Details

analyze58.0ms (4.1%)

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
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
25%	25%	74.9%	0.1%	0%	0%	0%	5
37.5%	37.5%	62.4%	0.1%	0%	0%	0%	6
56.3%	56.2%	43.7%	0.1%	0%	0%	0%	7
65.6%	65.6%	34.3%	0.1%	0%	0%	0%	8
76.6%	76.5%	23.4%	0.1%	0%	0%	0%	9
82%	82%	18%	0.1%	0%	0%	0%	10
87.9%	87.8%	12.1%	0.1%	0%	0%	0%	11
90.8%	90.7%	9.2%	0.1%	0%	0%	0%	12

Compiler

Compiled 10 to 7 computations (30% saved)

sample847.0ms (60.2%)

Results

720.0ms	7721×	body	256	valid
49.0ms	230×	body	1024	valid
44.0ms	165×	body	2048	valid
20.0ms	140×	body	512	valid
0.0ms	1×	body	256	infinite

Bogosity

preprocess50.0ms (3.5%)

Algorithm

2×	egg-herbie

Rules

446×	`fma-neg_binary64`
114×	`fma-def_binary64`
90×	`cancel-sign-sub-inv_binary64`
62×	`sub-neg_binary64`
52×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	20	20
2	40	20
3	74	20
4	157	20
5	326	20
6	622	16
7	992	16
8	1290	16
9	1350	16
10	1354	16
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(+.f64 x (/.f64 (-.f64 x y) 2))
(+.f64 y (/.f64 (-.f64 y x) 2))

Outputs
(+.f64 x (/.f64 (-.f64 x y) 2))
(fma.f64 y -1/2 (*.f64 x 3/2))
(fma.f64 1/2 (-.f64 x y) x)
(fma.f64 (-.f64 x y) 1/2 x)
(+.f64 y (/.f64 (-.f64 y x) 2))
(+.f64 y (*.f64 -1/2 (-.f64 x y)))
(fma.f64 x -1/2 (*.f64 y 3/2))

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify28.0ms (2%)

Algorithm

1×	egg-herbie

Rules

254×	`fma-neg_binary64`
112×	`fma-def_binary64`
91×	`cancel-sign-sub-inv_binary64`
45×	`sub-neg_binary64`
40×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	13	10
2	24	10
3	43	10
4	87	10
5	170	10
6	324	10
7	504	8
8	748	8
9	988	8
10	1046	8

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(+.f64 x (/.f64 (-.f64 x y) 2))

Outputs
(+.f64 x (/.f64 (-.f64 x y) 2))
(fma.f64 y -1/2 (*.f64 x 3/2))

eval1.0ms (0%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.1b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.1b	(+.f64 x (/.f64 (-.f64 x y) 2))

Compiler

Compiled 9 to 6 computations (33.3% saved)

localize8.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (-.f64 x y) 2))

Compiler

Compiled 20 to 9 computations (55% saved)

series3.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(+.f64 x (/.f64 (-.f64 x y) 2))
1.0ms	y	@	-inf	(+.f64 x (/.f64 (-.f64 x y) 2))
1.0ms	x	@	0	(+.f64 x (/.f64 (-.f64 x y) 2))
1.0ms	x	@	-inf	(+.f64 x (/.f64 (-.f64 x y) 2))
0.0ms	y	@	inf	(+.f64 x (/.f64 (-.f64 x y) 2))

rewrite67.0ms (4.7%)

Algorithm

1×	batch-egg-rewrite

Rules

550×	`unpow-prod-down_binary64`
395×	`log-prod_binary64`
344×	`fma-def_binary64`
289×	`exp-prod_binary64`
259×	`pow-prod-down_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	171	8
2	2556	8

Stop Event

1×	node limit

Counts

1 → 74

Calls

Call 1

Inputs
(+.f64 x (/.f64 (-.f64 x y) 2))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 x 1/2) (-.f64 (.f64 y 1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 (-.f64 x y) 1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 (-.f64 x y) 1/2))) (/.f64 (.f64 (pow.f64 (-.f64 x y) 2) 1/4) (-.f64 x (.f64 (-.f64 x y) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 x (.f64 x 1/2)) (.f64 y 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (-.f64 x y) 1/2 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 (-.f64 x y) 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 2) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (pow.f64 (-.f64 x y) 3) 1/8 (pow.f64 x 3)) (/.f64 1 (fma.f64 (.f64 (-.f64 x y) 1/2) (-.f64 (.f64 (-.f64 x y) 1/2) x) (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (pow.f64 (-.f64 x y) 3) 1/8 (pow.f64 x 3)) (pow.f64 (/.f64 1 (fma.f64 (.f64 (-.f64 x y) 1/2) (-.f64 (.f64 (-.f64 x y) 1/2) x) (.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (.f64 x x) (.f64 (pow.f64 (-.f64 x y) 2) 1/4)) (/.f64 1 (-.f64 x (.f64 (-.f64 x y) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (.f64 x x) (.f64 (pow.f64 (-.f64 x y) 2) 1/4)) (pow.f64 (/.f64 1 (-.f64 x (.f64 (-.f64 x y) 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/3) (fma.f64 (-.f64 x y) 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (.f64 (fma.f64 (-.f64 x y) 1/2 x) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) 2) 3) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (.f64 (-.f64 x y) 1/2) (-.f64 (.f64 (-.f64 x y) 1/2) x) (.f64 x x)) (fma.f64 (pow.f64 (-.f64 x y) 3) 1/8 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 x (.f64 (-.f64 x y) 1/2)) (-.f64 (.f64 x x) (.f64 (pow.f64 (-.f64 x y) 2) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 (-.f64 x y) 3) 1/8 (pow.f64 x 3)) (fma.f64 (.f64 (-.f64 x y) 1/2) (-.f64 (.f64 (-.f64 x y) 1/2) x) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 (-.f64 x y) 3) 1/8 (pow.f64 x 3)) (fma.f64 (pow.f64 (-.f64 x y) 2) 1/4 (-.f64 (.f64 x x) (.f64 x (.f64 (-.f64 x y) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 x x) (.f64 (pow.f64 (-.f64 x y) 2) 1/4)) (-.f64 x (.f64 (-.f64 x y) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (pow.f64 (-.f64 x y) 3) 1/8 (pow.f64 x 3))) (neg.f64 (fma.f64 (.f64 (-.f64 x y) 1/2) (-.f64 (.f64 (-.f64 x y) 1/2) x) (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 (pow.f64 (-.f64 x y) 2) 1/4))) (neg.f64 (-.f64 x (.f64 (-.f64 x y) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (pow.f64 (-.f64 x y) 2) 1/4) (.f64 x x)) (-.f64 (.f64 (-.f64 x y) 1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (fma.f64 (-.f64 x y) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (.f64 (-.f64 x y) 1/2) (-.f64 (.f64 (-.f64 x y) 1/2) x) (.f64 x x)) (fma.f64 (pow.f64 (-.f64 x y) 3) 1/8 (pow.f64 x 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 x (.f64 (-.f64 x y) 1/2)) (-.f64 (.f64 x x) (.f64 (pow.f64 (-.f64 x y) 2) 1/4))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 (-.f64 x y) 1/2 x))) 2)) (cbrt.f64 (log.f64 (fma.f64 (-.f64 x y) 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 (-.f64 x y) 1/2 x)))) (sqrt.f64 (log.f64 (fma.f64 (-.f64 x y) 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (-.f64 x y) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (-.f64 x y) 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 x)) (sqrt.f64 (exp.f64 (-.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 x) (+.f64 1 (expm1.f64 (.f64 (-.f64 x y) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 x)) (+.f64 1 (expm1.f64 (.f64 (-.f64 x y) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 (-.f64 x y) 1/2))) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (sqrt.f64 (exp.f64 (-.f64 x y))) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 (-.f64 x y) 1/2))) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (-.f64 x y) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (-.f64 x y) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (-.f64 x y) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 (-.f64 x y) 1/2 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (fma.f64 (-.f64 x y) 1/2 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (fma.f64 (-.f64 x y) 1/2 x)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1 (.f64 (-.f64 x y) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/2 (neg.f64 (-.f64 (.f64 y 1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 x y) 1/2 x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (-.f64 x y) 1/2) 1 x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (.f64 (-.f64 x y) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 (-.f64 x y) 1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x 1/2) (neg.f64 (-.f64 (.f64 y 1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 (-.f64 x y) 1/2)) (pow.f64 (cbrt.f64 (.f64 (-.f64 x y) 1/2)) 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 (-.f64 x y) 1/2)) 2) (cbrt.f64 (.f64 (-.f64 x y) 1/2)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 2) (.f64 (-.f64 x y) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (.f64 (-.f64 x y) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 x y)) 2) (.f64 (cbrt.f64 (-.f64 x y)) 1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 (-.f64 x y) 1/2)) (sqrt.f64 (.f64 (-.f64 x y) 1/2)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (.f64 (-.f64 x y) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 x y)) (.f64 (sqrt.f64 (-.f64 x y)) 1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (-.f64 x y)) -1/2 x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (-.f64 x y) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 x 1/2)) 2) (cbrt.f64 (.f64 x 1/2)) (neg.f64 (-.f64 (.f64 y 1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (neg.f64 (-.f64 (*.f64 y 1/2) x)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 x 1/2) (-.f64 (*.f64 y 1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 (-.f64 x y) 1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (-.f64 x (*.f64 (-.f64 x y) 1/2))) (/.f64 (*.f64 (pow.f64 (-.f64 x y) 2) 1/4) (-.f64 x (*.f64 (-.f64 x y) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 x (*.f64 x 1/2)) (*.f64 y 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (-.f64 x y) 1/2 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 (-.f64 x y) 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 2) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 (-.f64 x y) 3) 1/8 (pow.f64 x 3)) (/.f64 1 (fma.f64 (*.f64 (-.f64 x y) 1/2) (-.f64 (*.f64 (-.f64 x y) 1/2) x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (pow.f64 (-.f64 x y) 3) 1/8 (pow.f64 x 3)) (pow.f64 (/.f64 1 (fma.f64 (*.f64 (-.f64 x y) 1/2) (-.f64 (*.f64 (-.f64 x y) 1/2) x) (*.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (*.f64 (pow.f64 (-.f64 x y) 2) 1/4)) (/.f64 1 (-.f64 x (*.f64 (-.f64 x y) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (*.f64 x x) (*.f64 (pow.f64 (-.f64 x y) 2) 1/4)) (pow.f64 (/.f64 1 (-.f64 x (*.f64 (-.f64 x y) 1/2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (fma.f64 (-.f64 x y) 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 (fma.f64 (-.f64 x y) 1/2 x) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 5/2) 1/3) (cbrt.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) 2) 3) (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (*.f64 (-.f64 x y) 1/2) (-.f64 (*.f64 (-.f64 x y) 1/2) x) (*.f64 x x)) (fma.f64 (pow.f64 (-.f64 x y) 3) 1/8 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 x (*.f64 (-.f64 x y) 1/2)) (-.f64 (*.f64 x x) (*.f64 (pow.f64 (-.f64 x y) 2) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 (-.f64 x y) 3) 1/8 (pow.f64 x 3)) (fma.f64 (*.f64 (-.f64 x y) 1/2) (-.f64 (*.f64 (-.f64 x y) 1/2) x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 (-.f64 x y) 3) 1/8 (pow.f64 x 3)) (fma.f64 (pow.f64 (-.f64 x y) 2) 1/4 (-.f64 (*.f64 x x) (*.f64 x (*.f64 (-.f64 x y) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) (*.f64 (pow.f64 (-.f64 x y) 2) 1/4)) (-.f64 x (*.f64 (-.f64 x y) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (pow.f64 (-.f64 x y) 3) 1/8 (pow.f64 x 3))) (neg.f64 (fma.f64 (*.f64 (-.f64 x y) 1/2) (-.f64 (*.f64 (-.f64 x y) 1/2) x) (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (*.f64 x x) (*.f64 (pow.f64 (-.f64 x y) 2) 1/4))) (neg.f64 (-.f64 x (*.f64 (-.f64 x y) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 (-.f64 x y) 2) 1/4) (*.f64 x x)) (-.f64 (*.f64 (-.f64 x y) 1/2) x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (fma.f64 (-.f64 x y) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (*.f64 (-.f64 x y) 1/2) (-.f64 (*.f64 (-.f64 x y) 1/2) x) (*.f64 x x)) (fma.f64 (pow.f64 (-.f64 x y) 3) 1/8 (pow.f64 x 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 x (*.f64 (-.f64 x y) 1/2)) (-.f64 (*.f64 x x) (*.f64 (pow.f64 (-.f64 x y) 2) 1/4))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 (-.f64 x y) 1/2 x))) 2)) (cbrt.f64 (log.f64 (fma.f64 (-.f64 x y) 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 (-.f64 x y) 1/2 x)))) (sqrt.f64 (log.f64 (fma.f64 (-.f64 x y) 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (-.f64 x y) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 (-.f64 x y) 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 x)) (sqrt.f64 (exp.f64 (-.f64 x y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 x) (+.f64 1 (expm1.f64 (*.f64 (-.f64 x y) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 x)) (+.f64 1 (expm1.f64 (*.f64 (-.f64 x y) 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 (-.f64 x y) 1/2))) (exp.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (sqrt.f64 (exp.f64 (-.f64 x y))) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (+.f64 1 (expm1.f64 (*.f64 (-.f64 x y) 1/2))) (+.f64 1 (expm1.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (-.f64 x y) 1/2 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (-.f64 x y) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (-.f64 x y) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (-.f64 x y) 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 (-.f64 x y) 1/2 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (fma.f64 (-.f64 x y) 1/2 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 (-.f64 x y) 1/2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 (-.f64 x y) 1/2 x)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1 (*.f64 (-.f64 x y) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1/2 (neg.f64 (-.f64 (*.f64 y 1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 x y) 1/2 x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (-.f64 x y) 1/2) 1 x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x (*.f64 (-.f64 x y) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 (-.f64 x y) 1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x 1/2) (neg.f64 (-.f64 (*.f64 y 1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (-.f64 x y) 1/2)) (pow.f64 (cbrt.f64 (*.f64 (-.f64 x y) 1/2)) 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 (-.f64 x y) 1/2)) 2) (cbrt.f64 (*.f64 (-.f64 x y) 1/2)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 2) (*.f64 (-.f64 x y) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) (*.f64 (-.f64 x y) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (-.f64 x y)) 2) (*.f64 (cbrt.f64 (-.f64 x y)) 1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (-.f64 x y) 1/2)) (sqrt.f64 (*.f64 (-.f64 x y) 1/2)) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) (*.f64 (-.f64 x y) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 x y)) (*.f64 (sqrt.f64 (-.f64 x y)) 1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (-.f64 x y)) -1/2 x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/2 (-.f64 x y) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x 1/2)) 2) (cbrt.f64 (*.f64 x 1/2)) (neg.f64 (-.f64 (*.f64 y 1/2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x 1/2)) (sqrt.f64 (*.f64 x 1/2)) (neg.f64 (-.f64 (*.f64 y 1/2) x)))))))

simplify13.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

15×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`associate-+l+_binary64`
2×	`associate-+r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	168
1	32	168
2	46	168

Stop Event

1×

saturated

Counts

98 → 81

Calls

Call 1

Inputs
(*.f64 -1/2 y)
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(*.f64 3/2 x)
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(*.f64 3/2 x)
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(+.f64 (*.f64 1/2 x) x)
(+.f64 (.f64 -1/2 y) (+.f64 (.f64 1/2 x) x))
(+.f64 (.f64 -1/2 y) (+.f64 (.f64 1/2 x) x))
(+.f64 (.f64 -1/2 y) (+.f64 (.f64 1/2 x) x))
(*.f64 -1/2 y)
(+.f64 (.f64 1/2 x) (+.f64 (.f64 -1/2 y) x))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 -1/2 y) x))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 -1/2 y) x))
(*.f64 -1/2 y)
(+.f64 (.f64 1/2 x) (+.f64 (.f64 -1/2 y) x))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 -1/2 y) x))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 -1/2 y) x))

Outputs
(*.f64 -1/2 y)
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(fma.f64 3/2 x (*.f64 -1/2 y))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(fma.f64 3/2 x (*.f64 -1/2 y))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(fma.f64 3/2 x (*.f64 -1/2 y))
(*.f64 3/2 x)
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(fma.f64 3/2 x (*.f64 -1/2 y))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(fma.f64 3/2 x (*.f64 -1/2 y))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(fma.f64 3/2 x (*.f64 -1/2 y))
(*.f64 3/2 x)
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(fma.f64 3/2 x (*.f64 -1/2 y))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(fma.f64 3/2 x (*.f64 -1/2 y))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(fma.f64 3/2 x (*.f64 -1/2 y))
(+.f64 (*.f64 1/2 x) x)
(*.f64 3/2 x)
(+.f64 (.f64 -1/2 y) (+.f64 (.f64 1/2 x) x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(fma.f64 3/2 x (*.f64 -1/2 y))
(+.f64 (.f64 -1/2 y) (+.f64 (.f64 1/2 x) x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(fma.f64 3/2 x (*.f64 -1/2 y))
(+.f64 (.f64 -1/2 y) (+.f64 (.f64 1/2 x) x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(fma.f64 3/2 x (*.f64 -1/2 y))
(*.f64 -1/2 y)
(+.f64 (.f64 1/2 x) (+.f64 (.f64 -1/2 y) x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(fma.f64 3/2 x (*.f64 -1/2 y))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 -1/2 y) x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(fma.f64 3/2 x (*.f64 -1/2 y))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 -1/2 y) x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(fma.f64 3/2 x (*.f64 -1/2 y))
(*.f64 -1/2 y)
(+.f64 (.f64 1/2 x) (+.f64 (.f64 -1/2 y) x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(fma.f64 3/2 x (*.f64 -1/2 y))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 -1/2 y) x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(fma.f64 3/2 x (*.f64 -1/2 y))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 -1/2 y) x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(fma.f64 3/2 x (*.f64 -1/2 y))

eval24.0ms (1.7%)

Compiler: Compiled 1125 to 625 computations (44.4% saved)

prune14.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	78	3	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	4	82

Error

Counts

82 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	28.3b	(*.f64 3/2 x)
▶	0b	(fma.f64 3/2 x (*.f64 -1/2 y))
▶	34.3b	(*.f64 -1/2 y)
✓	0.1b	(+.f64 x (/.f64 (-.f64 x y) 2))

Compiler

Compiled 27 to 20 computations (25.9% saved)

localize3.0ms (0.2%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

localize3.0ms (0.2%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

localize7.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 3/2 x (*.f64 -1/2 y))

Compiler

Compiled 15 to 10 computations (33.3% saved)

series3.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(fma.f64 3/2 x (*.f64 -1/2 y))
0.0ms	x	@	-inf	(fma.f64 3/2 x (*.f64 -1/2 y))
0.0ms	y	@	0	(fma.f64 3/2 x (*.f64 -1/2 y))
0.0ms	y	@	-inf	(fma.f64 3/2 x (*.f64 -1/2 y))
0.0ms	y	@	inf	(fma.f64 3/2 x (*.f64 -1/2 y))

rewrite53.0ms (3.8%)

Algorithm

1×	batch-egg-rewrite

Rules

618×	`pow1_binary64`
572×	`add-log-exp_binary64`
572×	`log1p-expm1-u_binary64`
572×	`expm1-log1p-u_binary64`
562×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	141	8
2	1531	8

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs
(fma.f64 3/2 x (*.f64 -1/2 y))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 -1/2 y) (.f64 3/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 3/2 x) (.f64 -1/2 y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 3/2 x) 1) (.f64 -1/2 y))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 3/2 x (.f64 -1/2 y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 3/2 x (.f64 -1/2 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 3/2 x (.f64 -1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 3/2 x (.f64 -1/2 y))) (pow.f64 (cbrt.f64 (fma.f64 3/2 x (.f64 -1/2 y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 3/2 x (.f64 -1/2 y))) 2) (cbrt.f64 (fma.f64 3/2 x (.f64 -1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 3/2 x (.f64 -1/2 y))) (sqrt.f64 (fma.f64 3/2 x (.f64 -1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 3/2 x) 3) (pow.f64 (.f64 -1/2 y) 3)) (+.f64 (.f64 (.f64 3/2 x) (.f64 3/2 x)) (-.f64 (.f64 (.f64 y y) 1/4) (.f64 (.f64 3/2 x) (.f64 -1/2 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 3/2 x) (.f64 3/2 x)) (.f64 (.f64 y y) 1/4)) (-.f64 (.f64 3/2 x) (.f64 -1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 3/2 x (.f64 -1/2 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 3/2 x (.f64 -1/2 y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 3/2 x (.f64 -1/2 y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 3/2 x (.f64 -1/2 y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 3/2 x (.f64 -1/2 y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 3/2 x (.f64 -1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 3/2 x (.f64 -1/2 y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 3/2 x (.f64 -1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 3/2 x (.f64 -1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 3/2 x (.f64 -1/2 y))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 -1/2 y) (*.f64 3/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 3/2 x) (*.f64 -1/2 y))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 3/2 x) 1) (*.f64 -1/2 y))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 3/2 x (*.f64 -1/2 y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 3/2 x (*.f64 -1/2 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 3/2 x (*.f64 -1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 3/2 x (*.f64 -1/2 y))) (pow.f64 (cbrt.f64 (fma.f64 3/2 x (*.f64 -1/2 y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 3/2 x (*.f64 -1/2 y))) 2) (cbrt.f64 (fma.f64 3/2 x (*.f64 -1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 3/2 x (*.f64 -1/2 y))) (sqrt.f64 (fma.f64 3/2 x (*.f64 -1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 3/2 x) 3) (pow.f64 (*.f64 -1/2 y) 3)) (+.f64 (*.f64 (*.f64 3/2 x) (*.f64 3/2 x)) (-.f64 (*.f64 (*.f64 y y) 1/4) (*.f64 (*.f64 3/2 x) (*.f64 -1/2 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 3/2 x) (*.f64 3/2 x)) (*.f64 (*.f64 y y) 1/4)) (-.f64 (*.f64 3/2 x) (*.f64 -1/2 y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 3/2 x (*.f64 -1/2 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 3/2 x (*.f64 -1/2 y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 3/2 x (*.f64 -1/2 y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 3/2 x (*.f64 -1/2 y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 3/2 x (*.f64 -1/2 y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 3/2 x (*.f64 -1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 3/2 x (*.f64 -1/2 y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 3/2 x (*.f64 -1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 3/2 x (*.f64 -1/2 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 3/2 x (*.f64 -1/2 y))))))))

simplify12.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	168
1	12	168
2	15	168

Stop Event

1×

saturated

Counts

45 → 24

Calls

Call 1

Inputs
(*.f64 -1/2 y)
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(*.f64 3/2 x)
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(*.f64 3/2 x)
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(*.f64 3/2 x)
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(*.f64 -1/2 y)
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(*.f64 -1/2 y)
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))

Outputs
(*.f64 -1/2 y)
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(*.f64 3/2 x)
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(*.f64 3/2 x)
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(*.f64 3/2 x)
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(*.f64 -1/2 y)
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(*.f64 -1/2 y)
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))
(+.f64 (.f64 -1/2 y) (.f64 3/2 x))
(fma.f64 -1/2 y (*.f64 3/2 x))

eval7.0ms (0.5%)

Compiler: Compiled 252 to 189 computations (25% saved)

prune5.0ms (0.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	24	4	28

Error

Counts

28 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	28.3b	(*.f64 3/2 x)
✓	0b	(fma.f64 3/2 x (*.f64 -1/2 y))
✓	34.3b	(*.f64 -1/2 y)
✓	0.1b	(+.f64 x (/.f64 (-.f64 x y) 2))

Compiler

Compiled 27 to 20 computations (25.9% saved)

regimes15.0ms (1.1%)

Counts

4 → 1

Calls

Call 1

Inputs
(*.f64 3/2 x)
(*.f64 -1/2 y)
(+.f64 x (/.f64 (-.f64 x y) 2))
(fma.f64 3/2 x (*.f64 -1/2 y))

Outputs
(fma.f64 3/2 x (*.f64 -1/2 y))

Calls

3 calls:

6.0ms	(+.f64 x (/.f64 (-.f64 x y) 2))
4.0ms	x
4.0ms	y

Results

Error	Segments	Branch
0b	1	`x`
0b	1	`y`
0b	1	`(+.f64 x (/.f64 (-.f64 x y) 2))`

Compiler

Compiled 36 to 24 computations (33.3% saved)

regimes15.0ms (1.1%)

Counts

3 → 1

Calls

Call 1

Inputs
(*.f64 3/2 x)
(*.f64 -1/2 y)
(+.f64 x (/.f64 (-.f64 x y) 2))

Outputs
(+.f64 x (/.f64 (-.f64 x y) 2))

Calls

3 calls:

6.0ms	x
4.0ms	(+.f64 x (/.f64 (-.f64 x y) 2))
4.0ms	y

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`y`
0.1b	1	`(+.f64 x (/.f64 (-.f64 x y) 2))`

Compiler

Compiled 30 to 20 computations (33.3% saved)

regimes39.0ms (2.7%)

Accuracy

Total -51.0b remaining (-474%)

Threshold costs -51.0b (-474%)

Counts

2 → 5

Calls

Call 1

Inputs
(*.f64 3/2 x)
(*.f64 -1/2 y)

Outputs
(*.f64 3/2 x)
(*.f64 -1/2 y)
(*.f64 3/2 x)
(*.f64 -1/2 y)
(*.f64 3/2 x)

Calls

2 calls:

22.0ms	y
16.0ms	x

Results

Error	Segments	Branch
10.8b	5	`x`
13.6b	7	`y`

Compiler

Compiled 14 to 10 computations (28.6% saved)

bsearch73.0ms (5.2%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
17.0ms	13268111000.88214	4419295797513501.0
16.0ms	-1.3947860810472575e-53	-7.316468694850264e-54
23.0ms	-108031933248673090.0	-58242120392965520.0
17.0ms	-1.413136565225612e+74	-3.5744658142166845e+73

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify7.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	66
1	30	66
2	35	66
3	37	66
4	38	66

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(fma.f64 3/2 x (*.f64 -1/2 y))
(+.f64 x (/.f64 (-.f64 x y) 2))
(if (<=.f64 x -141313656522561204830767401930471598823532868220412267952706868650354671616) (.f64 3/2 x) (if (<=.f64 x -108031933248673088) (.f64 -1/2 y) (if (<=.f64 x -3008268668569449/215679573337205118357336120696157045389097155380324579848828881993728) (.f64 3/2 x) (if (<=.f64 x 6956311380430495/524288) (.f64 -1/2 y) (*.f64 3/2 x)))))
(*.f64 3/2 x)

Outputs
(fma.f64 3/2 x (*.f64 -1/2 y))
(+.f64 x (/.f64 (-.f64 x y) 2))
(if (<=.f64 x -141313656522561204830767401930471598823532868220412267952706868650354671616) (.f64 3/2 x) (if (<=.f64 x -108031933248673088) (.f64 -1/2 y) (if (<=.f64 x -3008268668569449/215679573337205118357336120696157045389097155380324579848828881993728) (.f64 3/2 x) (if (<=.f64 x 6956311380430495/524288) (.f64 -1/2 y) (*.f64 3/2 x)))))
(*.f64 3/2 x)

Compiler

Compiled 55 to 40 computations (27.3% saved)

soundness12.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

15×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`associate-+l+_binary64`
2×	`associate-+r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	168
1	32	168
2	46	168

Stop Event

1×

saturated

Compiler

Compiled 70 to 54 computations (22.9% saved)

end39.0ms (2.8%)

Compiler: Compiled 49 to 34 computations (30.6% saved)

Details

analyze58.0ms (4.1%)

sample847.0ms (60.2%)

preprocess50.0ms (3.5%)

simplify28.0ms (2%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize8.0ms (0.5%)

series3.0ms (0.2%)

rewrite67.0ms (4.7%)

simplify13.0ms (0.9%)

eval24.0ms (1.7%)

prune14.0ms (1%)

localize3.0ms (0.2%)

localize3.0ms (0.2%)

localize7.0ms (0.5%)

series3.0ms (0.2%)

rewrite53.0ms (3.8%)

simplify12.0ms (0.8%)

eval7.0ms (0.5%)

prune5.0ms (0.4%)

regimes15.0ms (1.1%)

regimes15.0ms (1.1%)

regimes39.0ms (2.7%)

bsearch73.0ms (5.2%)

simplify7.0ms (0.5%)

soundness12.0ms (0.9%)

end39.0ms (2.8%)

Profiling