Details

analyze7.0ms (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 8 computations (20% saved)

sample1.4s (26.1%)

Results

1.2s	8256×	body	256	valid
1.0ms	6×	body	256	invalid

preprocess105.0ms (2%)

Algorithm

2×	egg-herbie

Rules

1278×	`fma-def_binary64`
776×	`distribute-rgt-out_binary64`
559×	`hypot-def_binary64`
494×	`count-2_binary64`
444×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	4
2	30	4
3	53	4
4	118	4
5	384	4
6	1382	4
7	2642	4
8	4009	4
9	4972	4
10	5749	4
11	6776	4
12	7662	4
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

Outputs
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(hypot.f64 x x)

Compiler

Compiled 10 to 8 computations (20% saved)

simplify100.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1278×	`fma-def_binary64`
776×	`distribute-rgt-out_binary64`
559×	`hypot-def_binary64`
494×	`count-2_binary64`
444×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	4
2	30	4
3	53	4
4	118	4
5	384	4
6	1382	4
7	2642	4
8	4009	4
9	4972	4
10	5749	4
11	6776	4
12	7662	4

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

Outputs
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(hypot.f64 x x)

eval1.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% 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)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 5 to 2 computations (60% saved)

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	@	inf	(hypot.f64 x x)
1.0ms	x	@	0	(hypot.f64 x x)

rewrite76.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

356×	`log1p-udef_binary64`
279×	`associate-r_binary64`
271×	`pow1_binary64`
259×	`associate-l_binary64`
259×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	60	4
2	696	4
3	7879	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 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 0 0)) 2))) (log.f64 (cbrt.f64 (exp.f64 (/.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 (.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) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 x (.f64 (+.f64 x x) (/.f64 0 0)))))) (#(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 (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 (/.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 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 (/.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 (.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 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)) 1) (+.f64 0 (pow.f64 x 4)))))) (#(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 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) 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) 9)))) (#(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) 6)))) (#(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) 5/2)))) (#(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) 4/3)))) (#(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 (cbrt.f64 (pow.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 expm1.f64 (log1p.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)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 0 0)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 0 0)) 1/2))))) (#(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))))))

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

simplify12.0ms (0.2%)

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))

eval20.0ms (0.4%)

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

prune41.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	98	7	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	98	8	106

Error

0.0b

Counts

106 → 8

Alt Table

Click to see full alt table

Status	Error	Program
▶	60.5b	(.f64 (.f64 x x) 2)
▶	32.3b	(*.f64 (sqrt.f64 2) x)
▶	64.0b	(/.f64 0 0)
▶	60.5b	(*.f64 (+.f64 x x) x)
	52.1b	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
	32.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	0.1b	(hypot.f64 x x)
▶	30.8b	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 102 to 76 computations (25.5% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 12 to 8 computations (33.3% saved)

series3.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite54.0ms (1%)

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	1473	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 expm1.f64 (log1p.f64 (.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)))))))

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 expm1.f64 (log1p.f64 (*.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)))))))

simplify12.0ms (0.2%)

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))

localize2.0ms (0%)

Compiler: Compiled 5 to 5 computations (0% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 11 to 5 computations (54.5% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite42.0ms (0.8%)

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	1124	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 expm1.f64 (log1p.f64 (*.f64 (*.f64 x x) 2)))))) (#(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)))))))

simplify172.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
617×	`cube-prod_binary64`
558×	`fabs-mul_binary64`
523×	`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	43	84
4	105	84
5	329	84
6	1259	84
7	2132	84
8	2296	84
9	2480	84
10	2688	84
11	2984	84
12	3379	84
13	3860	84
14	4426	84
15	5118	84
16	5951	84
17	6343	84
18	6631	84
19	6911	84
20	6985	84
21	7019	84
22	7960	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%)

Compiler: Compiled 10 to 3 computations (70% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

series1.0ms (0%)

Counts

1 → 0

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	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)

rewrite36.0ms (0.7%)

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 (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 (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 (+.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 expm1.f64 (log1p.f64 (*.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)))))))

simplify6.0ms (0.1%)

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

eval10.0ms (0.2%)

Compiler: Compiled 362 to 266 computations (26.5% saved)

prune13.0ms (0.3%)

Pruning

11 alts after pruning (5 fresh and 6 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	0	2	2
Picked	0	1	1
Done	0	5	5
Total	45	11	56

Error

0.0b

Counts

56 → 11

Alt Table

Click to see full alt table

Status	Error	Program
✓	60.5b	(.f64 (.f64 x x) 2)
✓	32.3b	(*.f64 (sqrt.f64 2) x)
✓	64.0b	(/.f64 0 0)
✓	60.5b	(*.f64 (+.f64 x x) x)
✓	0.1b	(hypot.f64 x x)
▶	49.8b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
▶	33.1b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
✓	30.8b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	60.9b	(-.f64 (+.f64 1 (.f64 (.f64 x x) 2)) 1)
▶	52.1b	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
▶	32.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))

Compiler

Compiled 127 to 100 computations (21.3% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))

Compiler

Compiled 18 to 5 computations (72.2% saved)

series2.0ms (0%)

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)))

rewrite189.0ms (3.6%)

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	1820	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 hypot.f64 (sqrt.f64 x) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.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)))))

simplify18.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

248×	`fma-def_binary64`
22×	`distribute-rgt-in_binary64`
21×	`associate-l_binary64`
21×	`sub-neg_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	119	100
5	167	100
6	239	100
7	276	100
8	322	100
9	499	100
10	527	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))
(.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) x))
(.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) x))
(.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) x))
(.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) (neg.f64 x))

localize13.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(.f64 (.f64 x x) 2)
✓	1.1b	(-.f64 (+.f64 1 (.f64 (.f64 x x) 2)) 1)

Compiler

Compiled 28 to 16 computations (42.9% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite100.0ms (1.9%)

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	2375	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 (exp.f64 x) (*.f64 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 expm1.f64 (log1p.f64 (*.f64 x (*.f64 x 2))))))) (#(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)))))

simplify194.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
617×	`cube-prod_binary64`
558×	`fabs-mul_binary64`
523×	`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	43	84
4	105	84
5	329	84
6	1259	84
7	2132	84
8	2296	84
9	2480	84
10	2688	84
11	2984	84
12	3379	84
13	3860	84
14	4426	84
15	5118	84
16	5951	84
17	6343	84
18	6631	84
19	6911	84
20	6985	84
21	7019	84
22	7960	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))

localize33.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (*.f64 (sqrt.f64 2) x) 3)
	0.4b	(*.f64 (sqrt.f64 2) x)
✓	38.9b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))

Compiler

Compiled 23 to 19 computations (17.4% saved)

series10.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
2.0ms	x	@	0	(pow.f64 (*.f64 (sqrt.f64 2) x) 3)
1.0ms	x	@	-inf	(pow.f64 (*.f64 (sqrt.f64 2) x) 3)
1.0ms	x	@	inf	(pow.f64 (*.f64 (sqrt.f64 2) x) 3)
1.0ms	x	@	0	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))

rewrite87.0ms (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	1638	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 expm1.f64 (log1p.f64 (*.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 -.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 expm1.f64 (log1p.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 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))))))))

simplify224.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	244
1	36	244
2	103	244
3	276	244
4	783	244
5	1358	244
6	2805	244
7	2927	244
8	3219	244
9	3491	244
10	3718	244
11	3949	244
12	4241	244
13	4590	244
14	5420	244
15	5945	244
16	6627	244
17	6935	244
18	7303	244
19	7633	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 (.f64 x (cbrt.f64 -1)) (neg.f64 (sqrt.f64 2)))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) (neg.f64 x)))
(.f64 (sqrt.f64 2) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 -1) x)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 x (cbrt.f64 -1))))
(.f64 (.f64 x (cbrt.f64 -1)) (neg.f64 (sqrt.f64 2)))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) (neg.f64 x)))
(.f64 (sqrt.f64 2) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 -1) x)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 x (cbrt.f64 -1))))
(.f64 (.f64 x (cbrt.f64 -1)) (neg.f64 (sqrt.f64 2)))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) (neg.f64 x)))
(.f64 (sqrt.f64 2) (.f64 x (neg.f64 (cbrt.f64 -1))))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 -1) x)))
(neg.f64 (.f64 (sqrt.f64 2) (.f64 x (cbrt.f64 -1))))
(.f64 (.f64 x (cbrt.f64 -1)) (neg.f64 (sqrt.f64 2)))
(.f64 (sqrt.f64 2) (.f64 (cbrt.f64 -1) (neg.f64 x)))
(.f64 (sqrt.f64 2) (.f64 x (neg.f64 (cbrt.f64 -1))))
(*.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 3))
(.f64 (sqrt.f64 2) (.f64 2 (pow.f64 x 3)))
(.f64 (sqrt.f64 2) (.f64 (pow.f64 x 3) 2))
(.f64 (.f64 (sqrt.f64 2) 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 (sqrt.f64 2) (.f64 (pow.f64 x 3) 2))
(.f64 (.f64 (sqrt.f64 2) 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 (sqrt.f64 2) (.f64 (pow.f64 x 3) 2))
(.f64 (.f64 (sqrt.f64 2) 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 (sqrt.f64 2) (.f64 (pow.f64 x 3) 2))
(.f64 (.f64 (sqrt.f64 2) 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 (sqrt.f64 2) (.f64 (pow.f64 x 3) 2))
(.f64 (.f64 (sqrt.f64 2) 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 (sqrt.f64 2) (.f64 (pow.f64 x 3) 2))
(.f64 (.f64 (sqrt.f64 2) 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 (sqrt.f64 2) (.f64 (pow.f64 x 3) 2))
(.f64 (.f64 (sqrt.f64 2) 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 (sqrt.f64 2) (.f64 (pow.f64 x 3) 2))
(.f64 (.f64 (sqrt.f64 2) 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 (sqrt.f64 2) (.f64 (pow.f64 x 3) 2))
(.f64 (.f64 (sqrt.f64 2) 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 (sqrt.f64 2) (.f64 (pow.f64 x 3) 2))
(.f64 (.f64 (sqrt.f64 2) 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 (sqrt.f64 2) (.f64 (pow.f64 x 3) 2))
(.f64 (.f64 (sqrt.f64 2) 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 (sqrt.f64 2) (.f64 (pow.f64 x 3) 2))
(.f64 (.f64 (sqrt.f64 2) 2) (pow.f64 x 3))

localize22.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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)

Compiler

Compiled 21 to 17 computations (19% saved)

series13.0ms (0.2%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	x	@	-inf	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
3.0ms	x	@	0	(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	@	-inf	(sqrt.f64 (*.f64 (sqrt.f64 2) x))
1.0ms	x	@	0	(sqrt.f64 (*.f64 (sqrt.f64 2) x))

rewrite92.0ms (1.8%)

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	1322	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 2) (*.f64 (cbrt.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 (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 expm1.f64 (log1p.f64 (*.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 -.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 expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x))))))) (#(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))))))))

simplify11.0ms (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

localize147.0ms (2.8%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	10.1b	(sqrt.f64 (*.f64 2 (pow.f64 x 6)))
✓	15.9b	(sqrt.f64 (+.f64 0 (pow.f64 x 4)))
✓	39.6b	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))

Compiler

Compiled 47 to 38 computations (19.1% saved)

series4.0ms (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	@	0	(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
0.0ms	x	@	inf	(sqrt.f64 (*.f64 2 (pow.f64 x 6)))
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))))

rewrite118.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	30
1	288	22
2	3364	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 (/.f64 (sqrt.f64 2) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 2) (/.f64 1 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (sqrt.f64 2) (/.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 2) (/.f64 1 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (sqrt.f64 2) (/.f64 1 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (/.f64 1 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 x 3) (sqrt.f64 2)) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (sqrt.f64 2) (/.f64 1 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 (pow.f64 x -2)) 1/6) (cbrt.f64 (/.f64 2 (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 2 (pow.f64 x -2))) (pow.f64 (/.f64 2 (pow.f64 x -2)) 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 (pow.f64 x -2)) 1/4) (pow.f64 (/.f64 2 (pow.f64 x -2)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 2 (pow.f64 x 6)) 1/4) (*.f64 (pow.f64 (*.f64 2 (pow.f64 x 6)) 1/4) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 2) (neg.f64 (pow.f64 x 3))) (/.f64 1 (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -2) (*.f64 (pow.f64 x 3) (sqrt.f64 2)))))) (#(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 2 (pow.f64 x 6)) 1/4) 1) (/.f64 (pow.f64 (*.f64 2 (pow.f64 x 6)) 1/4) (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (*.f64 (cbrt.f64 x) x)) (/.f64 (*.f64 (pow.f64 x 3) (sqrt.f64 2)) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 2) (*.f64 (cbrt.f64 x) x)) (/.f64 (pow.f64 x 3) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (*.f64 2 (pow.f64 x 6)) 1/4) (*.f64 (cbrt.f64 x) x)) (/.f64 (pow.f64 (*.f64 2 (pow.f64 x 6)) 1/4) (pow.f64 (cbrt.f64 x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (/.f64 (*.f64 (pow.f64 x 3) (sqrt.f64 2)) 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 *.f64 (/.f64 (*.f64 (cbrt.f64 2) (*.f64 x x)) (*.f64 (cbrt.f64 x) x)) (pow.f64 (/.f64 2 (pow.f64 x -2)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 2) (/.f64 1 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 2 (pow.f64 x -2)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 2 (pow.f64 x -2)) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 2 (pow.f64 x -2)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 2 (pow.f64 x -2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 2 (pow.f64 x -2)) -1/2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 1) (log.f64 (/.f64 (sqrt.f64 2) (/.f64 1 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 (pow.f64 x -2)) -1/2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (/.f64 (sqrt.f64 2) (/.f64 1 x)))) 2)) (cbrt.f64 (log.f64 (/.f64 (sqrt.f64 2) (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 (sqrt.f64 2) (/.f64 1 x))))) (sqrt.f64 (log.f64 (/.f64 (sqrt.f64 2) (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 (pow.f64 x 3) (sqrt.f64 2)) (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 2 (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (sqrt.f64 2) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 2) (/.f64 1 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 2 (pow.f64 x -2)) 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 expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 2) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 2) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (sqrt.f64 2) (/.f64 1 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 2) (/.f64 1 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 2 (pow.f64 x -2)) 3/2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 2 (pow.f64 x -2)) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 2 (pow.f64 x -2)) 1/4)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 2 (pow.f64 x -2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (/.f64 2 (pow.f64 x -2)) -1/2)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 2) (/.f64 1 x))) 1) 1))))))

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

simplify158.0ms (3%)

Algorithm

1×	egg-herbie

Rules

902×	`fma-def_binary64`
682×	`distribute-rgt-neg-in_binary64`
680×	`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	223	244
4	701	244
5	1269	244
6	2407	244
7	3742	244
8	5131	244
9	5861	244
10	6723	244
11	7948	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)))

eval219.0ms (4.2%)

Compiler: Compiled 4556 to 3538 computations (22.3% saved)

prune76.0ms (1.4%)

Pruning

15 alts after pruning (9 fresh and 6 done)

	Pruned	Kept	Total
New	380	9	389
Fresh	0	0	0
Picked	1	0	1
Done	4	6	10
Total	385	15	400

Error

0.0b

Counts

400 → 15

Alt Table

Click to see full alt table

Status	Error	Program
✓	60.5b	(.f64 (.f64 x x) 2)
✓	32.3b	(*.f64 (sqrt.f64 2) x)
	28.4b	(pow.f64 (pow.f64 (/.f64 2 (pow.f64 x -2)) -1/2) -1)
▶	49.8b	(cbrt.f64 (.f64 (.f64 (.f64 2 (.f64 x x)) x) (sqrt.f64 2)))
	62.2b	(/.f64 1 (+.f64 x x))
✓	32.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
▶	28.3b	(sqrt.f64 (/.f64 2 (pow.f64 x -2)))
	32.2b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
▶	58.9b	(-.f64 (+.f64 1 (+.f64 x x)) 1)
▶	56.9b	(+.f64 x x)
	44.3b	(.f64 (/.f64 (sqrt.f64 2) x) (.f64 x x))
✓	60.5b	(*.f64 (+.f64 x x) x)
✓	0.1b	(hypot.f64 x x)
✓	30.8b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	32.3b	(+.f64 0 (/.f64 (sqrt.f64 2) (/.f64 1 x)))

Compiler

Compiled 185 to 141 computations (23.8% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.8b	(/.f64 2 (pow.f64 x -2))
✓	26.3b	(sqrt.f64 (/.f64 2 (pow.f64 x -2)))

Compiler

Compiled 18 to 14 computations (22.2% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite115.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

628×	`pow1_binary64`
586×	`add-log-exp_binary64`
585×	`log1p-expm1-u_binary64`
585×	`expm1-log1p-u_binary64`
572×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	152	13
2	1697	13

Stop Event

1×	node limit

Counts

2 → 53

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 2 (pow.f64 x -2)))
(/.f64 2 (pow.f64 x -2))

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

simplify83.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-def_binary64`
402×	`distribute-rgt-neg-out_binary64`
365×	`fma-neg_binary64`
337×	`distribute-rgt-neg-in_binary64`
318×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	164
1	20	164
2	43	164
3	83	164
4	205	164
5	632	164
6	988	164
7	1635	164
8	2038	164
9	2907	164
10	3744	164
11	4611	164
12	5738	164

Stop Event

1×	node limit

Counts

77 → 56

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

localize2.0ms (0%)

Compiler: Compiled 5 to 2 computations (60% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.0b	(-.f64 (+.f64 1 (+.f64 x x)) 1)

Compiler

Compiled 18 to 9 computations (50% saved)

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)

rewrite56.0ms (1.1%)

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	2348	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 x 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 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 (*.f64 (fma.f64 2 x 1) (+.f64 x x)) (*.f64 -1 (+.f64 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 (hypot.f64 1 (+.f64 x x)) 1) (-.f64 (hypot.f64 1 (+.f64 x x)) 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 2 (pow.f64 x 3))) (fma.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 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 (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 hypot.f64 (sqrt.f64 x) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.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 (hypot.f64 1 (+.f64 x x)) (hypot.f64 1 (+.f64 x x)) -1)))))

simplify8.0ms (0.2%)

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)

localize11.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 (sqrt.f64 2) (/.f64 1 x))

Compiler

Compiled 24 to 20 computations (16.7% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite46.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

642×	`pow1_binary64`
598×	`add-log-exp_binary64`
598×	`log1p-expm1-u_binary64`
598×	`expm1-log1p-u_binary64`
585×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	147	6
2	1747	6

Stop Event

1×	node limit

Counts

1 → 34

Calls

Call 1

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

simplify7.0ms (0.1%)

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

46 → 34

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)

localize43.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	0.1b	(.f64 (.f64 2 (*.f64 x x)) x)
✓	0.1b	(.f64 (.f64 (.f64 2 (.f64 x x)) x) (sqrt.f64 2))
✓	38.9b	(cbrt.f64 (.f64 (.f64 (.f64 2 (.f64 x x)) x) (sqrt.f64 2)))

Compiler

Compiled 41 to 23 computations (43.9% saved)

series10.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	(cbrt.f64 (.f64 (.f64 (.f64 2 (.f64 x x)) x) (sqrt.f64 2)))
2.0ms	x	@	-inf	(cbrt.f64 (.f64 (.f64 (.f64 2 (.f64 x x)) x) (sqrt.f64 2)))
1.0ms	x	@	inf	(cbrt.f64 (.f64 (.f64 (.f64 2 (.f64 x x)) x) (sqrt.f64 2)))
0.0ms	x	@	-inf	(.f64 (.f64 2 (*.f64 x x)) x)
0.0ms	x	@	0	(.f64 (.f64 (.f64 2 (.f64 x x)) x) (sqrt.f64 2))

rewrite191.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

750×	`pow1_binary64`
695×	`add-log-exp_binary64`
695×	`log1p-expm1-u_binary64`
695×	`expm1-log1p-u_binary64`
677×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	49
1	183	29
2	2145	29

Stop Event

1×	node limit

Counts

4 → 67

Calls

Call 1

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

simplify109.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

984×	`fma-def_binary64`
570×	`distribute-rgt-neg-in_binary64`
568×	`distribute-lft-neg-in_binary64`
561×	`associate-l_binary64`
427×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	476
1	64	476
2	173	476
3	551	476
4	1938	476
5	2670	476
6	4095	476
7	5762	476

Stop Event

1×	node limit

Counts

115 → 74

Calls

Call 1

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

eval262.0ms (5%)

Compiler: Compiled 2714 to 2030 computations (25.2% saved)

prune55.0ms (1%)

Pruning

15 alts after pruning (7 fresh and 8 done)

	Pruned	Kept	Total
New	251	6	257
Fresh	3	1	4
Picked	0	1	1
Done	3	7	10
Total	257	15	272

Error

0.0b

Counts

272 → 15

Alt Table

Click to see full alt table

Status	Error	Program
	32.3b	(/.f64 (sqrt.f64 2) (/.f64 1 x))
✓	32.3b	(*.f64 (sqrt.f64 2) x)
	62.2b	(/.f64 1 (+.f64 x x))
✓	56.9b	(+.f64 x x)
✓	32.9b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
✓	28.3b	(sqrt.f64 (/.f64 2 (pow.f64 x -2)))
✓	49.8b	(cbrt.f64 (.f64 (.f64 (.f64 2 (.f64 x x)) x) (sqrt.f64 2)))
	28.1b	(/.f64 1 (sqrt.f64 (*.f64 (pow.f64 x -2) 1/2)))
	44.3b	(.f64 (/.f64 (sqrt.f64 2) x) (.f64 x x))
	60.5b	(*.f64 (+.f64 x x) (+.f64 x x))
✓	60.5b	(*.f64 (+.f64 x x) x)
✓	0.1b	(hypot.f64 x x)
	58.9b	(+.f64 (+.f64 1 x) (-.f64 x 1))
✓	30.8b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	60.5b	(.f64 4 (.f64 x x))

Compiler

Compiled 105 to 73 computations (30.5% saved)

regimes87.0ms (1.6%)

Counts

27 → 1

Calls

Call 1

Inputs
(+.f64 x x)
(/.f64 0 0)
(/.f64 1 (+.f64 x x))
(.f64 4 (.f64 x x))
(/.f64 1 (+.f64 x x))
(.f64 (.f64 x x) 2)
(*.f64 (+.f64 x x) x)
(*.f64 (+.f64 x x) (+.f64 x x))
(+.f64 (+.f64 1 x) (-.f64 x 1))
(-.f64 (+.f64 1 (+.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))
(/.f64 (sqrt.f64 2) (/.f64 1 x))
(.f64 (/.f64 (sqrt.f64 2) x) (.f64 x x))
(+.f64 0 (/.f64 (sqrt.f64 2) (/.f64 1 x)))
(sqrt.f64 (/.f64 2 (pow.f64 x -2)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(/.f64 1 (sqrt.f64 (*.f64 (pow.f64 x -2) 1/2)))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(cbrt.f64 (.f64 (.f64 (.f64 2 (.f64 x x)) x) (sqrt.f64 2)))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
(pow.f64 (pow.f64 (/.f64 2 (pow.f64 x -2)) -1/2) -1)
(/.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
12.0ms	(pow.f64 x 2)
12.0ms	(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))
11.0ms	(pow.f64 x 2)
10.0ms	(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))

Results

Error	Segments	Branch
0.1b	1	`x`
0.1b	1	`(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))`
0.1b	1	`(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))`
0.1b	1	`(+.f64 (pow.f64 x 2) (pow.f64 x 2))`
0.1b	1	`(+.f64 (pow.f64 x 2) (pow.f64 x 2))`
0.1b	1	`(pow.f64 x 2)`
0.1b	1	`(pow.f64 x 2)`

Compiler

Compiled 225 to 155 computations (31.1% saved)

regimes16.0ms (0.3%)

Counts

11 → 2

Calls

Call 1

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

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

Calls

1 calls:

13.0ms

Results

Error	Segments	Branch
55.9b	2	`x`

Compiler

Compiled 64 to 32 computations (50% saved)

bsearch28.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
28.0ms	-2.0925672469871087e-305	1.175499337423358e-308

Compiler

Compiled 13 to 10 computations (23.1% saved)

regimes10.0ms (0.2%)

Counts

5 → 2

Calls

Call 1

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

Outputs
(.f64 4 (.f64 x x))
(+.f64 x x)

Calls

1 calls:

9.0ms

Results

Error	Segments	Branch
55.9b	2	`x`

Compiler

Compiled 24 to 13 computations (45.8% saved)

bsearch28.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
28.0ms	-2.0925672469871087e-305	1.175499337423358e-308

Compiler

Compiled 13 to 10 computations (23.1% saved)

regimes5.0ms (0.1%)

Accuracy

Total -7.1b remaining (-12.4%)

Threshold costs -7.1b (-12.4%)

Counts

3 → 1

Calls

Call 1

Inputs
(+.f64 x x)
(/.f64 0 0)
(/.f64 1 (+.f64 x x))

Outputs
(+.f64 x x)

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
56.9b	1	`x`

Compiler

Compiled 14 to 8 computations (42.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	42
1	16	42

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(hypot.f64 x x)
(if (<=.f64 x -8272271991938797/395316900990841051469717474060385365331165331570590074915822964897324881968740911898360124416869383779662261453743773264433220190206627884505885546759254902190463719290168674539974429183775813166483921247017080212035170866063852926988483116502264758478144641625700721781901200420372075258176420915324230983022866681823232) (.f64 (.f64 x x) 2) (+.f64 x x))
(if (<=.f64 x -8272271991938797/395316900990841051469717474060385365331165331570590074915822964897324881968740911898360124416869383779662261453743773264433220190206627884505885546759254902190463719290168674539974429183775813166483921247017080212035170866063852926988483116502264758478144641625700721781901200420372075258176420915324230983022866681823232) (.f64 4 (.f64 x x)) (+.f64 x x))
(+.f64 x x)

Outputs
(hypot.f64 x x)
(if (<=.f64 x -8272271991938797/395316900990841051469717474060385365331165331570590074915822964897324881968740911898360124416869383779662261453743773264433220190206627884505885546759254902190463719290168674539974429183775813166483921247017080212035170866063852926988483116502264758478144641625700721781901200420372075258176420915324230983022866681823232) (.f64 (.f64 x x) 2) (+.f64 x x))
(if (<=.f64 x -8272271991938797/395316900990841051469717474060385365331165331570590074915822964897324881968740911898360124416869383779662261453743773264433220190206627884505885546759254902190463719290168674539974429183775813166483921247017080212035170866063852926988483116502264758478144641625700721781901200420372075258176420915324230983022866681823232) (.f64 4 (.f64 x x)) (+.f64 x x))
(if (<=.f64 x -8272271991938797/395316900990841051469717474060385365331165331570590074915822964897324881968740911898360124416869383779662261453743773264433220190206627884505885546759254902190463719290168674539974429183775813166483921247017080212035170866063852926988483116502264758478144641625700721781901200420372075258176420915324230983022866681823232) (.f64 (.f64 x x) 4) (+.f64 x x))
(+.f64 x x)

Compiler

Compiled 34 to 20 computations (41.2% saved)

soundness205.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

1278×	`fma-def_binary64`
776×	`distribute-rgt-out_binary64`
559×	`hypot-def_binary64`
494×	`count-2_binary64`
444×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	4
2	30	4
3	53	4
4	118	4
5	384	4
6	1382	4
7	2642	4
8	4009	4
9	4972	4
10	5749	4
11	6776	4
12	7662	4

Stop Event

1×	node limit

Compiler

Compiled 31 to 19 computations (38.7% saved)

end26.0ms (0.5%)

Compiler: Compiled 31 to 14 computations (54.8% saved)

Iter	Nodes	Cost
0	12	100
1	21	100
2	53	100
3	104	100
4	119	100
5	167	100
6	239	100
7	276	100
8	322	100
9	499	100
10	527	100

Iter	Nodes	Cost
0	12	100
1	21	100
2	53	100
3	104	100
4	119	100
5	167	100
6	239	100
7	276	100
8	322	100
9	499	100
10	527	100

Details

analyze7.0ms (0.1%)

sample1.4s (26.1%)

preprocess105.0ms (2%)

simplify100.0ms (1.9%)

eval1.0ms (0%)

prune1.0ms (0%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite76.0ms (1.4%)

simplify12.0ms (0.2%)

eval20.0ms (0.4%)

prune41.0ms (0.8%)

localize6.0ms (0.1%)

series3.0ms (0%)

rewrite54.0ms (1%)

simplify12.0ms (0.2%)

localize2.0ms (0%)

localize4.0ms (0.1%)

series2.0ms (0%)

rewrite42.0ms (0.8%)

simplify172.0ms (3.3%)

localize4.0ms (0.1%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite36.0ms (0.7%)

simplify6.0ms (0.1%)

eval10.0ms (0.2%)

prune13.0ms (0.3%)

localize7.0ms (0.1%)

series2.0ms (0%)

rewrite189.0ms (3.6%)

simplify18.0ms (0.3%)

localize13.0ms (0.3%)

series2.0ms (0%)

rewrite100.0ms (1.9%)

simplify194.0ms (3.7%)

localize33.0ms (0.6%)

series10.0ms (0.2%)

rewrite87.0ms (1.7%)

simplify224.0ms (4.2%)

localize22.0ms (0.4%)

series13.0ms (0.2%)

rewrite92.0ms (1.8%)

simplify11.0ms (0.2%)

localize147.0ms (2.8%)

series4.0ms (0.1%)

rewrite118.0ms (2.2%)

simplify158.0ms (3%)

eval219.0ms (4.2%)

prune76.0ms (1.4%)

localize9.0ms (0.2%)

series2.0ms (0%)

rewrite115.0ms (2.2%)

simplify83.0ms (1.6%)

localize2.0ms (0%)

localize7.0ms (0.1%)

series1.0ms (0%)

rewrite56.0ms (1.1%)

simplify8.0ms (0.2%)

localize11.0ms (0.2%)

series1.0ms (0%)

rewrite46.0ms (0.9%)

simplify7.0ms (0.1%)

localize43.0ms (0.8%)

series10.0ms (0.2%)

rewrite191.0ms (3.6%)

simplify109.0ms (2.1%)

eval262.0ms (5%)

prune55.0ms (1%)

regimes87.0ms (1.6%)

regimes16.0ms (0.3%)

bsearch28.0ms (0.5%)

regimes10.0ms (0.2%)

bsearch28.0ms (0.5%)

regimes5.0ms (0.1%)

simplify4.0ms (0.1%)

soundness205.0ms (3.9%)

end26.0ms (0.5%)

Profiling

Iter	Nodes	Cost
0	12	100
1	21	100
2	53	100
3	104	100
4	119	100
5	167	100
6	239	100
7	276	100
8	322	100
9	499	100
10	527	100