Details

analyze424.0ms (23.4%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
25%	74.9%	0.1%	8
31.2%	64%	4.8%	9
46.8%	47.6%	5.6%	10
53.8%	40.2%	6%	11
57.3%	33.7%	8.9%	12
66.9%	23.9%	9.2%	13
70.3%	20.3%	9.4%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample860.0ms (47.5%)

Results

805.0ms	8252×	body	128	valid
32.0ms	332×	body	128	invalid
1.0ms	4×	body	1024	valid

Compiler

Compiled 26 to 18 computations (30.8% saved)

preprocess15.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

22×	`fma-def_binary64`
17×	`+-commutative_binary64`
12×	`associate-+r+_binary64`
12×	`associate-+l+_binary64`
3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	52
1	40	44
2	81	44
3	97	44
0	3	3

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
2

Call 2

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

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

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify27.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	14	11
2	25	11
3	29	11

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 42 to 26 computations (38.1% saved)

localize5.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series5.0ms (0.3%)

Counts

1 → 36

Calls

9 calls:

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

rewrite58.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

888×	`log1p-expm1-u_binary64`
888×	`expm1-log1p-u_binary64`
93×	`add-sqr-sqrt_binary64`
88×	`*-un-lft-identity_binary64`
88×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	178	9
2	2376	9

Stop Event

1×	node limit

Counts

1 → 36

Calls

Call 1

Inputs
(+.f64 (/.f64 x 2) (fma.f64 x y z))

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

Outputs

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

simplify14.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	336
1	24	280
2	37	253
3	41	253

Stop Event

1×

saturated

Counts

72 → 45

Calls

Call 1

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

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

prune26.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	3	46

Error

Counts

46 → 3

Alt Table

Status	Error	Program
	32.3b	(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (fma.f64 x y z))
▶	0.0b	(fma.f64 x (+.f64 y 1/2) z)
✓	0.0b	(+.f64 (/.f64 x 2) (fma.f64 x y z))

Compiler

Compiled 703 to 348 computations (50.5% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (+.f64 y 1/2) z)

series4.0ms (0.2%)

Counts

1 → 36

Calls

9 calls:

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

rewrite36.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

773×	`pow1_binary64`
717×	`log1p-expm1-u_binary64`
717×	`expm1-log1p-u_binary64`
78×	`add-sqr-sqrt_binary64`
75×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	150	8
2	1864	8

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

Inputs
(fma.f64 x (+.f64 y 1/2) z)

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

Outputs

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

simplify12.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	336
1	24	280
2	37	253
3	41	253

Stop Event

1×

saturated

Counts

59 → 32

Calls

Call 1

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

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

prune26.0ms (1.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	32	3	35

Error

Counts

35 → 3

Alt Table

Status	Error	Program
▶	32.3b	(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (fma.f64 x y z))
✓	0.0b	(fma.f64 x (+.f64 y 1/2) z)
✓	0.0b	(+.f64 (/.f64 x 2) (fma.f64 x y z))

Compiler

Compiled 362 to 228 computations (37% saved)

localize16.0ms (0.9%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (fma.f64 x y z))

series6.0ms (0.3%)

Counts

1 → 28

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (fma.f64 x y z))
1.0ms	x	@	inf	(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (fma.f64 x y z))
1.0ms	x	@	-inf	(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (fma.f64 x y z))
1.0ms	y	@	0	(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (fma.f64 x y z))
1.0ms	z	@	0	(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (fma.f64 x y z))

rewrite40.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

812×	`pow1_binary64`
744×	`log1p-expm1-u_binary64`
744×	`expm1-log1p-u_binary64`
88×	`add-sqr-sqrt_binary64`
86×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	179	9
2	2030	9

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

Inputs
(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (fma.f64 x y z))

Outputs

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

simplify68.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

648×	`sqr-pow_binary64`
385×	`cube-prod_binary64`
377×	`fabs-mul_binary64`
338×	`associate-l_binary64`
283×	`pow-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	298
1	32	180
2	56	180
3	85	180
4	140	180
5	321	180
6	1023	180
7	1516	180
8	1665	180
9	1820	180
10	1997	180
11	2250	180
12	2599	180
13	3004	180
14	3461	180
15	4017	180
16	4700	180

Stop Event

1×	node limit

Counts

51 → 33

Calls

Call 1

Inputs
z
(+.f64 (*.f64 y x) z)
(*.f64 y x)
(*.f64 y x)
(+.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(*.f64 y x)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(*.f64 y x)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(+.f64 (.f64 y x) (.f64 (pow.f64 (sqrt.f64 1/2) 2) x))
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
z
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
z
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))

Outputs
z
(+.f64 (*.f64 y x) z)
(fma.f64 y x z)
(*.f64 y x)
(*.f64 y x)
(+.f64 (*.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z)
(fma.f64 (pow.f64 (sqrt.f64 1/2) 2) x z)
(fma.f64 x 1/2 z)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(fma.f64 y x (fma.f64 (pow.f64 (sqrt.f64 1/2) 2) x z))
(fma.f64 x (+.f64 y 1/2) z)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(fma.f64 y x (fma.f64 (pow.f64 (sqrt.f64 1/2) 2) x z))
(fma.f64 x (+.f64 y 1/2) z)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(fma.f64 y x (fma.f64 (pow.f64 (sqrt.f64 1/2) 2) x z))
(fma.f64 x (+.f64 y 1/2) z)
(*.f64 y x)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(fma.f64 y x (fma.f64 (pow.f64 (sqrt.f64 1/2) 2) x z))
(fma.f64 x (+.f64 y 1/2) z)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(fma.f64 y x (fma.f64 (pow.f64 (sqrt.f64 1/2) 2) x z))
(fma.f64 x (+.f64 y 1/2) z)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(fma.f64 y x (fma.f64 (pow.f64 (sqrt.f64 1/2) 2) x z))
(fma.f64 x (+.f64 y 1/2) z)
(*.f64 y x)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(fma.f64 y x (fma.f64 (pow.f64 (sqrt.f64 1/2) 2) x z))
(fma.f64 x (+.f64 y 1/2) z)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(fma.f64 y x (fma.f64 (pow.f64 (sqrt.f64 1/2) 2) x z))
(fma.f64 x (+.f64 y 1/2) z)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(fma.f64 y x (fma.f64 (pow.f64 (sqrt.f64 1/2) 2) x z))
(fma.f64 x (+.f64 y 1/2) z)
(+.f64 (.f64 y x) (.f64 (pow.f64 (sqrt.f64 1/2) 2) x))
(*.f64 x (+.f64 y (pow.f64 (sqrt.f64 1/2) 2)))
(*.f64 x (+.f64 y 1/2))
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(fma.f64 y x (fma.f64 (pow.f64 (sqrt.f64 1/2) 2) x z))
(fma.f64 x (+.f64 y 1/2) z)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(fma.f64 y x (fma.f64 (pow.f64 (sqrt.f64 1/2) 2) x z))
(fma.f64 x (+.f64 y 1/2) z)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(fma.f64 y x (fma.f64 (pow.f64 (sqrt.f64 1/2) 2) x z))
(fma.f64 x (+.f64 y 1/2) z)
z
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(fma.f64 y x (fma.f64 (pow.f64 (sqrt.f64 1/2) 2) x z))
(fma.f64 x (+.f64 y 1/2) z)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(fma.f64 y x (fma.f64 (pow.f64 (sqrt.f64 1/2) 2) x z))
(fma.f64 x (+.f64 y 1/2) z)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(fma.f64 y x (fma.f64 (pow.f64 (sqrt.f64 1/2) 2) x z))
(fma.f64 x (+.f64 y 1/2) z)
z
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(fma.f64 y x (fma.f64 (pow.f64 (sqrt.f64 1/2) 2) x z))
(fma.f64 x (+.f64 y 1/2) z)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(fma.f64 y x (fma.f64 (pow.f64 (sqrt.f64 1/2) 2) x z))
(fma.f64 x (+.f64 y 1/2) z)
(+.f64 (.f64 y x) (+.f64 (.f64 (pow.f64 (sqrt.f64 1/2) 2) x) z))
(fma.f64 y x (fma.f64 (pow.f64 (sqrt.f64 1/2) 2) x z))
(fma.f64 x (+.f64 y 1/2) z)

prune17.0ms (1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	33	3	36

Error

Counts

36 → 3

Alt Table

Status	Error	Program
✓	32.3b	(fma.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (.f64 x 1/2)) (fma.f64 x y z))
✓	0.0b	(fma.f64 x (+.f64 y 1/2) z)
✓	0.0b	(+.f64 (/.f64 x 2) (fma.f64 x y z))

Compiler

Compiled 379 to 193 computations (49.1% saved)

regimes88.0ms (4.9%)

Accuracy

Total 0.0b remaining (82.7%)

Threshold costs 0.0b (82.7%)

Counts

15 → 1

Compiler

Compiled 143 to 75 computations (47.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 x 1/2 (fma.f64 x y z))

Outputs
(fma.f64 x 1/2 (fma.f64 x y z))

end52.0ms (2.9%)

Stop Event

1×

done

Compiler

Compiled 56 to 36 computations (35.7% saved)

Details

analyze424.0ms (23.4%)

sample860.0ms (47.5%)

preprocess15.0ms (0.9%)

simplify27.0ms (1.5%)

prune3.0ms (0.1%)

localize5.0ms (0.3%)

series5.0ms (0.3%)

rewrite58.0ms (3.2%)

simplify14.0ms (0.8%)

prune26.0ms (1.4%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite36.0ms (2%)

simplify12.0ms (0.7%)

prune26.0ms (1.4%)

localize16.0ms (0.9%)

series6.0ms (0.3%)

rewrite40.0ms (2.2%)

simplify68.0ms (3.8%)

prune17.0ms (1%)

regimes88.0ms (4.9%)

simplify2.0ms (0.1%)

end52.0ms (2.9%)

Profiling