Details

analyze156.0ms (6.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
50%	46.8%	3.2%	7
59.3%	37.5%	3.2%	8
67.1%	25.8%	7.1%	9
72.6%	20.3%	7.1%	10
76.9%	13.5%	9.7%	11
79.8%	10.5%	9.7%	12
82%	6.9%	11.1%	13
83.6%	5.4%	11.1%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample924.0ms (40.5%)

Results

900.0ms	8256×	body	128	valid
13.0ms	122×	body	128	invalid

preprocess68.0ms (3%)

Algorithm

2×	egg-herbie

Rules

1297×	`fma-neg_binary64`
333×	`cancel-sign-sub-inv_binary64`
300×	`fma-def_binary64`
262×	`sub-neg_binary64`
200×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	32
1	44	28
2	106	24
3	247	24
4	557	22
5	1221	22
6	2255	22
7	3430	22
8	3826	22
9	3844	22
10	3844	22
11	4502	22
12	4502	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 (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
(+.f64 (-.f64 (.f64 y (-.f64 x 1)) (.f64 x 1/2)) 918938533204673/1000000000000000)

Outputs
(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
(+.f64 (-.f64 (.f64 x (+.f64 y -1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)
(fma.f64 x (-.f64 y 1) (fma.f64 y -1/2 918938533204673/1000000000000000))
(fma.f64 x (+.f64 y -1) (fma.f64 y -1/2 918938533204673/1000000000000000))
(fma.f64 y (+.f64 x -1/2) (-.f64 918938533204673/1000000000000000 x))
(-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)
(+.f64 (-.f64 (.f64 y (-.f64 x 1)) (.f64 x 1/2)) 918938533204673/1000000000000000)
(+.f64 918938533204673/1000000000000000 (-.f64 (.f64 y (+.f64 x -1)) (.f64 x 1/2)))
(+.f64 918938533204673/1000000000000000 (fma.f64 y (+.f64 x -1) (*.f64 x -1/2)))
(fma.f64 y (+.f64 x -1) (fma.f64 x -1/2 918938533204673/1000000000000000))
(fma.f64 x -1/2 (fma.f64 y (+.f64 x -1) 918938533204673/1000000000000000))
(fma.f64 x (+.f64 y -1/2) (-.f64 918938533204673/1000000000000000 y))
(-.f64 918938533204673/1000000000000000 (fma.f64 x (-.f64 1/2 y) y))

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify31.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-neg_binary64`
578×	`fma-def_binary64`
222×	`cancel-sign-sub-inv_binary64`
114×	`sub-neg_binary64`
81×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	27	14
2	62	12
3	129	12
4	268	11
5	580	11
6	1075	11
7	1794	11
8	2581	11
9	2752	11
10	2779	11

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)

Outputs
(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
(+.f64 (fma.f64 x (+.f64 y -1) (neg.f64 (*.f64 y 1/2))) 918938533204673/1000000000000000)
(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)
(fma.f64 x (+.f64 y -1) (fma.f64 y -1/2 918938533204673/1000000000000000))
(fma.f64 y (+.f64 x -1/2) (-.f64 918938533204673/1000000000000000 x))
(-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)

eval1.0ms (0%)

Compiler: Compiled 21 to 15 computations (28.6% saved)

prune2.0ms (0.1%)

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

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
	0.0b	(-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)
▶	0.0b	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)

Compiler

Compiled 46 to 34 computations (26.1% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (-.f64 y 1))
✓	0.0b	(-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2))

series7.0ms (0.3%)

Counts

2 → 48

Calls

12 calls:

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

rewrite65.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

459×	`log-prod_binary64`
426×	`fma-def_binary64`
238×	`fma-neg_binary64`
174×	`expm1-udef_binary64`
174×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	208	18
2	2752	18

Stop Event

1×	node limit

Counts

2 → 195

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (+.f64 y -1)) (.f64 y -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (+.f64 y -1)) (.f64 (.f64 y -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (+.f64 y -1)) (fma.f64 y -1/2 (fma.f64 y -1/2 (.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) (fma.f64 y -1/2 (.f64 y 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) (fma.f64 (.f64 y -1/2) 1 (.f64 y 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) (fma.f64 (neg.f64 (cbrt.f64 (.f64 y 1/2))) (cbrt.f64 (.f64 (.f64 y y) 1/4)) (.f64 y 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) (.f64 (fma.f64 y -1/2 (.f64 y 1/2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) (+.f64 (fma.f64 y -1/2 (.f64 y 1/2)) (fma.f64 y -1/2 (.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 y -1/2 (.f64 y 1/2)) (fma.f64 x (+.f64 y -1) (.f64 y -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 y -1/2) (.f64 x (+.f64 y -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)))) (cbrt.f64 (exp.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)))))) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))) (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))) 2) (cbrt.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))) (sqrt.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 (.f64 x (+.f64 y -1)) 3) (.f64 1/8 (pow.f64 y 3))) (/.f64 1 (fma.f64 (.f64 y 1/2) (fma.f64 x (+.f64 y -1) (.f64 y 1/2)) (pow.f64 (.f64 x (+.f64 y -1)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 (.f64 x (+.f64 y -1)) 2) (.f64 (.f64 y y) 1/4)) (/.f64 1 (fma.f64 x (+.f64 y -1) (.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (sqrt.f64 (+.f64 y -1)) (sqrt.f64 x) (sqrt.f64 (.f64 y 1/2))) (-.f64 (sqrt.f64 (.f64 x (+.f64 y -1))) (sqrt.f64 (.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (.f64 y 1/2) (fma.f64 x (+.f64 y -1) (.f64 y 1/2)) (pow.f64 (.f64 x (+.f64 y -1)) 2)) (-.f64 (pow.f64 (.f64 x (+.f64 y -1)) 3) (.f64 1/8 (pow.f64 y 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x (+.f64 y -1) (.f64 y 1/2)) (-.f64 (pow.f64 (.f64 x (+.f64 y -1)) 2) (.f64 (.f64 y y) 1/4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 x (+.f64 y -1)) 3) (.f64 1/8 (pow.f64 y 3))) (fma.f64 (.f64 y 1/2) (fma.f64 x (+.f64 y -1) (.f64 y 1/2)) (pow.f64 (.f64 x (+.f64 y -1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 x (+.f64 y -1)) 2) (.f64 (.f64 y y) 1/4)) (fma.f64 x (+.f64 y -1) (.f64 y 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (.f64 x (+.f64 y -1)) 3) (.f64 1/8 (pow.f64 y 3)))) (neg.f64 (fma.f64 (.f64 y 1/2) (fma.f64 x (+.f64 y -1) (.f64 y 1/2)) (pow.f64 (.f64 x (+.f64 y -1)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 (.f64 x (+.f64 y -1)) 2) (.f64 (.f64 y y) 1/4))) (neg.f64 (fma.f64 x (+.f64 y -1) (.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 x (+.f64 y -1)) 3) (pow.f64 (.f64 y -1/2) 3)) (+.f64 (pow.f64 (.f64 x (+.f64 y -1)) 2) (-.f64 (.f64 (.f64 y -1/2) (.f64 y -1/2)) (.f64 (.f64 x (+.f64 y -1)) (.f64 y -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) 3) (pow.f64 (fma.f64 y -1/2 (.f64 y 1/2)) 3)) (+.f64 (pow.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) 2) (-.f64 (.f64 (fma.f64 y -1/2 (.f64 y 1/2)) (fma.f64 y -1/2 (.f64 y 1/2))) (.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) (fma.f64 y -1/2 (.f64 y 1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (.f64 x (+.f64 y -1)) 2) (.f64 (.f64 y -1/2) (.f64 y -1/2))) (fma.f64 x (+.f64 y -1) (neg.f64 (.f64 y -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) 2) (.f64 (fma.f64 y -1/2 (.f64 y 1/2)) (fma.f64 y -1/2 (.f64 y 1/2)))) (-.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) (fma.f64 y -1/2 (.f64 y 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (.f64 x (+.f64 y -1)))) (pow.f64 (exp.f64 y) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (pow.f64 (exp.f64 x) (+.f64 y -1)) (+.f64 1 (expm1.f64 (.f64 y 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (/.f64 (+.f64 1 (expm1.f64 (.f64 x (+.f64 y -1)))) (+.f64 1 (expm1.f64 (.f64 y 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 x (+.f64 y -1)))) (exp.f64 (.f64 y -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (pow.f64 (exp.f64 x) (+.f64 y -1)) (/.f64 1 (pow.f64 (exp.f64 y) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (.f64 x (+.f64 y -1)))) (/.f64 1 (pow.f64 (exp.f64 y) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)))) (exp.f64 (fma.f64 y -1/2 (.f64 y 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (fma.f64 y -1/2 (.f64 y 1/2))) (exp.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (fma.f64 y -1/2 (.f64 y 1/2))) (+.f64 1 (expm1.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (.f64 y -1/2)) (pow.f64 (exp.f64 x) (+.f64 y -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (/.f64 1 (pow.f64 (exp.f64 y) 1/2)) (pow.f64 (exp.f64 x) (+.f64 y -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (.f64 y -1/2)) (+.f64 1 (expm1.f64 (.f64 x (+.f64 y -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (/.f64 1 (pow.f64 (exp.f64 y) 1/2)) (+.f64 1 (expm1.f64 (.f64 x (+.f64 y -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x (+.f64 y -1) (.f64 y -1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (+.f64 y -1) (.f64 y -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (+.f64 y -1) (.f64 (.f64 y -1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 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Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x (+.f64 y -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 y x) (*.f64 -1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x y) (*.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (+.f64 y -1))) (cbrt.f64 (pow.f64 (exp.f64 x) (+.f64 y -1))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) (+.f64 y -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 y -1)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) (+.f64 y -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (+.f64 y -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 y 3) -1) x) (+.f64 (fma.f64 y y 1) y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 y y -1) x) (+.f64 y 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 (pow.f64 y 3) -1)) (+.f64 (fma.f64 y y 1) y))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (fma.f64 y y -1)) (+.f64 y 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 y -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (+.f64 y -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (+.f64 y -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (+.f64 y -1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (+.f64 y -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (+.f64 y -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (+.f64 y -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (+.f64 y -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x y (*.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y x (*.f64 -1 x))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (+.f64 y -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (+.f64 y -1))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (+.f64 y -1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (+.f64 y -1))))))))

simplify36.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

293×	`fma-neg_binary64`
278×	`fma-def_binary64`
72×	`cancel-sign-sub-inv_binary64`
48×	`sub-neg_binary64`
39×	`unsub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	391
1	57	373
2	145	373
3	292	373
4	641	373
5	1032	373
6	1234	373
7	1268	373
8	1271	373

Stop Event

1×

saturated

Counts

243 → 210

Calls

Call 1

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

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

eval119.0ms (5.2%)

Compiler: Compiled 4373 to 3170 computations (27.5% saved)

prune823.0ms (36.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	209	1	210
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	211	1	212

Error

Counts

212 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0b	(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)

Compiler

Compiled 24 to 18 computations (25% saved)

localize6.0ms (0.3%)

eval0.0ms (0%)

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

prune1.0ms (0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

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

Error

Counts

1 → 1

Alt Table

Click to see full alt table

Status	Error	Program
✓	0b	(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)

Compiler

Compiled 12 to 9 computations (25% saved)

regimes16.0ms (0.7%)

Accuracy

Total -0.0b remaining (-∞%)

Threshold costs -0.0b (-∞%)

Counts

3 → 1

Calls

Call 1

Inputs

(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)

(-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)

(+.f64 (-.f64 (*.f64 x (-.f64 y 1)) (*.f64 y 1/2)) 918938533204673/1000000000000000)

Outputs
(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)

Results

Time	Error	Segments	Branch
3.0ms	0b	1	`x`
3.0ms	0b	1	`y`
3.0ms	0b	1	`(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)`
5.0ms	0b	1	`(-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2))`

Compiler

Compiled 61 to 44 computations (27.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	13	14

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)

Outputs
(+.f64 (fma.f64 x (+.f64 y -1) (*.f64 y -1/2)) 918938533204673/1000000000000000)

end16.0ms (0.7%)

Stop Event

1×

done

Compiler

Compiled 24 to 18 computations (25% saved)

Details

analyze156.0ms (6.9%)

sample924.0ms (40.5%)

preprocess68.0ms (3%)

simplify31.0ms (1.4%)

eval1.0ms (0%)

prune2.0ms (0.1%)

localize6.0ms (0.3%)

series7.0ms (0.3%)

rewrite65.0ms (2.9%)

simplify36.0ms (1.6%)

eval119.0ms (5.2%)

prune823.0ms (36.1%)

localize6.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

regimes16.0ms (0.7%)

simplify2.0ms (0.1%)

end16.0ms (0.7%)

Profiling