Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12

Compiler

Compiled 10 to 5 computations (50% saved)

sample824.0ms (30.2%)

Results

812.0ms	8256×	body	256	valid
0.0ms	2×	body	256	invalid

preprocess16.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-r_binary64`
2×	`count-2_binary64`
1×	`associate-l_binary64`
1×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	11	4
2	14	4
3	17	4
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Outputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(hypot.f64 x x)

Compiler

Compiled 10 to 5 computations (50% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-r_binary64`
2×	`count-2_binary64`
1×	`associate-l_binary64`
1×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	11	4
2	14	4
3	17	4

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

Outputs
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(hypot.f64 x x)

eval0.0ms (0%)

Compiler: Compiled 12 to 5 computations (58.3% saved)

prune1.0ms (0%)

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

0.1b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.1b	(hypot.f64 x x)

Compiler

Compiled 4 to 2 computations (50% saved)

localize2.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 x x)
✓	0.1b	(hypot.f64 x x)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(hypot.f64 x x)
1.0ms	x	@	0	(hypot.f64 x x)
1.0ms	x	@	inf	(hypot.f64 x x)

rewrite108.0ms (4%)

Algorithm

1×	batch-egg-rewrite

Rules

356×	`log1p-udef_binary64`
275×	`associate-r_binary64`
271×	`pow1_binary64`
260×	`add-sqr-sqrt_binary64`
255×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	60	4
2	695	4
3	7800	4

Stop Event

1×	node limit

Counts

1 → 103

Calls

Call 1

Inputs
(hypot.f64 x x)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x x) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (/.f64 0 0)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 0 0))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 0 0)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 x x) (/.f64 0 0)) (.f64 (.f64 x x) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 0 0) (.f64 x x)) (.f64 (/.f64 0 0) (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 0 0)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (.f64 (+.f64 x x) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (.f64 (+.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x x) (.f64 (+.f64 x x) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 0 0) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 0 0) (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 0 0) (pow.f64 1 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 0 0) (pow.f64 1 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (cbrt.f64 x) 5)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 x) (.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (.f64 x (cbrt.f64 x)) (.f64 x (cbrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 x) (+.f64 (pow.f64 x 3/2) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 0 (/.f64 1 0))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 x (cbrt.f64 x)) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 x 3/2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (.f64 x x) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 0 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 x x) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 x) 5) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4 (pow.f64 x 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/3) (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 2 1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (sqrt.f64 x)) (pow.f64 x 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (pow.f64 (cbrt.f64 x) 2)) (.f64 x (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (pow.f64 x 3/2)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (pow.f64 (cbrt.f64 x) 5)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 0 0) x) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 0 0) 2) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 0 (pow.f64 x 4)) (.f64 2 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 0 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (pow.f64 x 6)) (+.f64 0 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 2 (pow.f64 x 6)) (.f64 2 (pow.f64 x 6))) (.f64 (+.f64 0 (pow.f64 x 4)) (+.f64 0 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 0 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 0) (sqrt.f64 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 0 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 0 (.f64 2 (pow.f64 x 6))) (.f64 0 (+.f64 0 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 2 (pow.f64 x 6)) 0) (.f64 (+.f64 0 (pow.f64 x 4)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 0 0)) 3) 1) (+.f64 (.f64 (+.f64 1 (/.f64 0 0)) (+.f64 1 (/.f64 0 0))) (+.f64 1 (+.f64 1 (/.f64 0 0)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (+.f64 1 (/.f64 0 0)) (+.f64 1 (/.f64 0 0))) 1) (+.f64 (+.f64 1 (/.f64 0 0)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 0 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 0 (/.f64 0 0)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 2 (pow.f64 x 6)) 1) (+.f64 0 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (/.f64 0 0) (.f64 2 (pow.f64 x 6))) (+.f64 0 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 4/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 5)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 5/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 0 0))) 2)) (cbrt.f64 (log.f64 (/.f64 0 0))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 0 0)))) (sqrt.f64 (log.f64 (/.f64 0 0))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (neg.f64 (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 0 0)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 0 0)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 0 0)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x x) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 x (cbrt.f64 x)) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 0 0)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (/.f64 0 0)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 0 0))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 0 0)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) (/.f64 0 0)) (*.f64 (*.f64 x x) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 0 0) (*.f64 x x)) (*.f64 (/.f64 0 0) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 0 0)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 (+.f64 x x) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 (+.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) (*.f64 (+.f64 x x) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 0 0) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 0 0) (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 0 0) (pow.f64 1 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 0 0) (pow.f64 1 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (cbrt.f64 x) 5)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (*.f64 x (cbrt.f64 x)) (*.f64 x (cbrt.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (+.f64 (pow.f64 x 3/2) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 0 (/.f64 1 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (cbrt.f64 x)) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 3/2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (*.f64 x x) (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 0 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x x) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 5) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (pow.f64 x 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (sqrt.f64 x)) (pow.f64 x 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 2)) (*.f64 x (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 x 3/2)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 5)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 0 0) x) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 0 0) 2) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 0 (pow.f64 x 4)) (*.f64 2 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 0 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (pow.f64 x 6)) (+.f64 0 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (*.f64 2 (pow.f64 x 6))) (*.f64 (+.f64 0 (pow.f64 x 4)) (+.f64 0 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 0 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 0) (sqrt.f64 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 0 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 0 (*.f64 2 (pow.f64 x 6))) (*.f64 0 (+.f64 0 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) 0) (*.f64 (+.f64 0 (pow.f64 x 4)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 0 0)) 3) 1) (+.f64 (*.f64 (+.f64 1 (/.f64 0 0)) (+.f64 1 (/.f64 0 0))) (+.f64 1 (+.f64 1 (/.f64 0 0)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 0 0)) (+.f64 1 (/.f64 0 0))) 1) (+.f64 (+.f64 1 (/.f64 0 0)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 0 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 0 (/.f64 0 0)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 6)) 1) (+.f64 0 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 0 0) (*.f64 2 (pow.f64 x 6))) (+.f64 0 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 4/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 5)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 0 0) 5/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 0 0))) 2)) (cbrt.f64 (log.f64 (/.f64 0 0))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 0 0)))) (sqrt.f64 (log.f64 (/.f64 0 0))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (neg.f64 (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 0 0))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 0 0)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 x (cbrt.f64 x)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 0 0)))))))

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	25	80
3	29	80
4	33	80
5	51	80
6	73	80
7	84	80
8	96	80
9	121	80

Stop Event

1×

saturated

Counts

115 → 105

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))

eval22.0ms (0.8%)

Compiler: Compiled 899 to 665 computations (26% saved)

prune18.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	99	6	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	7	106

Error

0.0b

Counts

106 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	60.6b	(.f64 (.f64 x x) 2)
▶	31.2b	(*.f64 (sqrt.f64 2) x)
	52.3b	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
✓	0.1b	(hypot.f64 x x)
▶	31.7b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	31.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	64.0b	(/.f64 0 0)

Compiler

Compiled 90 to 70 computations (22.2% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.4b	(*.f64 (sqrt.f64 2) x)
✓	0.4b	(*.f64 (sqrt.f64 2) x)

series2.0ms (0.1%)

Counts

1 → 0

Calls

3 calls:

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

rewrite35.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

417×	`pow1_binary64`
403×	`add-sqr-sqrt_binary64`
395×	`*-un-lft-identity_binary64`
386×	`add-log-exp_binary64`
386×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	100	6
2	1075	6

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

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

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

Outputs

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

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

15 → 15

Calls

Call 1

Inputs

Outputs

localize1.0ms (0%)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite52.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

423×	`pow1_binary64`
409×	`add-sqr-sqrt_binary64`
402×	`*-un-lft-identity_binary64`
390×	`add-log-exp_binary64`
390×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	101	7
2	1121	7

Stop Event

1×	node limit

Counts

1 → 16

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (*.f64 x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (*.f64 x x) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (*.f64 x x) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 x 4) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (*.f64 x x) 2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (*.f64 x x) 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 4) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (*.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (*.f64 x x) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (*.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (*.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (*.f64 x x) 2)))))))

simplify137.0ms (5%)

Algorithm

1×	egg-herbie

Rules

1104×	`sqr-pow_binary64`
618×	`cube-prod_binary64`
550×	`fabs-mul_binary64`
536×	`pow-sqr_binary64`
445×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	84
1	11	84
2	22	84
3	44	84
4	105	84
5	316	84
6	1215	84
7	2089	84
8	2253	84
9	2437	84
10	2645	84
11	2937	84
12	3328	84
13	3806	84
14	4369	84
15	5051	84
16	5888	84
17	6278	84
18	6564	84
19	6838	84
20	6912	84
21	6948	84
22	7889	84

Stop Event

1×	node limit

Counts

28 → 18

Calls

Call 1

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

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

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.4b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	0.4b	(*.f64 (sqrt.f64 2) (neg.f64 x))

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(*.f64 (sqrt.f64 2) (neg.f64 x))
0.0ms	x	@	inf	(*.f64 (sqrt.f64 2) (neg.f64 x))
0.0ms	x	@	-inf	(*.f64 (sqrt.f64 2) (neg.f64 x))

rewrite35.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

450×	`pow1_binary64`
437×	`add-sqr-sqrt_binary64`
428×	`*-un-lft-identity_binary64`
418×	`add-log-exp_binary64`
417×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	125	6
2	1472	6

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

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

Outputs

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

simplify11.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	96
1	12	96
2	25	96
3	29	96
4	33	96
5	51	96
6	73	96
7	84	96
8	96	96
9	121	96

Stop Event

1×

saturated

Counts

25 → 15

Calls

Call 1

Inputs
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))

Outputs
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	0.2b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
0.0ms	x	@	0	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
0.0ms	x	@	inf	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))

rewrite49.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

417×	`pow1_binary64`
408×	`prod-diff_binary64`
401×	`add-sqr-sqrt_binary64`
394×	`add-log-exp_binary64`
393×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	129	4
2	1826	4

Stop Event

1×	node limit

Counts

1 → 38

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 x x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x x) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) 0) (/.f64 (*.f64 x x) 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x 0) (*.f64 2 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (pow.f64 x 3)) (fma.f64 x x 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 0 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 3)) (*.f64 2 (pow.f64 x 3))) (*.f64 (fma.f64 x x 0) (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 3))) (cbrt.f64 (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 0) (sqrt.f64 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (pow.f64 x 3))) (neg.f64 (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 0 (*.f64 2 (pow.f64 x 3))) (*.f64 0 (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 3)) 0) (*.f64 (fma.f64 x x 0) 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 3)) (+.f64 x x)) (fma.f64 x x 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 0 (+.f64 x x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (*.f64 2 (pow.f64 x 3))) (fma.f64 x x 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 x x) (*.f64 2 (pow.f64 x 3))) (fma.f64 x x 0))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 x) (sqrt.f64 x))))))

simplify15.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

248×	`fma-def_binary64`
23×	`distribute-rgt-in_binary64`
21×	`sub-neg_binary64`
20×	`associate-l_binary64`
19×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	100
1	21	100
2	53	100
3	104	100
4	118	100
5	166	100
6	238	100
7	275	100
8	321	100
9	498	100
10	526	100

Stop Event

1×

saturated

Counts

50 → 41

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) x))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -1) (sqrt.f64 -2))))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 -2))))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) x))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -1) (sqrt.f64 -2))))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 -2))))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) x))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -1) (sqrt.f64 -2))))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 -2))))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) x))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -1) (sqrt.f64 -2))))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 -2))))

eval18.0ms (0.7%)

Compiler: Compiled 675 to 449 computations (33.5% saved)

prune20.0ms (0.7%)

Pruning

12 alts after pruning (7 fresh and 5 done)

	Pruned	Kept	Total
New	83	6	89
Fresh	0	1	1
Picked	0	1	1
Done	1	4	5
Total	84	12	96

Error

0.0b

Counts

96 → 12

Alt Table

Click to see full alt table

Status	Error	Program
▶	62.3b	(/.f64 1 (+.f64 x x))
▶	32.1b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
✓	31.7b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	58.6b	(-.f64 (+.f64 1 (+.f64 x x)) 1)
✓	60.6b	(.f64 (.f64 x x) 2)
✓	31.2b	(*.f64 (sqrt.f64 2) x)
	52.3b	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
✓	0.1b	(hypot.f64 x x)
▶	60.9b	(-.f64 (+.f64 1 (.f64 (.f64 x x) 2)) 1)
▶	56.7b	(+.f64 x x)
✓	31.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
	52.4b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))

Compiler

Compiled 145 to 112 computations (22.8% saved)

localize5.0ms (0.2%)

Local error

Found 6 expressions with local error:

New	Error	Program
	0.4b	(*.f64 (sqrt.f64 2) x)
	0.3b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
	0.1b	(sqrt.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(sqrt.f64 (*.f64 (sqrt.f64 2) x))
✓	0.3b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
	0.4b	(*.f64 (sqrt.f64 2) x)

series6.0ms (0.2%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
2.0ms	x	@	-inf	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
1.0ms	x	@	inf	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
1.0ms	x	@	0	(sqrt.f64 (*.f64 (sqrt.f64 2) x))
1.0ms	x	@	-inf	(sqrt.f64 (*.f64 (sqrt.f64 2) x))

rewrite47.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

490×	`pow1_binary64`
471×	`add-sqr-sqrt_binary64`
462×	`*-un-lft-identity_binary64`
454×	`add-log-exp_binary64`
454×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	144	14
2	1321	14

Stop Event

1×	node limit

Counts

2 → 50

Calls

Call 1

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

Outputs

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

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

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

50 → 50

Calls

Call 1

Inputs

Outputs

localize2.0ms (0.1%)

localize3.0ms (0.1%)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	2.8b	(-.f64 (+.f64 1 (+.f64 x x)) 1)
✓	2.8b	(-.f64 (+.f64 1 (+.f64 x x)) 1)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(-.f64 (+.f64 1 (+.f64 x x)) 1)
0.0ms	x	@	inf	(-.f64 (+.f64 1 (+.f64 x x)) 1)
0.0ms	x	@	-inf	(-.f64 (+.f64 1 (+.f64 x x)) 1)

rewrite45.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

654×	`pow1_binary64`
621×	`add-log-exp_binary64`
619×	`log1p-expm1-u_binary64`
619×	`expm1-log1p-u_binary64`
611×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	145	4
2	2266	4

Stop Event

1×	node limit

Counts

1 → 93

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (+.f64 x x)) 1)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (fma.f64 2 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (fma.f64 2 x -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x x) (+.f64 (+.f64 x x) (*.f64 -2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x x) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x x) (*.f64 (fma.f64 2 x -1) (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 2 x 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (fma.f64 2 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 2 x -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 x) (-.f64 x 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 x) (+.f64 x -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (fma.f64 2 x 1) (+.f64 x x)) (*.f64 -1 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (+.f64 x x)) (*.f64 x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 x x) (fma.f64 2 x 1)) (*.f64 (+.f64 x x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (+.f64 x x) x) (*.f64 (+.f64 x x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x x) (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (/.f64 1 (+.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 0 (/.f64 1 0))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 x (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 8 (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 2) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x x) 3/2) (pow.f64 (+.f64 x x) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (fma.f64 2 x 1)) 1) (-.f64 (sqrt.f64 (fma.f64 2 x 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 x x) 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (+.f64 x x) 2) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x 0) (*.f64 2 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (-.f64 1 (*.f64 (fma.f64 2 x 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (pow.f64 x 3)) (fma.f64 x x 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 (+.f64 x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (-.f64 (fma.f64 2 x 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 0 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 3)) (*.f64 2 (pow.f64 x 3))) (*.f64 (fma.f64 x x 0) (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (*.f64 (+.f64 (+.f64 x x) 2) (+.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 3))) (cbrt.f64 (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (cbrt.f64 (+.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (cbrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 0) (sqrt.f64 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (sqrt.f64 (+.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (*.f64 2 (pow.f64 x 3)) 3) (pow.f64 (fma.f64 x x 0) 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (neg.f64 (+.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (*.f64 2 (pow.f64 x 3))) (neg.f64 (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (*.f64 (+.f64 (+.f64 x x) 2) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)) (+.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 0 (*.f64 2 (pow.f64 x 3))) (*.f64 0 (fma.f64 x x 0)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 3)) 0) (*.f64 (fma.f64 x x 0) 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 2 x -1) 3)) (+.f64 1 (-.f64 (*.f64 (fma.f64 2 x -1) (fma.f64 2 x -1)) (fma.f64 2 x -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (fma.f64 2 x -1) (fma.f64 2 x -1))) (-.f64 1 (fma.f64 2 x -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1) (+.f64 x x)) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 x x)) (+.f64 (+.f64 x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 2 (pow.f64 x 3)) (+.f64 x x)) (fma.f64 x x 0))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 0 (+.f64 x x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 x x) (+.f64 (pow.f64 (fma.f64 2 x 1) 3) -1)) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) (+.f64 (+.f64 x x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 x x) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (+.f64 (+.f64 x x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 x x) (*.f64 2 (pow.f64 x 3))) (fma.f64 x x 0))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x x) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 2 x 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 2 x 1)) 2) (cbrt.f64 (fma.f64 2 x 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 2 x 1)) (sqrt.f64 (fma.f64 2 x 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x hypot.f64 (sqrt.f64 x) (sqrt.f64 x))))))

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	48
1	5	48

Stop Event

1×

saturated

Counts

105 → 93

Calls

Call 1

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

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

localize5.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.8b	(-.f64 (+.f64 1 (.f64 (.f64 x x) 2)) 1)
	0.0b	(.f64 (.f64 x x) 2)
	0.0b	(.f64 (.f64 x x) 2)
✓	1.8b	(-.f64 (+.f64 1 (.f64 (.f64 x x) 2)) 1)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite47.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

798×	`pow1_binary64`
749×	`add-log-exp_binary64`
748×	`log1p-expm1-u_binary64`
748×	`expm1-log1p-u_binary64`
736×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	177	7
2	2285	7

Stop Event

1×	node limit

Counts

1 → 45

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (.f64 (.f64 x x) 2)) 1)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (fma.f64 x (*.f64 x 2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (fma.f64 x (*.f64 x 2) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (*.f64 x 2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (fma.f64 x (*.f64 x 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x (*.f64 x 2) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (*.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (*.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (*.f64 x 2))) (cbrt.f64 (*.f64 4 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))) (cbrt.f64 (*.f64 x (*.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (*.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x 4)) (*.f64 (pow.f64 (cbrt.f64 x) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (sqrt.f64 2)) (*.f64 x (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (*.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 x (*.f64 x 2) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 x (*.f64 x 2) 1) 2) (+.f64 (*.f64 x (*.f64 x 2)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 x (*.f64 x 2) 1) 2) -1) (/.f64 1 (+.f64 (*.f64 x (*.f64 x 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (hypot.f64 1 (*.f64 x (sqrt.f64 2))) 1) (-.f64 (hypot.f64 1 (*.f64 x (sqrt.f64 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 x (*.f64 x 2) 1) 2) (+.f64 (*.f64 x (*.f64 x 2)) 2)) (+.f64 (pow.f64 (fma.f64 x (*.f64 x 2) 1) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (*.f64 x (*.f64 x 2)) 2) (+.f64 (pow.f64 (fma.f64 x (*.f64 x 2) 1) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 x (*.f64 x 2) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 x (*.f64 x 2) 1) 2) (+.f64 (*.f64 x (*.f64 x 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 x (*.f64 x 2) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 x (*.f64 x 2) 1) 2) (-.f64 1 (*.f64 (fma.f64 x (*.f64 x 2) 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 x (*.f64 x 2) 1) 2) -1) (+.f64 (*.f64 x (*.f64 x 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 x (*.f64 x 2) 1) 2) -1) (-.f64 (fma.f64 x (*.f64 x 2) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 x (*.f64 x 2) 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 x (*.f64 x 2) 1) 2) (+.f64 (*.f64 x (*.f64 x 2)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 x (*.f64 x 2) 1) 2) -1)) (neg.f64 (+.f64 (*.f64 x (*.f64 x 2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 x (*.f64 x 2) -1) 3)) (+.f64 1 (-.f64 (*.f64 (fma.f64 x (*.f64 x 2) -1) (fma.f64 x (*.f64 x 2) -1)) (fma.f64 x (*.f64 x 2) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (fma.f64 x (*.f64 x 2) -1) (fma.f64 x (*.f64 x 2) -1))) (-.f64 1 (fma.f64 x (*.f64 x 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 x 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 8 (pow.f64 (*.f64 x x) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 4 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 8 (pow.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x (*.f64 x 2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 x (*.f64 x 2) 1)) 2) (cbrt.f64 (fma.f64 x (*.f64 x 2) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (*.f64 x (sqrt.f64 2))) (hypot.f64 1 (*.f64 x (sqrt.f64 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 x 2))))))))

simplify137.0ms (5%)

Algorithm

1×	egg-herbie

Rules

1104×	`sqr-pow_binary64`
618×	`cube-prod_binary64`
550×	`fabs-mul_binary64`
536×	`pow-sqr_binary64`
445×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	84
1	11	84
2	22	84
3	44	84
4	105	84
5	316	84
6	1215	84
7	2089	84
8	2253	84
9	2437	84
10	2645	84
11	2937	84
12	3328	84
13	3806	84
14	4369	84
15	5051	84
16	5888	84
17	6278	84
18	6564	84
19	6838	84
20	6912	84
21	6948	84
22	7889	84

Stop Event

1×	node limit

Counts

57 → 46

Calls

Call 1

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

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

eval72.0ms (2.6%)

Compiler: Compiled 2575 to 1893 computations (26.5% saved)

prune72.0ms (2.6%)

Pruning

13 alts after pruning (4 fresh and 9 done)

	Pruned	Kept	Total
New	219	3	222
Fresh	1	1	2
Picked	1	0	1
Done	0	9	9
Total	221	13	234

Error

0.0b

Counts

234 → 13

Alt Table

Click to see full alt table

Status	Error	Program
✓	62.3b	(/.f64 1 (+.f64 x x))
✓	32.1b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
✓	31.7b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	58.6b	(-.f64 (+.f64 1 (+.f64 x x)) 1)
✓	60.6b	(.f64 (.f64 x x) 2)
✓	31.2b	(*.f64 (sqrt.f64 2) x)
▶	52.3b	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
✓	0.1b	(hypot.f64 x x)
▶	52.4b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
✓	56.7b	(+.f64 x x)
✓	31.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	60.6b	(.f64 4 (.f64 x x))
▶	31.2b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

Compiler

Compiled 93 to 71 computations (23.7% saved)

localize5.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
	0.2b	(*.f64 (pow.f64 2 1/4) x)
✓	0.2b	(*.f64 (pow.f64 2 1/4) x)
✓	0.3b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

series42.0ms (1.5%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
40.0ms	x	@	0	(*.f64 (pow.f64 2 1/4) x)
0.0ms	x	@	inf	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
0.0ms	x	@	inf	(*.f64 (pow.f64 2 1/4) x)
0.0ms	x	@	-inf	(*.f64 (pow.f64 2 1/4) x)
0.0ms	x	@	-inf	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

rewrite50.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

610×	`pow1_binary64`
566×	`add-log-exp_binary64`
566×	`log1p-expm1-u_binary64`
566×	`expm1-log1p-u_binary64`
554×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	148	13
2	1611	13

Stop Event

1×	node limit

Counts

2 → 22

Calls

Call 1

Inputs
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(*.f64 (pow.f64 2 1/4) x)

Outputs

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

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

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	72
1	6	72

Stop Event

1×

saturated

Counts

34 → 23

Calls

Call 1

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

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

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(.f64 4 (.f64 x x))
✓	0.0b	(.f64 4 (.f64 x x))

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(.f64 4 (.f64 x x))
0.0ms	x	@	inf	(.f64 4 (.f64 x x))
0.0ms	x	@	-inf	(.f64 4 (.f64 x x))

rewrite32.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

422×	`pow1_binary64`
408×	`add-sqr-sqrt_binary64`
401×	`*-un-lft-identity_binary64`
392×	`add-log-exp_binary64`
392×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	102	7
2	1126	7

Stop Event

1×	node limit

Counts

1 → 14

Calls

Call 1

Inputs
(.f64 4 (.f64 x x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 4 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 4) (*.f64 x x))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 4) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 4) (*.f64 x x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 4) (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 4 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 4 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 4 (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (cbrt.f64 (*.f64 x 2)) 2) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 16 (pow.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 4) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 4 (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 4 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 2 (log.f64 (*.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 4 (*.f64 x x))))))))

simplify134.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

1105×	`sqr-pow_binary64`
618×	`cube-prod_binary64`
554×	`fabs-mul_binary64`
536×	`pow-sqr_binary64`
441×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	12	84
2	23	84
3	44	84
4	107	84
5	335	84
6	1216	84
7	2088	84
8	2252	84
9	2436	84
10	2644	84
11	2934	84
12	3327	84
13	3805	84
14	4366	84
15	5050	84
16	5887	84
17	6281	84
18	6569	84
19	6845	84
20	6921	84
21	6955	84
22	7896	84

Stop Event

1×	node limit

Counts

26 → 16

Calls

Call 1

Inputs
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))

Outputs
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))

localize5.0ms (0.2%)

Local error

Found 6 expressions with local error:

New	Error	Program
	41.4b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
	0.4b	(*.f64 (sqrt.f64 2) x)
	0.2b	(pow.f64 (*.f64 (sqrt.f64 2) x) 3)
✓	0.2b	(pow.f64 (*.f64 (sqrt.f64 2) x) 3)
	0.4b	(*.f64 (sqrt.f64 2) x)
✓	41.4b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))

series5.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
1.0ms	x	@	-inf	(pow.f64 (*.f64 (sqrt.f64 2) x) 3)
1.0ms	x	@	0	(pow.f64 (*.f64 (sqrt.f64 2) x) 3)
1.0ms	x	@	inf	(pow.f64 (*.f64 (sqrt.f64 2) x) 3)
0.0ms	x	@	0	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))

rewrite45.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

582×	`pow1_binary64`
550×	`add-log-exp_binary64`
549×	`log1p-expm1-u_binary64`
549×	`expm1-log1p-u_binary64`
535×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	170	15
2	1635	15

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

Inputs
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(pow.f64 (*.f64 (sqrt.f64 2) x) 3)

Outputs

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

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

simplify150.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

934×	`unswap-sqr_binary64`
771×	`sqr-pow_binary64`
545×	`cube-prod_binary64`
468×	`fma-def_binary64`
386×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	244
1	36	244
2	103	244
3	269	244
4	773	244
5	1353	244
6	2800	244
7	2922	244
8	3214	244
9	3486	244
10	3705	244
11	3936	244
12	4228	244
13	4571	244
14	5403	244
15	5928	244
16	6610	244
17	6918	244
18	7278	244
19	7610	244
20	7982	244

Stop Event

1×	node limit

Counts

78 → 58

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 -1) x)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 -1) x)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 -1) x)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 -1) x)))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 -1) x)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 x (cbrt.f64 -1))))
(.f64 (sqrt.f64 2) (neg.f64 (.f64 x (cbrt.f64 -1))))
(.f64 (sqrt.f64 2) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 (cbrt.f64 -1) (.f64 (sqrt.f64 2) (neg.f64 x)))
(.f64 x (neg.f64 (.f64 (sqrt.f64 2) (cbrt.f64 -1))))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) (neg.f64 x)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 -1) x)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 x (cbrt.f64 -1))))
(.f64 (sqrt.f64 2) (neg.f64 (.f64 x (cbrt.f64 -1))))
(.f64 (sqrt.f64 2) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 (cbrt.f64 -1) (.f64 (sqrt.f64 2) (neg.f64 x)))
(.f64 x (neg.f64 (.f64 (sqrt.f64 2) (cbrt.f64 -1))))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) (neg.f64 x)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 -1) x)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 x (cbrt.f64 -1))))
(.f64 (sqrt.f64 2) (neg.f64 (.f64 x (cbrt.f64 -1))))
(.f64 (sqrt.f64 2) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 (cbrt.f64 -1) (.f64 (sqrt.f64 2) (neg.f64 x)))
(.f64 x (neg.f64 (.f64 (sqrt.f64 2) (cbrt.f64 -1))))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) (neg.f64 x)))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 -1) x)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 x (cbrt.f64 -1))))
(.f64 (sqrt.f64 2) (neg.f64 (.f64 x (cbrt.f64 -1))))
(.f64 (sqrt.f64 2) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 (cbrt.f64 -1) (.f64 (sqrt.f64 2) (neg.f64 x)))
(.f64 x (neg.f64 (.f64 (sqrt.f64 2) (cbrt.f64 -1))))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) (neg.f64 x)))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(.f64 (sqrt.f64 2) (.f64 2 (pow.f64 x 3)))
(.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 x 3))
(.f64 2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(.f64 (sqrt.f64 2) (.f64 2 (pow.f64 x 3)))
(.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 x 3))
(.f64 2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(.f64 (sqrt.f64 2) (.f64 2 (pow.f64 x 3)))
(.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 x 3))
(.f64 2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(.f64 (sqrt.f64 2) (.f64 2 (pow.f64 x 3)))
(.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 x 3))
(.f64 2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(.f64 (sqrt.f64 2) (.f64 2 (pow.f64 x 3)))
(.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 x 3))
(.f64 2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(.f64 (sqrt.f64 2) (.f64 2 (pow.f64 x 3)))
(.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 x 3))
(.f64 2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(.f64 (sqrt.f64 2) (.f64 2 (pow.f64 x 3)))
(.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 x 3))
(.f64 2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(.f64 (sqrt.f64 2) (.f64 2 (pow.f64 x 3)))
(.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 x 3))
(.f64 2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(.f64 (sqrt.f64 2) (.f64 2 (pow.f64 x 3)))
(.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 x 3))
(.f64 2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(.f64 (sqrt.f64 2) (.f64 2 (pow.f64 x 3)))
(.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 x 3))
(.f64 2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(.f64 (sqrt.f64 2) (.f64 2 (pow.f64 x 3)))
(.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 x 3))
(.f64 2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(.f64 (sqrt.f64 2) (.f64 2 (pow.f64 x 3)))
(.f64 (.f64 2 (sqrt.f64 2)) (pow.f64 x 3))
(.f64 2 (.f64 (sqrt.f64 2) (pow.f64 x 3)))

localize8.0ms (0.3%)

Local error

Found 6 expressions with local error:

New	Error	Program
	42.3b	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
	14.3b	(sqrt.f64 (+.f64 0 (pow.f64 x 4)))
	7.5b	(sqrt.f64 (*.f64 2 (pow.f64 x 6)))
✓	7.5b	(sqrt.f64 (*.f64 2 (pow.f64 x 6)))
✓	14.3b	(sqrt.f64 (+.f64 0 (pow.f64 x 4)))
✓	42.3b	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))

series3.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(sqrt.f64 (*.f64 2 (pow.f64 x 6)))
0.0ms	x	@	inf	(sqrt.f64 (*.f64 2 (pow.f64 x 6)))
0.0ms	x	@	0	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
0.0ms	x	@	inf	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
0.0ms	x	@	-inf	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))

rewrite57.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

480×	`log-prod_binary64`
352×	`exp-prod_binary64`
280×	`pow-prod-down_binary64`
256×	`pow2_binary64`
190×	`pow-unpow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	30
1	286	22
2	3240	22

Stop Event

1×	node limit

Counts

3 → 141

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
(sqrt.f64 (+.f64 0 (pow.f64 x 4)))
(sqrt.f64 (*.f64 2 (pow.f64 x 6)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (*.f64 2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))))) 2)) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3)) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 2) (*.f64 x x)) (*.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) x) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 x x)) 1/6) (cbrt.f64 (*.f64 2 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) (pow.f64 (*.f64 2 (*.f64 x x)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (*.f64 (pow.f64 x 3) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (*.f64 x x)) 1/4) (pow.f64 (*.f64 2 (*.f64 x x)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 4 (pow.f64 x 12)) 1/8) (*.f64 (pow.f64 (*.f64 4 (pow.f64 x 12)) 1/8) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (neg.f64 (sqrt.f64 2)) (pow.f64 x 3)) (pow.f64 (neg.f64 (*.f64 x x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) (*.f64 (sqrt.f64 2) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (cbrt.f64 2) (*.f64 x x)) 1) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) x) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 4 (pow.f64 x 12)) 1/8) 1) (/.f64 (pow.f64 (*.f64 4 (pow.f64 x 12)) 1/8) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x x)) -2) (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3)) (cbrt.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (cbrt.f64 2) (*.f64 x x)) (*.f64 (cbrt.f64 x) x)) (pow.f64 (*.f64 2 (*.f64 x x)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 x) x)) (/.f64 (pow.f64 x 3) (cbrt.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 4 (pow.f64 x 12)) 1/8) (*.f64 (cbrt.f64 x) x)) (/.f64 (pow.f64 (*.f64 4 (pow.f64 x 12)) 1/8) (cbrt.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (cbrt.f64 2) (*.f64 x x)) x) (/.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) x) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 x x)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 x x)) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 x x)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (*.f64 x x)) -1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 2 (pow.f64 x 6)) 3/2) (pow.f64 x 6)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (*.f64 2 (*.f64 x x)) -1/2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))))) 2)) (cbrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))))) (sqrt.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3)) (neg.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 2 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (*.f64 x x)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (*.f64 2 (pow.f64 x 6)) 3/2) (pow.f64 x 6)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 2 (*.f64 x x))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 x x)) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 x x)) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 x x)) 1/4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 2 (*.f64 x x)) -1/2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 2 (*.f64 x x)))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 x) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x x)) (*.f64 (cbrt.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 x) x) (cbrt.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (pow.f64 x 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 3/2) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 x 6) (pow.f64 x 4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 x 3) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (neg.f64 (pow.f64 x 8))) (sqrt.f64 (neg.f64 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 x 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 18) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 x) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cbrt.f64 x) x) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 x) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 12) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 8) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 x 3) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/2) (*.f64 4 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (*.f64 2 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (*.f64 2 (log.f64 x))) 2)) (cbrt.f64 (*.f64 2 (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (*.f64 2 (log.f64 x)))) (sqrt.f64 (*.f64 2 (log.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 x 6))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 2 (log.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 4 (log.f64 x)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 6 (log.f64 x)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (*.f64 x x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 x)) 6))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 x) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 6 (log.f64 x)) 1) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 4 (log.f64 x)) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 x) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 4 (log.f64 x)) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (*.f64 2 (log.f64 x)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x x)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (sqrt.f64 2) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 x 3))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 x 3)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (sqrt.f64 2) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 2) (*.f64 x x)) (*.f64 (cbrt.f64 (sqrt.f64 2)) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) x) (*.f64 (cbrt.f64 2) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 2) (pow.f64 x 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 4 (pow.f64 x 12)) 1/8) (pow.f64 (*.f64 4 (pow.f64 x 12)) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 3) (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (pow.f64 x 6)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 4 (pow.f64 x 12)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (pow.f64 x 6)) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 2 (pow.f64 x 6)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cbrt.f64 2) (*.f64 x x)) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) x) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 4 (pow.f64 x 12)) 1/8) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1/2) (fma.f64 6 (log.f64 x) (log.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3)))) 2)) (cbrt.f64 (log.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3))))) (sqrt.f64 (log.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 2 (pow.f64 x 6)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (fma.f64 6 (log.f64 x) (log.f64 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3/2 (fma.f64 6 (log.f64 x) (log.f64 2))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 1/4 (fma.f64 6 (log.f64 x) (log.f64 2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 6 (log.f64 x) (log.f64 2)) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (fma.f64 6 (log.f64 x) (log.f64 2)) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3))))))))

simplify84.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

902×	`fma-def_binary64`
703×	`distribute-rgt-neg-in_binary64`
693×	`distribute-lft-neg-in_binary64`
454×	`fma-neg_binary64`
306×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	244
1	32	244
2	82	244
3	225	244
4	661	244
5	1227	244
6	2365	244
7	3700	244
8	5097	244
9	5824	244
10	6674	244
11	7808	244

Stop Event

1×	node limit

Counts

177 → 146

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)
(*.f64 (sqrt.f64 2) (pow.f64 x 3))
(*.f64 (sqrt.f64 2) (pow.f64 x 3))
(*.f64 (sqrt.f64 2) (pow.f64 x 3))
(*.f64 (sqrt.f64 2) (pow.f64 x 3))
(*.f64 (sqrt.f64 2) (pow.f64 x 3))
(*.f64 (sqrt.f64 2) (pow.f64 x 3))
(*.f64 (sqrt.f64 2) (pow.f64 x 3))
(*.f64 (sqrt.f64 2) (pow.f64 x 3))
(.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 3)))

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(*.f64 (sqrt.f64 2) (pow.f64 x 3))
(*.f64 (sqrt.f64 2) (pow.f64 x 3))
(*.f64 (sqrt.f64 2) (pow.f64 x 3))
(*.f64 (sqrt.f64 2) (pow.f64 x 3))
(*.f64 (sqrt.f64 2) (pow.f64 x 3))
(*.f64 (sqrt.f64 2) (pow.f64 x 3))
(*.f64 (sqrt.f64 2) (pow.f64 x 3))
(*.f64 (sqrt.f64 2) (pow.f64 x 3))
(.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(neg.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3)))
(*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 x 3)))
(*.f64 (pow.f64 x 3) (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(neg.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3)))
(*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 x 3)))
(*.f64 (pow.f64 x 3) (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(neg.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3)))
(*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 x 3)))
(*.f64 (pow.f64 x 3) (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.f64 (sqrt.f64 2) (pow.f64 x 3)))
(neg.f64 (*.f64 (sqrt.f64 2) (pow.f64 x 3)))
(*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 x 3)))
(*.f64 (pow.f64 x 3) (neg.f64 (sqrt.f64 2)))

eval76.0ms (2.8%)

Compiler: Compiled 3104 to 2373 computations (23.6% saved)

prune39.0ms (1.4%)

Pruning

15 alts after pruning (4 fresh and 11 done)

	Pruned	Kept	Total
New	254	4	258
Fresh	0	0	0
Picked	1	0	1
Done	1	11	12
Total	256	15	271

Error

0.0b

Counts

271 → 15

Alt Table

Click to see full alt table

Status	Error	Program
✓	62.3b	(/.f64 1 (+.f64 x x))
✓	32.1b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
✓	31.7b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	58.6b	(-.f64 (+.f64 1 (+.f64 x x)) 1)
	52.0b	(/.f64 (sqrt.f64 (.f64 2 (pow.f64 x 6))) (.f64 x x))
✓	60.6b	(.f64 (.f64 x x) 2)
✓	31.2b	(*.f64 (sqrt.f64 2) x)
	31.7b	(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 1/4) 2)
✓	56.7b	(+.f64 x x)
	42.8b	(cbrt.f64 (pow.f64 (.f64 2 (.f64 x x)) 3/2))
✓	31.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	60.6b	(.f64 4 (.f64 x x))
✓	0.1b	(hypot.f64 x x)
	60.9b	(-.f64 (+.f64 1 (.f64 4 (.f64 x x))) 1)
✓	31.2b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

Compiler

Compiled 111 to 83 computations (25.2% saved)

regimes71.0ms (2.6%)

Counts

21 → 1

Calls

Call 1

Inputs
(+.f64 x x)
(/.f64 0 0)
(.f64 4 (.f64 x x))
(/.f64 1 (+.f64 x x))
(.f64 (.f64 x x) 2)
(-.f64 (+.f64 1 (+.f64 x x)) 1)
(-.f64 (+.f64 1 (.f64 4 (.f64 x x))) 1)
(-.f64 (+.f64 1 (.f64 (.f64 x x) 2)) 1)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 x x)) 3/2))
(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 1/4) 2)
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(/.f64 (sqrt.f64 (.f64 2 (pow.f64 x 6))) (.f64 x x))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))

Outputs
(hypot.f64 x x)

Calls

7 calls:

14.0ms	x
14.0ms	(*.f64 x x)
9.0ms	(+.f64 (.f64 x x) (.f64 x x))
7.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))
7.0ms	(*.f64 x x)

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
0.1b	1	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))`
0.1b	1	`(+.f64 (.f64 x x) (.f64 x x))`
0.1b	1	`(+.f64 (.f64 x x) (.f64 x x))`
0.1b	1	`(*.f64 x x)`
0.1b	1	`(*.f64 x x)`

Compiler

Compiled 188 to 114 computations (39.4% saved)

regimes18.0ms (0.6%)

Accuracy

Total -7.3b remaining (-12.9%)

Threshold costs -7.3b (-12.9%)

Counts

8 → 1

Calls

Call 1

Inputs
(+.f64 x x)
(/.f64 0 0)
(.f64 4 (.f64 x x))
(/.f64 1 (+.f64 x x))
(.f64 (.f64 x x) 2)
(-.f64 (+.f64 1 (+.f64 x x)) 1)
(-.f64 (+.f64 1 (.f64 4 (.f64 x x))) 1)
(-.f64 (+.f64 1 (.f64 (.f64 x x) 2)) 1)

Outputs
(+.f64 x x)

Calls

3 calls:

6.0ms	(*.f64 x x)
5.0ms	x
4.0ms	(*.f64 x x)

Results

Error	Segments	Branch
56.7b	1	`x`
56.7b	1	`(*.f64 x x)`
56.7b	1	`(*.f64 x x)`

Compiler

Compiled 57 to 33 computations (42.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8

Stop Event

1×

saturated

Calls

Call 1

Inputs
(hypot.f64 x x)
(+.f64 x x)

Outputs
(hypot.f64 x x)
(+.f64 x x)

end17.0ms (0.6%)

Stop Event

1×

fuel

Compiler

Compiled 15 to 7 computations (53.3% saved)

Iter	Nodes	Cost
0	12	100
1	21	100
2	53	100
3	104	100
4	118	100
5	166	100
6	238	100
7	275	100
8	321	100
9	498	100
10	526	100

Iter	Nodes	Cost
0	12	100
1	21	100
2	53	100
3	104	100
4	118	100
5	166	100
6	238	100
7	275	100
8	321	100
9	498	100
10	526	100

Details

analyze3.0ms (0.1%)

sample824.0ms (30.2%)

preprocess16.0ms (0.6%)

simplify6.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize2.0ms (0.1%)

series3.0ms (0.1%)

rewrite108.0ms (4%)

simplify11.0ms (0.4%)

eval22.0ms (0.8%)

prune18.0ms (0.7%)

localize3.0ms (0.1%)

series2.0ms (0.1%)

rewrite35.0ms (1.3%)

simplify6.0ms (0.2%)

localize1.0ms (0%)

localize3.0ms (0.1%)

series2.0ms (0.1%)

rewrite52.0ms (1.9%)

simplify137.0ms (5%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite35.0ms (1.3%)

simplify11.0ms (0.4%)

localize4.0ms (0.2%)

series2.0ms (0.1%)

rewrite49.0ms (1.8%)

simplify15.0ms (0.6%)

eval18.0ms (0.7%)

prune20.0ms (0.7%)

localize5.0ms (0.2%)

series6.0ms (0.2%)

rewrite47.0ms (1.7%)

simplify6.0ms (0.2%)

localize2.0ms (0.1%)

localize3.0ms (0.1%)

localize6.0ms (0.2%)

series1.0ms (0%)

rewrite45.0ms (1.6%)

simplify8.0ms (0.3%)

localize5.0ms (0.2%)

series1.0ms (0%)

rewrite47.0ms (1.7%)

simplify137.0ms (5%)

eval72.0ms (2.6%)

prune72.0ms (2.6%)

localize5.0ms (0.2%)

series42.0ms (1.5%)

rewrite50.0ms (1.8%)

simplify7.0ms (0.3%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite32.0ms (1.2%)

simplify134.0ms (4.9%)

localize5.0ms (0.2%)

series5.0ms (0.2%)

rewrite45.0ms (1.7%)

simplify150.0ms (5.5%)

localize8.0ms (0.3%)

series3.0ms (0.1%)

rewrite57.0ms (2.1%)

simplify84.0ms (3.1%)

eval76.0ms (2.8%)

prune39.0ms (1.4%)

regimes71.0ms (2.6%)

regimes18.0ms (0.6%)

simplify2.0ms (0.1%)

end17.0ms (0.6%)

Profiling

Iter	Nodes	Cost
0	12	100
1	21	100
2	53	100
3	104	100
4	118	100
5	166	100
6	238	100
7	275	100
8	321	100
9	498	100
10	526	100