* 1/2 (* x y))
(.f64 y (.f64 x #s(literal 1/2 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)

eval41.0ms (0.4%)

Compiler: Compiled 10128 to 987 computations (90.3% saved)

prune42.0ms (0.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	338	6	344
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	338	7	345

Accuracy

100.0%

Counts

345 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(-.f64 x (/.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) y)))
✓	99.9%	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
	64.1%	(-.f64 x (/.f64 y (.f64 y (.f64 x #s(literal 1/2 binary64)))))
▶	64.1%	(-.f64 x (/.f64 #s(literal 2 binary64) x))
▶	75.7%	(-.f64 x y)
▶	61.2%	(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
▶	64.7%	x

Compiler

Compiled 121 to 83 computations (31.4% saved)

simplify161.0ms (1.7%)

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(/.f64 #s(literal -2 binary64) (*.f64 x x))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x)))
✓	cost-diff	256	(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) x)
✓	cost-diff	0	(-.f64 x (/.f64 #s(literal 2 binary64) x))
✓	cost-diff	0	(-.f64 x y)
✓	cost-diff	0	(-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))
✓	cost-diff	0	(/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))
✓	cost-diff	256	(/.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) y))
✓	cost-diff	256	(-.f64 x (/.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) y)))

Rules

1926×	`sum3-define`
1412×	`fnmadd-define`
1272×	`fma-define`
1262×	`-lowering-.f32`
1262×	`-lowering-.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	20	96
1	48	94
2	120	88
3	392	87
4	964	83
5	3147	81
6	7197	81
0	8385	81

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize76.0ms (0.8%)

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.5%	(/.f64 #s(literal -2 binary64) (*.f64 x x))
✓	accuracy	77.7%	(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
✓	accuracy	100.0%	(/.f64 #s(literal 2 binary64) x)
✓	accuracy	100.0%	(-.f64 x (/.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(-.f64 x y)
✓	accuracy	100.0%	(/.f64 (*.f64 x y) #s(literal 2 binary64))
✓	accuracy	100.0%	(-.f64 x (/.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) y)))
✓	accuracy	99.6%	(/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64))))
✓	accuracy	89.4%	(/.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) y))

Results

49.0ms

256×

valid

Compiler

Compiled 106 to 21 computations (80.2% saved)

Precisions

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

ival-div: 10.0ms (43.3% of total)

ival-mult: 6.0ms (26% of total)

ival-sub: 5.0ms (21.6% of total)

ival-add: 1.0ms (4.3% of total)

const: 1.0ms (4.3% of total)

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

series33.0ms (0.4%)

Counts

12 → 216

Calls

Call 1

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

Outputs
#<alt (* -1 y)>
#<alt (- (* x (+ 1 (* 1/2 (pow y 2)))) y)>
#<alt (- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)>
#<alt (- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)>
#<alt x>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))>
#<alt x>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* y (- (* 1/2 (* x y)) 1)))>
#<alt (+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))>
#<alt (- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))>
#<alt (- x (* 2 (/ 1 x)))>
#<alt (- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt (- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))>
#<alt y>
#<alt (+ y (* -1/2 (* x (pow y 2))))>
#<alt (+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))>
#<alt (+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))>
#<alt (/ 2 x)>
#<alt (/ (- 2 (* 4 (/ 1 (* x y)))) x)>
#<alt (/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)>
#<alt (/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)>
#<alt (/ 2 x)>
#<alt (* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))>
#<alt y>
#<alt (* y (+ 1 (* -1/2 (* x y))))>
#<alt (* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))>
#<alt (* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))>
#<alt (- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))>
#<alt (/ 2 x)>
#<alt (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))>
#<alt (+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))>
#<alt (+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* x y)))>
#<alt (+ 1 (* x (- (* 1/4 (* x (pow y 2))) (* 1/2 y))))>
#<alt (+ 1 (* x (- (* x (- (* -1/8 (* x (pow y 3))) (* -1/4 (pow y 2)))) (* 1/2 y))))>
#<alt (/ 2 (* x y))>
#<alt (/ (- (* 2 (/ 1 y)) (* 4 (/ 1 (* x (pow y 2))))) x)>
#<alt (/ (- (+ (* 2 (/ 1 y)) (/ 8 (* (pow x 2) (pow y 3)))) (/ 4 (* x (pow y 2)))) x)>
#<alt (/ (- (+ (* 2 (/ 1 y)) (* 8 (/ 1 (* (pow x 2) (pow y 3))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 4)))) (/ 4 (* x (pow y 2))))) x)>
#<alt (/ 2 (* x y))>
#<alt (* -1 (/ (- (* 4 (/ 1 (* x (pow y 2)))) (* 2 (/ 1 y))) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 3)))) (* 4 (/ 1 (pow y 2)))) x)) (* 2 (/ 1 y))) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 4)))) (* 8 (/ 1 (pow y 3)))) x)) (* 4 (/ 1 (pow y 2)))) x)) (* 2 (/ 1 y))) x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* x y)))>
#<alt (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x))))>
#<alt (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x))))>
#<alt (/ 2 (* x y))>
#<alt (/ (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) y)>
#<alt (/ (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y))) y)>
#<alt (/ (- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) y)>
#<alt (/ 2 (* x y))>
#<alt (* -1 (/ (- (* 4 (/ 1 (* (pow x 2) y))) (* 2 (/ 1 x))) y))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x))) y))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x))) y))>
#<alt -1>
#<alt (- (* -1/2 (* x y)) 1)>
#<alt (- (* -1/2 (* x y)) 1)>
#<alt (- (* -1/2 (* x y)) 1)>
#<alt (* -1/2 (* x y))>
#<alt (* -1 (* x (+ (* 1/2 y) (/ 1 x))))>
#<alt (* -1 (* x (+ (* 1/2 y) (/ 1 x))))>
#<alt (* -1 (* x (+ (* 1/2 y) (/ 1 x))))>
#<alt (* -1/2 (* x y))>
#<alt (* -1 (* x (- (/ 1 x) (* -1/2 y))))>
#<alt (* -1 (* x (- (/ 1 x) (* -1/2 y))))>
#<alt (* -1 (* x (- (/ 1 x) (* -1/2 y))))>
#<alt -1>
#<alt (- (* -1/2 (* x y)) 1)>
#<alt (- (* -1/2 (* x y)) 1)>
#<alt (- (* -1/2 (* x y)) 1)>
#<alt (* -1/2 (* x y))>
#<alt (* -1 (* y (+ (* 1/2 x) (/ 1 y))))>
#<alt (* -1 (* y (+ (* 1/2 x) (/ 1 y))))>
#<alt (* -1 (* y (+ (* 1/2 x) (/ 1 y))))>
#<alt (* -1/2 (* x y))>
#<alt (* -1 (* y (- (/ 1 y) (* -1/2 x))))>
#<alt (* -1 (* y (- (/ 1 y) (* -1/2 x))))>
#<alt (* -1 (* y (- (/ 1 y) (* -1/2 x))))>
#<alt (* -1 y)>
#<alt (- x y)>
#<alt (- x y)>
#<alt (- x y)>
#<alt x>
#<alt (* x (+ 1 (* -1 (/ y x))))>
#<alt (* x (+ 1 (* -1 (/ y x))))>
#<alt (* x (+ 1 (* -1 (/ y x))))>
#<alt x>
#<alt (* -1 (* x (- (/ y x) 1)))>
#<alt (* -1 (* x (- (/ y x) 1)))>
#<alt (* -1 (* x (- (/ y x) 1)))>
#<alt x>
#<alt (+ x (* -1 y))>
#<alt (+ x (* -1 y))>
#<alt (+ x (* -1 y))>
#<alt (* -1 y)>
#<alt (* y (- (/ x y) 1))>
#<alt (* y (- (/ x y) 1))>
#<alt (* y (- (/ x y) 1))>
#<alt (* -1 y)>
#<alt (* -1 (* y (+ 1 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ x y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ x y)))))>
#<alt (/ -2 x)>
#<alt (/ (- (pow x 2) 2) x)>
#<alt (/ (- (pow x 2) 2) x)>
#<alt (/ (- (pow x 2) 2) x)>
#<alt x>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt x>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ -2 x)>
#<alt (/ (- (pow x 2) 2) x)>
#<alt (/ (- (pow x 2) 2) x)>
#<alt (/ (- (pow x 2) 2) x)>
#<alt x>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt (* x (- 1 (* 2 (/ 1 (pow x 2)))))>
#<alt x>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))>
#<alt (/ -2 (pow x 2))>
#<alt (/ (- (pow x 2) 2) (pow x 2))>
#<alt (/ (- (pow x 2) 2) (pow x 2))>
#<alt (/ (- (pow x 2) 2) (pow x 2))>
#<alt 1>
#<alt (- 1 (* 2 (/ 1 (pow x 2))))>
#<alt (- 1 (* 2 (/ 1 (pow x 2))))>
#<alt (- 1 (* 2 (/ 1 (pow x 2))))>
#<alt 1>
#<alt (- 1 (* 2 (/ 1 (pow x 2))))>
#<alt (- 1 (* 2 (/ 1 (pow x 2))))>
#<alt (- 1 (* 2 (/ 1 (pow x 2))))>
#<alt (/ -2 (pow x 2))>
#<alt (/ -2 (pow x 2))>
#<alt (/ -2 (pow x 2))>
#<alt (/ -2 (pow x 2))>
#<alt (/ -2 (pow x 2))>
#<alt (/ -2 (pow x 2))>
#<alt (/ -2 (pow x 2))>
#<alt (/ -2 (pow x 2))>
#<alt (/ -2 (pow x 2))>
#<alt (/ -2 (pow x 2))>
#<alt (/ -2 (pow x 2))>
#<alt (/ -2 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>
#<alt (* 1/2 (* x y))>

Calls

54 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(- x y)
1.0ms	x	@	0	(* x (+ 1 (/ -2 (* x x))))
0.0ms	x	@	-inf	(/ -1 (- -1 (/ (* x y) 2)))
0.0ms	x	@	0	(/ -2 (* x x))
0.0ms	x	@	inf	(/ -1 (- -1 (/ (* x y) 2)))

rewrite314.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

4492×	`-lowering-.f32`
4492×	`-lowering-.f64`
4338×	`/-lowering-/.f32`
4338×	`/-lowering-/.f64`
2192×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	78
1	145	70
2	1352	68
0	8710	68

Stop Event

1×	iter limit
1×	node limit

Counts

12 → 376

Calls

Call 1

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

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

simplify301.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

3464×	`-lowering-.f32`
3464×	`-lowering-.f64`
2986×	`/-lowering-/.f32`
2986×	`/-lowering-/.f64`
2468×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	321	1792
1	1149	1704
2	3259	1666
0	8617	1666

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

Inputs
(* -1 y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
x
(+ x (* -1 y))
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(- x (* 2 (/ 1 x)))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
y
(+ y (* -1/2 (* x (pow y 2))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(/ 2 x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/ 2 x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
y
(* y (+ 1 (* -1/2 (* x y))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(/ 2 x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
1
(+ 1 (* -1/2 (* x y)))
(+ 1 (* x (- (* 1/4 (* x (pow y 2))) (* 1/2 y))))
(+ 1 (* x (- (* x (- (* -1/8 (* x (pow y 3))) (* -1/4 (pow y 2)))) (* 1/2 y))))
(/ 2 (* x y))
(/ (- (* 2 (/ 1 y)) (* 4 (/ 1 (* x (pow y 2))))) x)
(/ (- (+ (* 2 (/ 1 y)) (/ 8 (* (pow x 2) (pow y 3)))) (/ 4 (* x (pow y 2)))) x)
(/ (- (+ (* 2 (/ 1 y)) (* 8 (/ 1 (* (pow x 2) (pow y 3))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 4)))) (/ 4 (* x (pow y 2))))) x)
(/ 2 (* x y))
(* -1 (/ (- (* 4 (/ 1 (* x (pow y 2)))) (* 2 (/ 1 y))) x))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 3)))) (* 4 (/ 1 (pow y 2)))) x)) (* 2 (/ 1 y))) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 4)))) (* 8 (/ 1 (pow y 3)))) x)) (* 4 (/ 1 (pow y 2)))) x)) (* 2 (/ 1 y))) x))
1
(+ 1 (* -1/2 (* x y)))
(+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x))))
(+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x))))
(/ 2 (* x y))
(/ (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) y)
(/ (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y))) y)
(/ (- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) y)
(/ 2 (* x y))
(* -1 (/ (- (* 4 (/ 1 (* (pow x 2) y))) (* 2 (/ 1 x))) y))
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x))) y))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x))) y))
-1
(- (* -1/2 (* x y)) 1)
(- (* -1/2 (* x y)) 1)
(- (* -1/2 (* x y)) 1)
(* -1/2 (* x y))
(* -1 (* x (+ (* 1/2 y) (/ 1 x))))
(* -1 (* x (+ (* 1/2 y) (/ 1 x))))
(* -1 (* x (+ (* 1/2 y) (/ 1 x))))
(* -1/2 (* x y))
(* -1 (* x (- (/ 1 x) (* -1/2 y))))
(* -1 (* x (- (/ 1 x) (* -1/2 y))))
(* -1 (* x (- (/ 1 x) (* -1/2 y))))
-1
(- (* -1/2 (* x y)) 1)
(- (* -1/2 (* x y)) 1)
(- (* -1/2 (* x y)) 1)
(* -1/2 (* x y))
(* -1 (* y (+ (* 1/2 x) (/ 1 y))))
(* -1 (* y (+ (* 1/2 x) (/ 1 y))))
(* -1 (* y (+ (* 1/2 x) (/ 1 y))))
(* -1/2 (* x y))
(* -1 (* y (- (/ 1 y) (* -1/2 x))))
(* -1 (* y (- (/ 1 y) (* -1/2 x))))
(* -1 (* y (- (/ 1 y) (* -1/2 x))))
(* -1 y)
(- x y)
(- x y)
(- x y)
x
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
(* x (+ 1 (* -1 (/ y x))))
x
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
(* -1 (* x (- (/ y x) 1)))
x
(+ x (* -1 y))
(+ x (* -1 y))
(+ x (* -1 y))
(* -1 y)
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* y (- (/ x y) 1))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(/ -2 x)
(/ (- (pow x 2) 2) x)
(/ (- (pow x 2) 2) x)
(/ (- (pow x 2) 2) x)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ -2 x)
(/ (- (pow x 2) 2) x)
(/ (- (pow x 2) 2) x)
(/ (- (pow x 2) 2) x)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(/ -2 (pow x 2))
(/ (- (pow x 2) 2) (pow x 2))
(/ (- (pow x 2) 2) (pow x 2))
(/ (- (pow x 2) 2) (pow x 2))
1
(- 1 (* 2 (/ 1 (pow x 2))))
(- 1 (* 2 (/ 1 (pow x 2))))
(- 1 (* 2 (/ 1 (pow x 2))))
1
(- 1 (* 2 (/ 1 (pow x 2))))
(- 1 (* 2 (/ 1 (pow x 2))))
(- 1 (* 2 (/ 1 (pow x 2))))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(/ -2 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))
(* 1/2 (* x y))

Outputs
(* -1 y)
(-.f64 #s(literal 0 binary64) y)
(- (* x (+ 1 (* 1/2 (pow y 2)))) y)
(-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 y (*.f64 y #s(literal 1/2 binary64))))) y)
(- (* x (+ 1 (+ (* -1/4 (* x (pow y 3))) (* 1/2 (pow y 2))))) y)
(-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 y y) (+.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x #s(literal -1/4 binary64)) y))))) y)
(- (* x (+ 1 (+ (* 1/2 (pow y 2)) (* x (+ (* -1/4 (pow y 3)) (* 1/8 (* x (pow y 4)))))))) y)
(-.f64 (.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 y y) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x #s(literal -1/4 binary64)) y)))) (.f64 x (.f64 #s(literal 1/8 binary64) (.f64 x (pow.f64 y #s(literal 4 binary64))))))) y)
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
(* x (- (+ 1 (/ 4 (* (pow x 3) y))) (* 2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 (/.f64 #s(literal 4 binary64) (.f64 y (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x)))))
(* x (- (+ 1 (* 4 (/ 1 (* (pow x 3) y)))) (+ (* 8 (/ 1 (* (pow x 4) (pow y 2)))) (* 2 (/ 1 (pow x 2))))))
(.f64 x (+.f64 (+.f64 (/.f64 #s(literal 4 binary64) (.f64 y (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x)))) (/.f64 (/.f64 #s(literal -8 binary64) (.f64 y y)) (pow.f64 x #s(literal 4 binary64)))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) (+ 1 (/ 4 (* (pow x 3) y))))))
(.f64 x (+.f64 (/.f64 #s(literal 4 binary64) (.f64 y (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x)))))
(* -1 (* x (- (+ (* -1 (/ (- (* 4 (/ 1 y)) (* 8 (/ 1 (* x (pow y 2))))) (pow x 3))) (* 2 (/ 1 (pow x 2)))) 1)))
(.f64 x (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 #s(literal 2 binary64) (.f64 x x)) (+.f64 (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 y (.f64 y x))) (/.f64 #s(literal -4 binary64) y)) (*.f64 x x)) x) #s(literal -1 binary64)))))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* y (- (* 1/2 (* x y)) 1)))
(+.f64 x (.f64 y (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 y x)))))
(+ x (* y (- (* y (+ (* -1/4 (* (pow x 2) y)) (* 1/2 x))) 1)))
(+.f64 x (.f64 y (+.f64 #s(literal -1 binary64) (.f64 y (+.f64 (.f64 #s(literal -1/4 binary64) (.f64 x (.f64 y x))) (.f64 x #s(literal 1/2 binary64)))))))
(- x (* 2 (/ 1 x)))
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(+.f64 x (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x))
(- (+ x (/ 4 (* (pow x 2) y))) (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))))
(+.f64 x (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (/.f64 #s(literal -8 binary64) (*.f64 y y)) x)) x)) x))
(- (+ x (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))))
(+.f64 (+.f64 x (/.f64 (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 y (.f64 y y)))) (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (/.f64 #s(literal -8 binary64) (*.f64 y y)) x)) x)) x))
(- x (* 2 (/ 1 x)))
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(- (+ x (* 4 (/ 1 (* (pow x 2) y)))) (* 2 (/ 1 x)))
(+.f64 x (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (*.f64 y x)) #s(literal -2 binary64)) x))
(- (+ x (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(+.f64 x (/.f64 (+.f64 #s(literal -2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) y) (/.f64 (/.f64 #s(literal -8 binary64) (*.f64 y y)) x)) x)) x))
(- (+ x (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y))) (* 2 (/ 1 x)))
(+.f64 x (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 4 binary64) (.f64 x x)) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 16 binary64) (pow.f64 x #s(literal 4 binary64))) y) (/.f64 #s(literal -8 binary64) (.f64 x (*.f64 x x)))) y)) y) (/.f64 #s(literal -2 binary64) x)))
y
(+ y (* -1/2 (* x (pow y 2))))
(.f64 y (+.f64 #s(literal 1 binary64) (.f64 (*.f64 y x) #s(literal -1/2 binary64))))
(+ y (* x (- (* 1/4 (* x (pow y 3))) (* 1/2 (pow y 2)))))
(+.f64 y (.f64 x (.f64 y (.f64 y (+.f64 (.f64 (*.f64 x #s(literal 1/4 binary64)) y) #s(literal -1/2 binary64))))))
(+ y (* x (- (* x (- (* -1/8 (* x (pow y 4))) (* -1/4 (pow y 3)))) (* 1/2 (pow y 2)))))
(+.f64 y (.f64 x (+.f64 (.f64 x (.f64 (.f64 x (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64))) (.f64 y (.f64 y (+.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) y) #s(literal -1/2 binary64)))))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ (- 2 (* 4 (/ 1 (* x y)))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(/ (- (+ 2 (/ 8 (* (pow x 2) (pow y 2)))) (/ 4 (* x y))) x)
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 y (.f64 y x))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(/ (- (+ 2 (* 8 (/ 1 (* (pow x 2) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 3)))) (/ 4 (* x y)))) x)
(/.f64 (+.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 y (.f64 y x))) (/.f64 #s(literal -4 binary64) y)) x)) (/.f64 #s(literal -16 binary64) (.f64 (.f64 y y) (.f64 y (.f64 x (*.f64 x x)))))) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(* -1 (/ (- (* 4 (/ 1 (* x y))) 2) x))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 2)))) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 y (.f64 y x))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 3)))) (* 8 (/ 1 (pow y 2)))) x)) (* 4 (/ 1 y))) x)) 2) x))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (-.f64 (/.f64 #s(literal -4 binary64) y) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 16 binary64) y) (.f64 y (.f64 y x))) (/.f64 #s(literal -8 binary64) (*.f64 y y))) x)) x)) x)
y
(* y (+ 1 (* -1/2 (* x y))))
(.f64 y (+.f64 #s(literal 1 binary64) (.f64 (*.f64 y x) #s(literal -1/2 binary64))))
(* y (+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x)))))
(.f64 y (+.f64 #s(literal 1 binary64) (.f64 y (+.f64 (.f64 (.f64 x (.f64 y x)) #s(literal 1/4 binary64)) (.f64 x #s(literal -1/2 binary64))))))
(* y (+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x)))))
(.f64 y (+.f64 #s(literal 1 binary64) (.f64 y (+.f64 (.f64 y (+.f64 (.f64 (.f64 y (.f64 x (.f64 x x))) #s(literal -1/8 binary64)) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) (.f64 x #s(literal -1/2 binary64))))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y)))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 y (.f64 y x))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y))))
(+.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 y (.f64 y x))) (/.f64 #s(literal -4 binary64) y)) x)) x) (/.f64 (/.f64 (/.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64))) y) (*.f64 y y)))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y))))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x)
(+ (* -1 (/ (- (* 4 (/ 1 (pow x 2))) (* 8 (/ 1 (* (pow x 3) y)))) y)) (* 2 (/ 1 x)))
(/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 y (.f64 y x))) (/.f64 #s(literal -4 binary64) y)) x)) x)
(+ (* -1 (/ (+ (* -1 (/ (- (* 8 (/ 1 (pow x 3))) (* 16 (/ 1 (* (pow x 4) y)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x)))
(+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) (/.f64 (/.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64))) y)) y) (/.f64 #s(literal -4 binary64) (*.f64 x x))) y))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 y x) #s(literal -1/2 binary64)))
(+ 1 (* x (- (* 1/4 (* x (pow y 2))) (* 1/2 y))))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 y (+.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) y) #s(literal -1/2 binary64)))))
(+ 1 (* x (- (* x (- (* -1/8 (* x (pow y 3))) (* -1/4 (pow y 2)))) (* 1/2 y))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x (.f64 (.f64 y y) (+.f64 (.f64 (.f64 x #s(literal -1/8 binary64)) y) #s(literal 1/4 binary64)))) (*.f64 y #s(literal -1/2 binary64)))))
(/ 2 (* x y))
(/.f64 #s(literal 2 binary64) (*.f64 y x))
(/ (- (* 2 (/ 1 y)) (* 4 (/ 1 (* x (pow y 2))))) x)
(/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x) y)
(/ (- (+ (* 2 (/ 1 y)) (/ 8 (* (pow x 2) (pow y 3)))) (/ 4 (* x (pow y 2)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 2 binary64) y) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 8 binary64) (.f64 y (.f64 y y))) x) (/.f64 (/.f64 #s(literal -4 binary64) y) y)) x)) x)
(/ (- (+ (* 2 (/ 1 y)) (* 8 (/ 1 (* (pow x 2) (pow y 3))))) (+ (* 16 (/ 1 (* (pow x 3) (pow y 4)))) (/ 4 (* x (pow y 2))))) x)
(/.f64 (+.f64 (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 8 binary64) (.f64 y (.f64 y y))) x) (/.f64 (/.f64 #s(literal -4 binary64) y) y)) x) (-.f64 (/.f64 #s(literal 2 binary64) y) (/.f64 (/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x))) (pow.f64 y #s(literal 4 binary64))))) x)
(/ 2 (* x y))
(/.f64 #s(literal 2 binary64) (*.f64 y x))
(* -1 (/ (- (* 4 (/ 1 (* x (pow y 2)))) (* 2 (/ 1 y))) x))
(/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x) y)
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* x (pow y 3)))) (* 4 (/ 1 (pow y 2)))) x)) (* 2 (/ 1 y))) x))
(/.f64 (+.f64 (/.f64 #s(literal 2 binary64) y) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 8 binary64) (.f64 y (.f64 y y))) x) (/.f64 (/.f64 #s(literal -4 binary64) y) y)) x)) x)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* x (pow y 4)))) (* 8 (/ 1 (pow y 3)))) x)) (* 4 (/ 1 (pow y 2)))) x)) (* 2 (/ 1 y))) x))
(/.f64 (+.f64 (/.f64 #s(literal 2 binary64) y) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 y (.f64 y y))) (/.f64 #s(literal -16 binary64) (*.f64 x (pow.f64 y #s(literal 4 binary64))))) x) (/.f64 (/.f64 #s(literal -4 binary64) y) y)) x)) x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* x y)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 y x) #s(literal -1/2 binary64)))
(+ 1 (* y (- (* 1/4 (* (pow x 2) y)) (* 1/2 x))))
(+.f64 #s(literal 1 binary64) (.f64 y (+.f64 (.f64 (.f64 x (.f64 y x)) #s(literal 1/4 binary64)) (*.f64 x #s(literal -1/2 binary64)))))
(+ 1 (* y (- (* y (- (* -1/8 (* (pow x 3) y)) (* -1/4 (pow x 2)))) (* 1/2 x))))
(+.f64 #s(literal 1 binary64) (.f64 y (+.f64 (.f64 y (+.f64 (.f64 (.f64 y (.f64 x (.f64 x x))) #s(literal -1/8 binary64)) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) (*.f64 x #s(literal -1/2 binary64)))))
(/ 2 (* x y))
(/.f64 #s(literal 2 binary64) (*.f64 y x))
(/ (- (* 2 (/ 1 x)) (* 4 (/ 1 (* (pow x 2) y)))) y)
(/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x) y)
(/ (- (+ (* 2 (/ 1 x)) (/ 8 (* (pow x 3) (pow y 2)))) (/ 4 (* (pow x 2) y))) y)
(/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 y (.f64 y x))) (/.f64 #s(literal -4 binary64) y)) x)) x) y)
(/ (- (+ (* 2 (/ 1 x)) (* 8 (/ 1 (* (pow x 3) (pow y 2))))) (+ (* 16 (/ 1 (* (pow x 4) (pow y 3)))) (/ 4 (* (pow x 2) y)))) y)
(/.f64 (+.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 y (.f64 y x))) (/.f64 #s(literal -4 binary64) y)) x)) x) (/.f64 (/.f64 (/.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64))) y) (*.f64 y y))) y)
(/ 2 (* x y))
(/.f64 #s(literal 2 binary64) (*.f64 y x))
(* -1 (/ (- (* 4 (/ 1 (* (pow x 2) y))) (* 2 (/ 1 x))) y))
(/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (/.f64 #s(literal -4 binary64) y) x)) x) y)
(* -1 (/ (- (* -1 (/ (- (* 8 (/ 1 (* (pow x 3) y))) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x))) y))
(/.f64 (/.f64 (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 y (.f64 y x))) (/.f64 #s(literal -4 binary64) y)) x)) x) y)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 16 (/ 1 (* (pow x 4) y))) (* 8 (/ 1 (pow x 3)))) y)) (* 4 (/ 1 (pow x 2)))) y)) (* 2 (/ 1 x))) y))
(/.f64 (+.f64 (/.f64 #s(literal 2 binary64) x) (/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal 8 binary64) (.f64 x (.f64 x x))) (/.f64 (/.f64 #s(literal -16 binary64) (pow.f64 x #s(literal 4 binary64))) y)) y) (/.f64 #s(literal -4 binary64) (*.f64 x x))) y)) y)
-1
#s(literal -1 binary64)
(- (* -1/2 (* x y)) 1)
(-.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(- (* -1/2 (* x y)) 1)
(-.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(- (* -1/2 (* x y)) 1)
(-.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(* -1/2 (* x y))
(.f64 (.f64 y x) #s(literal -1/2 binary64))
(* -1 (* x (+ (* 1/2 y) (/ 1 x))))
(-.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(* -1 (* x (+ (* 1/2 y) (/ 1 x))))
(-.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(* -1 (* x (+ (* 1/2 y) (/ 1 x))))
(-.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(* -1/2 (* x y))
(.f64 (.f64 y x) #s(literal -1/2 binary64))
(* -1 (* x (- (/ 1 x) (* -1/2 y))))
(-.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(* -1 (* x (- (/ 1 x) (* -1/2 y))))
(-.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(* -1 (* x (- (/ 1 x) (* -1/2 y))))
(-.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
-1
#s(literal -1 binary64)
(- (* -1/2 (* x y)) 1)
(-.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(- (* -1/2 (* x y)) 1)
(-.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(- (* -1/2 (* x y)) 1)
(-.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(* -1/2 (* x y))
(.f64 (.f64 y x) #s(literal -1/2 binary64))
(* -1 (* y (+ (* 1/2 x) (/ 1 y))))
(-.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(* -1 (* y (+ (* 1/2 x) (/ 1 y))))
(-.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(* -1 (* y (+ (* 1/2 x) (/ 1 y))))
(-.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(* -1/2 (* x y))
(.f64 (.f64 y x) #s(literal -1/2 binary64))
(* -1 (* y (- (/ 1 y) (* -1/2 x))))
(-.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(* -1 (* y (- (/ 1 y) (* -1/2 x))))
(-.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(* -1 (* y (- (/ 1 y) (* -1/2 x))))
(-.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (.f64 y x)))
(* -1 y)
(-.f64 #s(literal 0 binary64) y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
(- x y)
(-.f64 x y)
x
(* x (+ 1 (* -1 (/ y x))))
(+.f64 x (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 1 binary64))))
(* x (+ 1 (* -1 (/ y x))))
(+.f64 x (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 1 binary64))))
(* x (+ 1 (* -1 (/ y x))))
(+.f64 x (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 1 binary64))))
x
(* -1 (* x (- (/ y x) 1)))
(+.f64 x (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 1 binary64))))
(* -1 (* x (- (/ y x) 1)))
(+.f64 x (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 1 binary64))))
(* -1 (* x (- (/ y x) 1)))
(+.f64 x (*.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) y) #s(literal 1 binary64))))
x
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(+ x (* -1 y))
(-.f64 x y)
(* -1 y)
(-.f64 #s(literal 0 binary64) y)
(* y (- (/ x y) 1))
(*.f64 y (+.f64 #s(literal -1 binary64) (/.f64 x y)))
(* y (- (/ x y) 1))
(*.f64 y (+.f64 #s(literal -1 binary64) (/.f64 x y)))
(* y (- (/ x y) 1))
(*.f64 y (+.f64 #s(literal -1 binary64) (/.f64 x y)))
(* -1 y)
(-.f64 #s(literal 0 binary64) y)
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(*.f64 y (+.f64 #s(literal -1 binary64) (/.f64 x y)))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(*.f64 y (+.f64 #s(literal -1 binary64) (/.f64 x y)))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(*.f64 y (+.f64 #s(literal -1 binary64) (/.f64 x y)))
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ (- (pow x 2) 2) x)
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(/ (- (pow x 2) 2) x)
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(/ (- (pow x 2) 2) x)
(+.f64 x (/.f64 #s(literal -2 binary64) x))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ (- (pow x 2) 2) x)
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(/ (- (pow x 2) 2) x)
(+.f64 x (/.f64 #s(literal -2 binary64) x))
(/ (- (pow x 2) 2) x)
(+.f64 x (/.f64 #s(literal -2 binary64) x))
x
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
(* x (- 1 (* 2 (/ 1 (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
x
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
(* -1 (* x (- (* 2 (/ 1 (pow x 2))) 1)))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(/ (- (pow x 2) 2) (pow x 2))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x)))
(/ (- (pow x 2) 2) (pow x 2))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x)))
(/ (- (pow x 2) 2) (pow x 2))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x)))
1
#s(literal 1 binary64)
(- 1 (* 2 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x)))
(- 1 (* 2 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x)))
(- 1 (* 2 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x)))
1
#s(literal 1 binary64)
(- 1 (* 2 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x)))
(- 1 (* 2 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x)))
(- 1 (* 2 (/ 1 (pow x 2))))
(+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (*.f64 x x)))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(/ -2 (pow x 2))
(/.f64 #s(literal -2 binary64) (*.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))
(* 1/2 (* x y))
(.f64 #s(literal 1/2 binary64) (.f64 y x))

eval69.0ms (0.7%)

Compiler: Compiled 10696 to 1312 computations (87.7% saved)

prune86.0ms (0.9%)

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	591	1	592
Fresh	0	1	1
Picked	0	5	5
Done	0	1	1
Total	591	8	599

Accuracy

100.0%

Counts

599 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	12.7%	(/.f64 #s(literal -2 binary64) x)
✓	99.9%	(-.f64 x (/.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) y)))
✓	99.9%	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
▶	64.1%	(-.f64 x (/.f64 y (.f64 y (.f64 x #s(literal 1/2 binary64)))))
✓	64.1%	(-.f64 x (/.f64 #s(literal 2 binary64) x))
✓	75.7%	(-.f64 x y)
✓	61.2%	(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
✓	64.7%	x

Compiler

Compiled 72 to 50 computations (30.6% saved)

simplify235.0ms (2.5%)

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal -2 binary64) x)
✓	cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 y (.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	256	(/.f64 y (.f64 y (.f64 x #s(literal 1/2 binary64))))
✓	cost-diff	256	(-.f64 x (/.f64 y (.f64 y (.f64 x #s(literal 1/2 binary64)))))

Rules

2162×	`-lowering-.f32`
2162×	`-lowering-.f64`
1426×	`--lowering--.f32`
1426×	`--lowering--.f64`
1286×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	32
1	17	24
2	47	24
3	135	24
4	256	24
5	502	24
6	1305	24
7	3651	24
8	6789	24
0	8059	24

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize35.0ms (0.4%)

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal -2 binary64) x)
✓	accuracy	100.0%	(.f64 y (.f64 x #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(-.f64 x (/.f64 y (.f64 y (.f64 x #s(literal 1/2 binary64)))))
✓	accuracy	78.0%	(/.f64 y (.f64 y (.f64 x #s(literal 1/2 binary64))))

Results

23.0ms

256×

valid

Compiler

Compiled 35 to 10 computations (71.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-div: 4.0ms (41.6% of total)

ival-mult: 4.0ms (41.6% of total)

ival-sub: 1.0ms (10.4% of total)

const: 0.0ms (0% of total)

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

series3.0ms (0%)

Counts

5 → 96

Calls

Call 1

Inputs
#<alt (- x (/ y (* y (* x 1/2))))>
#<alt (/ y (* y (* x 1/2)))>
#<alt (* y (* x 1/2))>
#<alt (* x 1/2)>
#<alt (/ -2 x)>

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

Calls

24 calls:

Time	Variable		Point	Expression
0.0ms	y	@	0	(- x (/ y (* y (* x 1/2))))
0.0ms	x	@	-inf	(* x 1/2)
0.0ms	y	@	0	(/ y (* y (* x 1/2)))
0.0ms	x	@	inf	(* x 1/2)
0.0ms	x	@	0	(* x 1/2)

rewrite251.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

2480×	`-lowering-.f32`
2480×	`-lowering-.f64`
1818×	`/-lowering-/.f32`
1818×	`/-lowering-/.f64`
1662×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	46	19
2	391	19
3	5262	19
0	8305	19

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 251

Calls

Call 1

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

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

simplify199.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

2018×	`fnmadd-define`
1496×	`fma-define`
1430×	`fma-lowering-fma.f32`
1430×	`fma-lowering-fma.f64`
1388×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	416
1	61	395
2	131	374
3	272	374
4	906	374
5	3111	374
6	6522	374
0	8017	374

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

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

eval66.0ms (0.7%)

Compiler: Compiled 4987 to 710 computations (85.8% saved)

prune39.0ms (0.4%)

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	346	1	347
Fresh	0	0	0
Picked	1	1	2
Done	0	6	6
Total	347	8	355

Accuracy

100.0%

Counts

355 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	12.7%	(/.f64 y (.f64 (.f64 x y) #s(literal -1/2 binary64)))
✓	12.7%	(/.f64 #s(literal -2 binary64) x)
✓	99.9%	(-.f64 x (/.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) y)))
✓	99.9%	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
✓	64.1%	(-.f64 x (/.f64 #s(literal 2 binary64) x))
✓	75.7%	(-.f64 x y)
✓	61.2%	(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
✓	64.7%	x

Compiler

Compiled 70 to 49 computations (30% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x y)
✓	cost-diff	0	(.f64 (.f64 x y) #s(literal -1/2 binary64))
✓	cost-diff	256	(/.f64 y (.f64 (.f64 x y) #s(literal -1/2 binary64)))

Rules

32×	`associate-/r*`
30×	`/-lowering-/.f32`
30×	`/-lowering-/.f64`
24×	`-lowering-.f32`
24×	`-lowering-.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	12	18
2	26	16
3	41	14
4	48	14
0	48	14

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize26.0ms (0.3%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x y)
✓	accuracy	100.0%	(.f64 (.f64 x y) #s(literal -1/2 binary64))
✓	accuracy	78.0%	(/.f64 y (.f64 (.f64 x y) #s(literal -1/2 binary64)))

Results

19.0ms

256×

valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

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

ival-mult: 6.0ms (69.1% of total)

ival-div: 2.0ms (23% of total)

const: 0.0ms (0% of total)

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

series2.0ms (0%)

Counts

3 → 72

Calls

Call 1

Inputs
#<alt (/ y (* (* x y) -1/2))>
#<alt (* (* x y) -1/2)>
#<alt (* x y)>

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

18 calls:

Time	Variable		Point	Expression
1.0ms	y	@	0	(/ y (* (* x y) -1/2))
0.0ms	x	@	0	(* (* x y) -1/2)
0.0ms	y	@	0	(* (* x y) -1/2)
0.0ms	y	@	inf	(/ y (* (* x y) -1/2))
0.0ms	y	@	-inf	(/ y (* (* x y) -1/2))

rewrite314.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

2242×	`-lowering-.f32`
2242×	`-lowering-.f64`
1688×	`/-lowering-/.f32`
1688×	`/-lowering-/.f64`
1388×	`log-div`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	20	15
2	103	11
3	643	11
4	4759	11
0	8632	11

Stop Event

1×	iter limit
1×	node limit

Counts

3 → 554

Calls

Call 1

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

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

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

24×	`-lowering-.f32`
24×	`-lowering-.f64`
10×	`*-commutative`
6×	`associate-r`
6×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	264
1	11	264
2	18	264
3	20	264
0	20	264

Stop Event

1×	iter limit
1×	saturated

Counts

72 → 72

Calls

Call 1

Inputs
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* x y))
(* -1/2 (* 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
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(/ -2 x)
(/.f64 #s(literal -2 binary64) x)
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) y))
(* -1/2 (* x y))
(.f64 x (.f64 #s(literal -1/2 binary64) 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)
(* x y)
(*.f64 x y)

eval75.0ms (0.8%)

Compiler: Compiled 8258 to 1338 computations (83.8% saved)

prune756.0ms (8.2%)

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	626	0	626
Fresh	0	0	0
Picked	0	1	1
Done	0	7	7
Total	626	8	634

Accuracy

100.0%

Counts

634 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	12.7%	(/.f64 y (.f64 (.f64 x y) #s(literal -1/2 binary64)))
✓	12.7%	(/.f64 #s(literal -2 binary64) x)
✓	99.9%	(-.f64 x (/.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) y)))
✓	99.9%	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
✓	64.1%	(-.f64 x (/.f64 #s(literal 2 binary64) x))
✓	75.7%	(-.f64 x y)
✓	61.2%	(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
✓	64.7%	x

Compiler

Compiled 135 to 81 computations (40% saved)

regimes31.0ms (0.3%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

3 calls:

23.0ms	y
4.0ms	(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
4.0ms	x

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))`

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes3.0s (31.8%)

Counts

7 → 3

Calls

Call 1

Inputs
x
(-.f64 x y)
(/.f64 #s(literal -2 binary64) x)
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(/.f64 y (.f64 (.f64 x y) #s(literal -1/2 binary64)))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))
(-.f64 x (/.f64 y (.f64 y (.f64 x #s(literal 1/2 binary64)))))

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

Calls

2 calls:

2.9s	x
3.0ms	y

Results

Accuracy	Segments	Branch
89.5%	3	`x`
92.7%	3	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes3.0ms (0%)

Counts

6 → 3

Calls

Call 1

Inputs
x
(-.f64 x y)
(/.f64 #s(literal -2 binary64) x)
(-.f64 x (/.f64 #s(literal 2 binary64) x))
(/.f64 y (.f64 (.f64 x y) #s(literal -1/2 binary64)))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) (.f64 x x))))

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
92.7%	3	`y`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes4.0ms (0%)

Counts

3 → 4

Calls

Call 1

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

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

Calls

2 calls:

2.0ms	y
2.0ms	x

Results

Accuracy	Segments	Branch
89.0%	4	`x`
83.0%	3	`y`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes2.0ms (0%)

Counts

2 → 3

Calls

Call 1

Inputs
x
(-.f64 x y)

Outputs
x
(-.f64 x y)
x

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
87.0%	3	`x`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes18.0ms (0.2%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
x

Outputs
x

Calls

2 calls:

16.0ms	y
1.0ms	x

Results

Accuracy	Segments	Branch
64.7%	1	`y`
64.7%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch36.0ms (0.4%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
12.0ms	3.2310811794200306e+92	1.0192205032512197e+95
14.0ms	-1.3343023104587272e+70	-1.3664483788099348e+63

Results

17.0ms

272×

valid

Compiler

Compiled 292 to 201 computations (31.2% saved)

Precisions

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

ival-div: 4.0ms (42.7% of total)

ival-add: 2.0ms (21.4% of total)

ival-mult: 2.0ms (21.4% of total)

ival-sub: 1.0ms (10.7% of total)

const: 0.0ms (0% of total)

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

bsearch30.0ms (0.3%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
14.0ms	3.2310811794200306e+92	1.0192205032512197e+95
14.0ms	-1.3343023104587272e+70	-1.3664483788099348e+63

Results

19.0ms

272×

valid

Compiler

Compiled 256 to 183 computations (28.5% saved)

Precisions

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

ival-div: 4.0ms (36.3% of total)

ival-mult: 4.0ms (36.3% of total)

ival-sub: 1.0ms (9.1% of total)

ival-add: 1.0ms (9.1% of total)

const: 0.0ms (0% of total)

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

bsearch36.0ms (0.4%)

Algorithm

3×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
12.0ms	1.135412854042459e-11	2.2594796563546622e-10
12.0ms	4.90799416131603e-55	1.9806542570686829e-50
9.0ms	-0.7153996059109962	-0.2078804955775682

Results

23.0ms

320×

valid

Compiler

Compiled 234 to 176 computations (24.8% saved)

Precisions

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

ival-div: 4.0ms (35.7% of total)

ival-mult: 3.0ms (26.7% of total)

ival-sub: 2.0ms (17.8% of total)

ival-add: 2.0ms (17.8% of total)

const: 1.0ms (8.9% of total)

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

bsearch24.0ms (0.3%)

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
14.0ms	2.404625917768266e-24	3.573101263383021e-21
8.0ms	-0.7153996059109962	-0.2078804955775682

Results

15.0ms

208×

valid

Compiler

Compiled 148 to 104 computations (29.7% saved)

Precisions

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

ival-div: 5.0ms (55.3% of total)

ival-mult: 2.0ms (22.1% of total)

ival-sub: 1.0ms (11.1% of total)

ival-add: 1.0ms (11.1% of total)

const: 0.0ms (0% of total)

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

simplify18.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

72×	`unsub-neg_binary64`
72×	`neg-mul-1_binary64`
38×	`*-commutative_binary64`
36×	`+-commutative_binary64`
36×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	87
1	67	87
2	90	87
3	115	87
4	143	87
5	165	87
6	218	87
7	303	87
8	306	87

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
(if (<=.f64 y #s(literal -52000000000000000898205552715978617138334793394789422401811073990656 binary64)) (-.f64 x (/.f64 y (.f64 y (.f64 x #s(literal 1/2 binary64))))) (if (<=.f64 y #s(literal 11599999999999999345255752532420604214457552482563417484084729299893314634944460807788059164672 binary64)) (-.f64 x y) (-.f64 x (/.f64 #s(literal 2 binary64) x))))
(if (<=.f64 y #s(literal -5200000000000000377163469183952022656023546930161914168694692808491008 binary64)) (-.f64 x (/.f64 #s(literal 2 binary64) x)) (if (<=.f64 y #s(literal 1250000000000000025273598908944933735720120404017947176422221070260005006247705386698372284416 binary64)) (-.f64 x y) (-.f64 x (/.f64 #s(literal 2 binary64) x))))
(if (<=.f64 x #s(literal -5854679515581645/9007199254740992 binary64)) x (if (<=.f64 x #s(literal 2561194933379311/26959946667150639794667015087019630673637144422540572481103610249216 binary64)) (-.f64 x y) (if (<=.f64 x #s(literal 2553251331026097/19342813113834066795298816 binary64)) (/.f64 #s(literal -2 binary64) x) x)))
(if (<=.f64 x #s(literal -3152519739159347/4503599627370496 binary64)) x (if (<=.f64 x #s(literal 2326148992623603/664613997892457936451903530140172288 binary64)) (-.f64 x y) x))
x

Outputs
(-.f64 x (/.f64 y (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
(+.f64 x (/.f64 y (-.f64 #s(literal -1 binary64) (/.f64 (*.f64 x y) #s(literal 2 binary64)))))
(if (<=.f64 y #s(literal -52000000000000000898205552715978617138334793394789422401811073990656 binary64)) (-.f64 x (/.f64 y (.f64 y (.f64 x #s(literal 1/2 binary64))))) (if (<=.f64 y #s(literal 11599999999999999345255752532420604214457552482563417484084729299893314634944460807788059164672 binary64)) (-.f64 x y) (-.f64 x (/.f64 #s(literal 2 binary64) x))))
(if (<=.f64 y #s(literal -5200000000000000377163469183952022656023546930161914168694692808491008 binary64)) (-.f64 x (/.f64 #s(literal 2 binary64) x)) (if (<=.f64 y #s(literal 1250000000000000025273598908944933735720120404017947176422221070260005006247705386698372284416 binary64)) (-.f64 x y) (-.f64 x (/.f64 #s(literal 2 binary64) x))))
(if (<=.f64 x #s(literal -5854679515581645/9007199254740992 binary64)) x (if (<=.f64 x #s(literal 2561194933379311/26959946667150639794667015087019630673637144422540572481103610249216 binary64)) (-.f64 x y) (if (<=.f64 x #s(literal 2553251331026097/19342813113834066795298816 binary64)) (/.f64 #s(literal -2 binary64) x) x)))
(if (<=.f64 x #s(literal -3152519739159347/4503599627370496 binary64)) x (if (<=.f64 x #s(literal 2326148992623603/664613997892457936451903530140172288 binary64)) (-.f64 x y) x))
x

soundness786.0ms (8.5%)

Rules

3952×	`-lowering-.f32`
3952×	`-lowering-.f64`
3464×	`-lowering-.f32`
3464×	`-lowering-.f64`
2986×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	231	1040
1	826	982
2	2365	947
3	7863	947
0	8125	947
0	321	1792
1	1149	1704
2	3259	1666
0	8617	1666

Stop Event

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

Compiler

Compiled 159 to 90 computations (43.4% saved)

preprocess112.0ms (1.2%)

Compiler: Compiled 212 to 110 computations (48.1% saved)

analyze52.0ms (0.6%)

sample903.0ms (9.7%)

preprocess121.0ms (1.3%)

explain104.0ms (1.1%)

eval18.0ms (0.2%)

prune1.0ms (0%)

simplify61.0ms (0.7%)

localize41.0ms (0.4%)

series11.0ms (0.1%)

rewrite470.0ms (5.1%)

simplify292.0ms (3.2%)

eval41.0ms (0.4%)

prune42.0ms (0.5%)

simplify161.0ms (1.7%)

localize76.0ms (0.8%)

series33.0ms (0.4%)

rewrite314.0ms (3.4%)

simplify301.0ms (3.2%)

eval69.0ms (0.7%)

prune86.0ms (0.9%)

simplify235.0ms (2.5%)

localize35.0ms (0.4%)

series3.0ms (0%)

rewrite251.0ms (2.7%)

simplify199.0ms (2.2%)

eval66.0ms (0.7%)

prune39.0ms (0.4%)

simplify6.0ms (0.1%)

localize26.0ms (0.3%)

series2.0ms (0%)

rewrite314.0ms (3.4%)

simplify12.0ms (0.1%)

eval75.0ms (0.8%)

prune756.0ms (8.2%)

regimes31.0ms (0.3%)

regimes3.0s (31.8%)

regimes3.0ms (0%)

regimes4.0ms (0%)

regimes2.0ms (0%)

regimes18.0ms (0.2%)

bsearch36.0ms (0.4%)

bsearch30.0ms (0.3%)

bsearch36.0ms (0.4%)

bsearch24.0ms (0.3%)

simplify18.0ms (0.2%)

soundness786.0ms (8.5%)

preprocess112.0ms (1.2%)

end0.0ms (0%)

Profiling