Details

analyze142.0ms (3.6%)

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
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
28.6%	25%	62.4%	0.1%	12.5%	0%	0%	6
36.4%	25%	43.7%	0.1%	31.2%	0%	0%	7
50%	31.2%	31.2%	0.1%	37.5%	0%	0%	8
62.5%	39%	23.4%	0.1%	37.5%	0%	0%	9
72.4%	42.9%	16.4%	0.1%	40.6%	0%	0%	10
79.6%	47.2%	12.1%	0.1%	40.6%	0%	0%	11
85.5%	49.4%	8.4%	0.1%	42.1%	0%	0%	12

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (31.1%)

Results

1.2s	8256×	body	256	valid
21.0ms	211×	body	256	infinite

Bogosity

preprocess67.0ms (1.7%)

Algorithm

2×	egg-herbie

Rules

26×	`fma-def_binary64`
11×	`+-commutative_binary64`
6×	`associate-+r+_binary64`
6×	`associate-+l+_binary64`
4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	28	22
2	62	22
3	76	22
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
(+.f64 (+.f64 (.f64 y 2) (.f64 y y)) (*.f64 x x))

Outputs
(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 x 2) (*.f64 y y))
(+.f64 (+.f64 (.f64 y 2) (.f64 y y)) (*.f64 x x))
(+.f64 (.f64 x x) (.f64 y (+.f64 2 y)))
(fma.f64 x x (*.f64 y (+.f64 2 y)))

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

14×	`fma-def_binary64`
6×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	17	11
2	34	11
3	42	11

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))

Outputs
(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 x 2) (*.f64 y y))

eval1.0ms (0%)

Compiler: Compiled 21 to 11 computations (47.6% saved)

prune1.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(fma.f64 x (+.f64 x 2) (*.f64 y y))
▶	0.0b	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))

Compiler

Compiled 23 to 14 computations (39.1% saved)

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 32 to 14 computations (56.3% saved)

series13.0ms (0.3%)

Counts

2 → 36

Calls

9 calls:

Time	Variable		Point	Expression
9.0ms	x	@	0	(+.f64 (.f64 x 2) (.f64 x x))
1.0ms	x	@	0	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
1.0ms	y	@	0	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
1.0ms	x	@	inf	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
1.0ms	y	@	inf	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))

rewrite84.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

577×	`fma-def_binary64`
467×	`log-prod_binary64`
356×	`pow-prod-down_binary64`
280×	`fma-neg_binary64`
262×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	203	18
2	2909	18

Stop Event

1×	node limit

Counts

2 → 167

Calls

Call 1

Inputs
(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
(+.f64 (.f64 x 2) (.f64 x x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (.f64 x (+.f64 x 2)) 2) (-.f64 (.f64 x (+.f64 x 2)) (.f64 y y))) (/.f64 (pow.f64 y 4) (-.f64 (.f64 x (+.f64 x 2)) (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2))) (pow.f64 (cbrt.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2))) 2) (cbrt.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 y (hypot.f64 x (sqrt.f64 (+.f64 x x)))) (hypot.f64 y (hypot.f64 x (sqrt.f64 (+.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (pow.f64 (.f64 x (+.f64 x 2)) 3) (pow.f64 y 6)) (/.f64 1 (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x (+.f64 x 2))) (pow.f64 (.f64 x (+.f64 x 2)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 (.f64 x (+.f64 x 2)) 2) (pow.f64 y 4)) (/.f64 1 (-.f64 (.f64 x (+.f64 x 2)) (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x (+.f64 x 2))) (pow.f64 (.f64 x (+.f64 x 2)) 2)) (+.f64 (pow.f64 (.f64 x (+.f64 x 2)) 3) (pow.f64 y 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) (-.f64 (pow.f64 (.f64 x (+.f64 x 2)) 2) (pow.f64 y 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 x (+.f64 x 2)) 3) (pow.f64 y 6)) (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x (+.f64 x 2))) (pow.f64 (.f64 x (+.f64 x 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 x (+.f64 x 2)) 3) (pow.f64 y 6)) (+.f64 (pow.f64 y 4) (-.f64 (pow.f64 (.f64 x (+.f64 x 2)) 2) (.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 x (+.f64 x 2)) 2) (pow.f64 y 4)) (-.f64 (.f64 x (+.f64 x 2)) (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (.f64 x (+.f64 x 2)) 3) (pow.f64 y 6))) (neg.f64 (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x (+.f64 x 2))) (pow.f64 (.f64 x (+.f64 x 2)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (.f64 x (+.f64 x 2)) 2) (pow.f64 y 4))) (neg.f64 (-.f64 (.f64 x (+.f64 x 2)) (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 3) 8 (pow.f64 (pow.f64 (hypot.f64 x y) 2) 3)) (fma.f64 (.f64 x x) 4 (-.f64 (pow.f64 (pow.f64 (hypot.f64 x y) 2) 2) (.f64 (+.f64 x x) (pow.f64 (hypot.f64 x y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 x x) 4) (pow.f64 (pow.f64 (hypot.f64 x y) 2) 2)) (-.f64 (+.f64 x x) (pow.f64 (hypot.f64 x y) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 y 4) (pow.f64 (.f64 x (+.f64 x 2)) 2)) (-.f64 (.f64 y y) (.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 y (hypot.f64 x (sqrt.f64 (+.f64 x x)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 x (+.f64 x 2))) (pow.f64 (.f64 x (+.f64 x 2)) 2)) (+.f64 (pow.f64 (.f64 x (+.f64 x 2)) 3) (pow.f64 y 6))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (.f64 x (+.f64 x 2)) (.f64 y y)) (-.f64 (pow.f64 (.f64 x (+.f64 x 2)) 2) (pow.f64 y 4))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (+.f64 x x))) (exp.f64 (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (+.f64 x x))) (pow.f64 (exp.f64 1) (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 x (+.f64 x 2)))) (pow.f64 (exp.f64 y) y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (pow.f64 (exp.f64 x) (+.f64 x 2)) (+.f64 1 (expm1.f64 (.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 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egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (hypot.f64 y (hypot.f64 x (sqrt.f64 (+.f64 x x))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 (log.f64 (fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (fma.f64 x 2 (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 2 (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 2 (.f64 (pow.f64 (hypot.f64 x y) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (+.f64 x 2) (.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 x (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 x (.f64 (pow.f64 (hypot.f64 x y) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x x) 1 (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x x) 1 (.f64 (pow.f64 (hypot.f64 x y) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x x) 1 (fma.f64 x 2 (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (+.f64 x 2)) 1 (.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y y (.f64 x (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 y y) 1 (.f64 x (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 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(#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) 2) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) 2) (.f64 (pow.f64 (hypot.f64 x y) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (fma.f64 x 2 (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 x (+.f64 x 2))) (pow.f64 (cbrt.f64 (.f64 x (+.f64 x 2))) 2) (.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 x (+.f64 x 2))) 2) (cbrt.f64 (.f64 x (+.f64 x 2))) (.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x x)) (pow.f64 (cbrt.f64 (+.f64 x x)) 2) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (+.f64 x x)) (pow.f64 (cbrt.f64 (+.f64 x x)) 2) (.f64 (pow.f64 (hypot.f64 x y) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 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x))))))

Outputs

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simplify186.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

796×	`sqr-pow_binary64`
666×	`fabs-mul_binary64`
666×	`cube-prod_binary64`
514×	`pow-sqr_binary64`
511×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	346
1	28	304
2	55	289
3	88	289
4	189	289
5	492	289
6	1678	289
7	2350	289
8	2682	289
9	2942	289
10	3281	289
11	3787	289
12	4450	289
13	5246	289
14	6179	289
15	6702	289
16	7117	289
17	7514	289
18	7637	289
19	7683	289

Stop Event

1×	node limit

Counts

203 → 178

Calls

Call 1

Inputs
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (pow.f64 x 2))

Outputs
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 2 x (fma.f64 x x (*.f64 y y)))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))

localize12.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (+.f64 x 2) (*.f64 y y))

Compiler

Compiled 19 to 9 computations (52.6% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite76.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

742×	`pow1_binary64`
690×	`add-log-exp_binary64`
689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
675×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	150	11
2	1860	11

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs
(fma.f64 x (+.f64 x 2) (*.f64 y y))

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

Outputs

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

simplify210.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

796×	`sqr-pow_binary64`
666×	`cube-prod_binary64`
663×	`fabs-mul_binary64`
514×	`pow-sqr_binary64`
505×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	262
1	34	214
2	59	214
3	87	214
4	192	214
5	511	214
6	1715	214
7	2370	214
8	2701	214
9	2961	214
10	3300	214
11	3806	214
12	4467	214
13	5261	214
14	6190	214
15	6711	214
16	7124	214
17	7517	214
18	7644	214
19	7690	214

Stop Event

1×	node limit

Counts

45 → 33

Calls

Call 1

Inputs
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(*.f64 (+.f64 2 x) x)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))

Outputs
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(*.f64 (+.f64 2 x) x)
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))

eval150.0ms (3.8%)

Compiler: Compiled 3020 to 1579 computations (47.7% saved)

prune77.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	204	7	211
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	205	8	213

Error

Counts

213 → 8

Alt Table

Click to see full alt table

Status	Error	Program
▶	17.5b	(+.f64 (.f64 2 x) (.f64 y y))
▶	24.0b	(*.f64 (+.f64 2 x) x)
	0.0b	(+.f64 (.f64 (+.f64 x 2) x) (.f64 y y))
▶	45.1b	(*.f64 x x)
✓	0.0b	(fma.f64 x (+.f64 x 2) (*.f64 y y))
	17.5b	(fma.f64 y y (*.f64 2 x))
▶	38.1b	(*.f64 y y)
▶	0.0b	(fma.f64 y y (*.f64 x (+.f64 x 2)))

Compiler

Compiled 120 to 76 computations (36.7% saved)

localize18.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y y (*.f64 x (+.f64 x 2)))

Compiler

Compiled 21 to 12 computations (42.9% saved)

series8.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	y	@	inf	(fma.f64 y y (*.f64 x (+.f64 x 2)))
1.0ms	y	@	0	(fma.f64 y y (*.f64 x (+.f64 x 2)))
1.0ms	y	@	-inf	(fma.f64 y y (*.f64 x (+.f64 x 2)))
1.0ms	x	@	-inf	(fma.f64 y y (*.f64 x (+.f64 x 2)))
1.0ms	x	@	inf	(fma.f64 y y (*.f64 x (+.f64 x 2)))

rewrite90.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

783×	`pow1_binary64`
729×	`add-log-exp_binary64`
728×	`log1p-expm1-u_binary64`
728×	`expm1-log1p-u_binary64`
716×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	153	11
2	1946	11

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

Inputs
(fma.f64 y y (*.f64 x (+.f64 x 2)))

Outputs

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

simplify207.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

796×	`sqr-pow_binary64`
666×	`cube-prod_binary64`
661×	`fabs-mul_binary64`
514×	`pow-sqr_binary64`
505×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	244
1	34	214
2	59	214
3	87	214
4	194	214
5	521	214
6	1723	214
7	2382	214
8	2713	214
9	2973	214
10	3314	214
11	3820	214
12	4479	214
13	5275	214
14	6204	214
15	6721	214
16	7130	214
17	7533	214
18	7654	214
19	7702	214

Stop Event

1×	node limit

Counts

46 → 34

Calls

Call 1

Inputs
(*.f64 (+.f64 2 x) x)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))

Outputs
(*.f64 (+.f64 2 x) x)
(*.f64 x (+.f64 2 x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 2 x) (*.f64 y y))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (.f64 x (+.f64 2 x)) (.f64 y y))
(fma.f64 x (+.f64 2 x) (*.f64 y y))

localize10.0ms (0.3%)

Compiler: Compiled 6 to 3 computations (50% saved)

localize6.0ms (0.2%)

Compiler: Compiled 6 to 3 computations (50% saved)

localize11.0ms (0.3%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

localize17.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 18 to 9 computations (50% saved)

series4.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite93.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

747×	`pow1_binary64`
696×	`add-log-exp_binary64`
695×	`log1p-expm1-u_binary64`
695×	`expm1-log1p-u_binary64`
680×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	150	8
2	1954	8

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 2 x (*.f64 y y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 2 x) 2) (-.f64 (*.f64 2 x) (*.f64 y y))) (/.f64 (pow.f64 y 4) (-.f64 (*.f64 2 x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 2 x (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 2 x (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 2 x (*.f64 y y))) (pow.f64 (cbrt.f64 (fma.f64 2 x (*.f64 y y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 2 x (*.f64 y y))) 2) (cbrt.f64 (fma.f64 2 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 y (sqrt.f64 (*.f64 2 x))) (hypot.f64 y (sqrt.f64 (*.f64 2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 y 6)) (/.f64 1 (+.f64 (pow.f64 (*.f64 2 x) 2) (-.f64 (pow.f64 y 4) (*.f64 2 (*.f64 x (*.f64 y y)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (*.f64 2 x) 2) (pow.f64 y 4)) (/.f64 1 (-.f64 (*.f64 2 x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (*.f64 2 x) 2) (-.f64 (pow.f64 y 4) (*.f64 2 (*.f64 x (*.f64 y y))))) (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 y 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 2 x) (*.f64 y y)) (-.f64 (pow.f64 (*.f64 2 x) 2) (pow.f64 y 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 y 6)) (+.f64 (pow.f64 (*.f64 2 x) 2) (-.f64 (pow.f64 y 4) (*.f64 2 (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 y 6)) (+.f64 (pow.f64 y 4) (-.f64 (pow.f64 (*.f64 2 x) 2) (*.f64 2 (*.f64 x (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 2 x) 2) (pow.f64 y 4)) (-.f64 (*.f64 2 x) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (*.f64 (pow.f64 x 3) 8) (pow.f64 y 6))) (neg.f64 (+.f64 (pow.f64 (*.f64 2 x) 2) (-.f64 (pow.f64 y 4) (*.f64 2 (*.f64 x (*.f64 y y)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 2 x) 2) (pow.f64 y 4))) (neg.f64 (-.f64 (*.f64 2 x) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 y 4) (pow.f64 (*.f64 2 x) 2)) (-.f64 (*.f64 y y) (*.f64 2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 2 x (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 2 x (*.f64 y y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 2 x (*.f64 y y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 y (sqrt.f64 (*.f64 2 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 2 x (*.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 2 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 2 x (*.f64 y y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 2 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 2 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 2 x (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 2 x (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 2 (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y y (*.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 2 x) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 y y) (*.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 y 4)) (pow.f64 (cbrt.f64 y) 2) (*.f64 2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 2 x)) 2) (cbrt.f64 (*.f64 2 x)) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 (*.f64 2 x)) (*.f64 y y))))))

simplify194.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

1366×	`sqr-pow_binary64`
695×	`pow-sqr_binary64`
617×	`cube-prod_binary64`
611×	`fabs-mul_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	168
1	15	168
2	25	168
3	36	168
4	65	168
5	167	168
6	587	168
7	1453	168
8	1637	168
9	1821	168
10	2029	168
11	2324	168
12	2717	168
13	3202	168
14	3768	168
15	4456	168
16	5297	168
17	5691	168
18	5979	168
19	6255	168
20	6329	168
21	6363	168
22	7304	168

Stop Event

1×	node limit

Counts

59 → 39

Calls

Call 1

Inputs
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (pow.f64 y 2))

Outputs
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(*.f64 2 x)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))

eval40.0ms (1%)

Compiler: Compiled 875 to 527 computations (39.8% saved)

prune58.0ms (1.5%)

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	1	1	2
Picked	0	1	1
Done	0	5	5
Total	72	9	81

Error

Counts

81 → 9

Alt Table

Click to see full alt table

Status	Error	Program
✓	17.5b	(+.f64 (.f64 2 x) (.f64 y y))
✓	24.0b	(*.f64 (+.f64 2 x) x)
▶	0.0b	(+.f64 (.f64 (+.f64 x 2) x) (.f64 y y))
✓	45.1b	(*.f64 x x)
✓	0.0b	(fma.f64 x (+.f64 x 2) (*.f64 y y))
✓	38.1b	(*.f64 y y)
▶	17.5b	(fma.f64 y y (*.f64 2 x))
▶	41.6b	(*.f64 2 x)
✓	0.0b	(fma.f64 y y (*.f64 x (+.f64 x 2)))

Compiler

Compiled 70 to 45 computations (35.7% saved)

localize20.0ms (0.5%)

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

localize17.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 25 to 13 computations (48% saved)

series3.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite81.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

972×	`pow1_binary64`
908×	`add-log-exp_binary64`
907×	`log1p-expm1-u_binary64`
907×	`expm1-log1p-u_binary64`
94×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	180	11
2	2476	11

Stop Event

1×	node limit

Counts

1 → 36

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x (+.f64 x 2) (*.f64 y y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2) (-.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y))) (/.f64 (pow.f64 y 4) (-.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x (+.f64 x 2) (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x (+.f64 x 2) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x (+.f64 x 2) (*.f64 y y))) (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 x 2) (*.f64 y y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 x 2) (*.f64 y y))) 2) (cbrt.f64 (fma.f64 x (+.f64 x 2) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 y (sqrt.f64 (*.f64 x (+.f64 x 2)))) (hypot.f64 y (sqrt.f64 (*.f64 x (+.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) (pow.f64 y 6)) (/.f64 1 (+.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2) (*.f64 (*.f64 y y) (-.f64 (*.f64 y y) (*.f64 x (+.f64 x 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2) (pow.f64 y 4)) (/.f64 1 (-.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2) (*.f64 (*.f64 y y) (-.f64 (*.f64 y y) (*.f64 x (+.f64 x 2))))) (+.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) (pow.f64 y 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)) (-.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2) (pow.f64 y 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) (pow.f64 y 6)) (+.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2) (*.f64 (*.f64 y y) (-.f64 (*.f64 y y) (*.f64 x (+.f64 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) (pow.f64 y 6)) (+.f64 (pow.f64 y 4) (-.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2) (*.f64 x (*.f64 (+.f64 x 2) (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2) (pow.f64 y 4)) (-.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 3) (pow.f64 y 6))) (neg.f64 (+.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2) (*.f64 (*.f64 y y) (-.f64 (*.f64 y y) (*.f64 x (+.f64 x 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 x (+.f64 x 2)) 2) (pow.f64 y 4))) (neg.f64 (-.f64 (*.f64 x (+.f64 x 2)) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 y 4) (pow.f64 (*.f64 x (+.f64 x 2)) 2)) (-.f64 (*.f64 y y) (*.f64 x (+.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (+.f64 x 2) (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (+.f64 x 2) (*.f64 y y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (+.f64 x 2) (*.f64 y y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 y (sqrt.f64 (*.f64 x (+.f64 x 2)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (+.f64 x 2) (*.f64 y y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (+.f64 x 2) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x (+.f64 x 2) (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (+.f64 x 2) (*.f64 y y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x (+.f64 x 2) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x (+.f64 x 2) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x (+.f64 x 2) (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (+.f64 x 2) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x 2) x (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y y (*.f64 x (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x (+.f64 x 2)) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 y y) (*.f64 x (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x (+.f64 x 2))) 2) (cbrt.f64 (*.f64 x (+.f64 x 2))) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 y 4)) (pow.f64 (cbrt.f64 y) 2) (*.f64 x (+.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x (+.f64 x 2))) (sqrt.f64 (*.f64 x (+.f64 x 2))) (*.f64 y y))))))

simplify206.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

796×	`sqr-pow_binary64`
666×	`cube-prod_binary64`
663×	`fabs-mul_binary64`
514×	`pow-sqr_binary64`
505×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	262
1	34	214
2	59	214
3	87	214
4	192	214
5	511	214
6	1715	214
7	2370	214
8	2701	214
9	2961	214
10	3300	214
11	3806	214
12	4467	214
13	5261	214
14	6190	214
15	6711	214
16	7124	214
17	7517	214
18	7644	214
19	7690	214

Stop Event

1×	node limit

Counts

60 → 48

Calls

Call 1

Inputs
(pow.f64 y 2)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(*.f64 (+.f64 2 x) x)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(pow.f64 y 2)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))

Outputs
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (*.f64 2 x) (pow.f64 y 2))
(fma.f64 2 x (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 2 x) (pow.f64 x 2))
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (*.f64 2 x) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(*.f64 (+.f64 2 x) x)
(fma.f64 2 x (*.f64 x x))
(*.f64 x (+.f64 2 x))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(pow.f64 y 2)
(*.f64 y y)
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))
(+.f64 (pow.f64 y 2) (*.f64 (+.f64 2 x) x))
(+.f64 (fma.f64 2 x (.f64 y y)) (.f64 x x))
(fma.f64 y y (*.f64 x (+.f64 2 x)))

localize12.0ms (0.3%)

Compiler: Compiled 14 to 8 computations (42.9% saved)

eval18.0ms (0.5%)

Compiler: Compiled 685 to 406 computations (40.7% saved)

prune11.0ms (0.3%)

Pruning

9 alts after pruning (0 fresh and 9 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	0	0
Picked	0	1	1
Done	0	8	8
Total	48	9	57

Error

Counts

57 → 9

Alt Table

Click to see full alt table

Status	Error	Program
✓	17.5b	(+.f64 (.f64 2 x) (.f64 y y))
✓	24.0b	(*.f64 (+.f64 2 x) x)
✓	0.0b	(+.f64 (.f64 (+.f64 x 2) x) (.f64 y y))
✓	45.1b	(*.f64 x x)
✓	0.0b	(fma.f64 x (+.f64 x 2) (*.f64 y y))
✓	38.1b	(*.f64 y y)
✓	17.5b	(fma.f64 y y (*.f64 2 x))
✓	41.6b	(*.f64 2 x)
✓	0.0b	(fma.f64 y y (*.f64 x (+.f64 x 2)))

Compiler

Compiled 70 to 45 computations (35.7% saved)

regimes78.0ms (2%)

Counts

11 → 1

Calls

Call 1

Inputs
(*.f64 2 x)
(*.f64 x x)
(*.f64 y y)
(*.f64 (+.f64 2 x) x)
(+.f64 (.f64 2 x) (.f64 y y))
(+.f64 (.f64 (+.f64 x 2) x) (.f64 y y))
(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(fma.f64 y y (*.f64 2 x))
(fma.f64 y y (*.f64 x (+.f64 x 2)))
(fma.f64 x (+.f64 x 2) (*.f64 y y))

Outputs
(fma.f64 y y (*.f64 x (+.f64 x 2)))

Calls

7 calls:

32.0ms	(*.f64 y y)
8.0ms	(+.f64 (.f64 x 2) (.f64 x x))
8.0ms	y
7.0ms	(+.f64 (.f64 x 2) (.f64 x x))
7.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`y`
0.0b	1	`(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))`
0.0b	1	`(+.f64 (.f64 x 2) (.f64 x x))`
0.0b	1	`(+.f64 (.f64 x 2) (.f64 x x))`
0.0b	1	`(*.f64 y y)`
0.0b	1	`(*.f64 y y)`

Compiler

Compiled 118 to 63 computations (46.6% saved)

regimes40.0ms (1%)

Counts

9 → 1

Calls

Call 1

Inputs
(*.f64 2 x)
(*.f64 x x)
(*.f64 y y)
(*.f64 (+.f64 2 x) x)
(+.f64 (.f64 2 x) (.f64 y y))
(+.f64 (.f64 (+.f64 x 2) x) (.f64 y y))
(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
(fma.f64 y y (*.f64 2 x))
(fma.f64 y y (*.f64 2 x))

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

Calls

6 calls:

7.0ms	(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))
7.0ms	(+.f64 (.f64 x 2) (.f64 x x))
6.0ms	(+.f64 (.f64 x 2) (.f64 x x))
6.0ms	x
6.0ms	y

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`y`
0.0b	1	`(+.f64 (+.f64 (.f64 x 2) (.f64 x x)) (*.f64 y y))`
0.0b	1	`(+.f64 (.f64 x 2) (.f64 x x))`
0.0b	1	`(+.f64 (.f64 x 2) (.f64 x x))`
0.0b	1	`(*.f64 y y)`

Compiler

Compiled 97 to 53 computations (45.4% saved)

regimes66.0ms (1.7%)

Counts

5 → 3

Calls

Call 1

Inputs
(*.f64 2 x)
(*.f64 x x)
(*.f64 y y)
(*.f64 (+.f64 2 x) x)
(+.f64 (.f64 2 x) (.f64 y y))

Outputs
(*.f64 (+.f64 2 x) x)
(+.f64 (.f64 2 x) (.f64 y y))
(*.f64 (+.f64 2 x) x)

Calls

3 calls:

31.0ms	(*.f64 y y)
19.0ms	y
15.0ms	x

Results

Error	Segments	Branch
4.0b	3	`x`
7.8b	3	`y`
8.1b	2	`(*.f64 y y)`

Compiler

Compiled 34 to 19 computations (44.1% saved)

bsearch38.0ms (1%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
19.0ms	0.032736531682852316	38.53340808082482
19.0ms	-292259633.10069704	-18273231.154325806

Compiler

Compiled 18 to 12 computations (33.3% saved)

regimes45.0ms (1.1%)

Counts

4 → 3

Calls

Call 1

Inputs
(*.f64 2 x)
(*.f64 x x)
(*.f64 y y)
(*.f64 (+.f64 2 x) x)

Outputs
(*.f64 y y)
(*.f64 (+.f64 2 x) x)
(*.f64 y y)

Calls

3 calls:

21.0ms	x
11.0ms	y
11.0ms	(*.f64 y y)

Results

Error	Segments	Branch
17.4b	5	`x`
9.0b	3	`y`
9.2b	2	`(*.f64 y y)`

Compiler

Compiled 27 to 16 computations (40.7% saved)

bsearch36.0ms (0.9%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
18.0ms	1.8948806182633805e-72	9.959740941363019e-64
18.0ms	-1.4895189036595543e-38	-2.1319564130686237e-47

Compiler

Compiled 18 to 12 computations (33.3% saved)

regimes53.0ms (1.3%)

Counts

3 → 5

Calls

Call 1

Inputs
(*.f64 2 x)
(*.f64 x x)
(*.f64 y y)

Outputs
(*.f64 y y)
(*.f64 2 x)
(*.f64 x x)
(*.f64 2 x)
(*.f64 y y)

Calls

3 calls:

24.0ms	x
17.0ms	y
10.0ms	(*.f64 y y)

Results

Error	Segments	Branch
18.9b	7	`x`
18.3b	5	`y`
18.7b	4	`(*.f64 y y)`

Compiler

Compiled 22 to 13 computations (40.9% saved)

bsearch71.0ms (1.8%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
19.0ms	1.8948806182633805e-72	9.959740941363019e-64
17.0ms	1.608162247183401e-87	2.0563901513583723e-85
17.0ms	4.5750946669891457e-163	7.802263225988407e-163
18.0ms	-2.9203625505413584e-62	-6.288945124401131e-72

Compiler

Compiled 18 to 12 computations (33.3% saved)

regimes26.0ms (0.7%)

Accuracy

Total -35.8b remaining (-140.4%)

Threshold costs -35.8b (-140.4%)

Counts

2 → 3

Calls

Call 1

Inputs
(*.f64 2 x)
(*.f64 x x)

Outputs
(*.f64 x x)
(*.f64 2 x)
(*.f64 x x)

Calls

2 calls:

15.0ms	y
10.0ms	x

Results

Error	Segments	Branch
25.5b	3	`x`
32.8b	5	`y`

Compiler

Compiled 14 to 9 computations (35.7% saved)

bsearch35.0ms (0.9%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
17.0ms	0.032736531682852316	38.53340808082482
18.0ms	-5504308.622068178	-0.0010798252602814689

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	159
1	50	159

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(fma.f64 y y (*.f64 x (+.f64 x 2)))
(+.f64 (.f64 (+.f64 x 2) x) (.f64 y y))
(if (<=.f64 x -612912874076393/2097152) (.f64 (+.f64 2 x) x) (if (<=.f64 x 1179457855106369/36028797018963968) (+.f64 (.f64 2 x) (.f64 y y)) (.f64 (+.f64 2 x) x)))
(if (<=.f64 y -2853351347367143/191561942608236107294793378393788647952342390272950272) (.f64 y y) (if (<=.f64 y 7538945293479375/3978585891278293137243057985174566720803649206378781739523711815145275976100267004264448) (.f64 (+.f64 2 x) x) (*.f64 y y)))
(if (<=.f64 y -3381548810576013/115792089237316195423570985008687907853269984665640564039457584007913129639936) (.f64 y y) (if (<=.f64 y 1853947905251549/4052261297735344686047273304385899561535592023674254785152009111026028136145418111718463914987406049109568248643848426935932764722081811824108276205189417663145685354884286644224) (.f64 2 x) (if (<=.f64 y 7203745875395729/4479489484355608421114884561136888556243290994469299069799978201927583742360321890761754986543214231552) (.f64 x x) (if (<=.f64 y 7538945293479375/3978585891278293137243057985174566720803649206378781739523711815145275976100267004264448) (.f64 2 x) (*.f64 y y)))))
(if (<=.f64 x -1477551594929603/268435456) (.f64 x x) (if (<=.f64 x 1179457855106369/36028797018963968) (.f64 2 x) (*.f64 x x)))
(*.f64 2 x)

Outputs
(fma.f64 y y (*.f64 x (+.f64 x 2)))
(+.f64 (.f64 (+.f64 x 2) x) (.f64 y y))
(+.f64 (.f64 x (+.f64 x 2)) (.f64 y y))
(if (<=.f64 x -612912874076393/2097152) (.f64 (+.f64 2 x) x) (if (<=.f64 x 1179457855106369/36028797018963968) (+.f64 (.f64 2 x) (.f64 y y)) (.f64 (+.f64 2 x) x)))
(if (<=.f64 x -612912874076393/2097152) (.f64 x (+.f64 x 2)) (if (<=.f64 x 1179457855106369/36028797018963968) (+.f64 (.f64 y y) (.f64 x 2)) (.f64 x (+.f64 x 2))))
(if (<=.f64 y -2853351347367143/191561942608236107294793378393788647952342390272950272) (.f64 y y) (if (<=.f64 y 7538945293479375/3978585891278293137243057985174566720803649206378781739523711815145275976100267004264448) (.f64 (+.f64 2 x) x) (*.f64 y y)))
(if (<=.f64 y -2853351347367143/191561942608236107294793378393788647952342390272950272) (.f64 y y) (if (<=.f64 y 7538945293479375/3978585891278293137243057985174566720803649206378781739523711815145275976100267004264448) (.f64 x (+.f64 x 2)) (*.f64 y y)))
(if (<=.f64 y -3381548810576013/115792089237316195423570985008687907853269984665640564039457584007913129639936) (.f64 y y) (if (<=.f64 y 1853947905251549/4052261297735344686047273304385899561535592023674254785152009111026028136145418111718463914987406049109568248643848426935932764722081811824108276205189417663145685354884286644224) (.f64 2 x) (if (<=.f64 y 7203745875395729/4479489484355608421114884561136888556243290994469299069799978201927583742360321890761754986543214231552) (.f64 x x) (if (<=.f64 y 7538945293479375/3978585891278293137243057985174566720803649206378781739523711815145275976100267004264448) (.f64 2 x) (*.f64 y y)))))
(if (<=.f64 y -3381548810576013/115792089237316195423570985008687907853269984665640564039457584007913129639936) (.f64 y y) (if (<=.f64 y 1853947905251549/4052261297735344686047273304385899561535592023674254785152009111026028136145418111718463914987406049109568248643848426935932764722081811824108276205189417663145685354884286644224) (.f64 x 2) (if (<=.f64 y 7203745875395729/4479489484355608421114884561136888556243290994469299069799978201927583742360321890761754986543214231552) (.f64 x x) (if (<=.f64 y 7538945293479375/3978585891278293137243057985174566720803649206378781739523711815145275976100267004264448) (.f64 x 2) (*.f64 y y)))))
(if (<=.f64 x -1477551594929603/268435456) (.f64 x x) (if (<=.f64 x 1179457855106369/36028797018963968) (.f64 2 x) (*.f64 x x)))
(if (<=.f64 x -1477551594929603/268435456) (.f64 x x) (if (<=.f64 x 1179457855106369/36028797018963968) (.f64 x 2) (*.f64 x x)))
(*.f64 2 x)
(*.f64 x 2)

Compiler

Compiled 126 to 78 computations (38.1% saved)

soundness0.0ms (0%)

end61.0ms (1.5%)

Compiler: Compiled 114 to 62 computations (45.6% saved)

Details

analyze142.0ms (3.6%)

sample1.2s (31.1%)

preprocess67.0ms (1.7%)

simplify8.0ms (0.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize11.0ms (0.3%)

series13.0ms (0.3%)

rewrite84.0ms (2.1%)

simplify186.0ms (4.7%)

localize12.0ms (0.3%)

series3.0ms (0.1%)

rewrite76.0ms (1.9%)

simplify210.0ms (5.3%)

eval150.0ms (3.8%)

prune77.0ms (1.9%)

localize18.0ms (0.5%)

series8.0ms (0.2%)

rewrite90.0ms (2.3%)

simplify207.0ms (5.3%)

localize10.0ms (0.3%)

localize6.0ms (0.2%)

localize11.0ms (0.3%)

localize17.0ms (0.4%)

series4.0ms (0.1%)

rewrite93.0ms (2.3%)

simplify194.0ms (4.9%)

eval40.0ms (1%)

prune58.0ms (1.5%)

localize20.0ms (0.5%)

localize17.0ms (0.4%)

series3.0ms (0.1%)

rewrite81.0ms (2%)

simplify206.0ms (5.2%)

localize12.0ms (0.3%)

eval18.0ms (0.5%)

prune11.0ms (0.3%)

regimes78.0ms (2%)

regimes40.0ms (1%)

regimes66.0ms (1.7%)

bsearch38.0ms (1%)

regimes45.0ms (1.1%)

bsearch36.0ms (0.9%)

regimes53.0ms (1.3%)

bsearch71.0ms (1.8%)

regimes26.0ms (0.7%)

bsearch35.0ms (0.9%)

simplify10.0ms (0.3%)

soundness0.0ms (0%)

end61.0ms (1.5%)

Profiling