Details

analyze7.0ms (0.2%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
50%	50%	50%	0%	0%	0%	0%	3
75%	75%	25%	0%	0%	0%	0%	4
87.5%	87.5%	12.5%	0%	0%	0%	0%	5
93.8%	93.7%	6.2%	0%	0%	0%	0%	6
96.9%	96.8%	3.1%	0%	0%	0%	0%	7
98.4%	98.4%	1.6%	0%	0%	0%	0%	8
99.2%	99.2%	0.8%	0%	0%	0%	0%	9
99.6%	99.6%	0.4%	0%	0%	0%	0%	10
99.8%	99.8%	0.2%	0%	0%	0%	0%	11
99.9%	99.9%	0.1%	0%	0%	0%	0%	12

Compiler

Compiled 10 to 8 computations (20% saved)

sample866.0ms (23.8%)

Results

854.0ms

8256×

body

256

valid

Bogosity

preprocess153.0ms (4.2%)

Algorithm

2×	egg-herbie

Rules

2476×	`fma-def`
1806×	`distribute-lft-out`
1312×	`count-2`
1058×	`hypot-def`
976×	`sqr-pow`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	14	7
2	35	7
3	59	7
4	122	7
5	306	7
6	1067	7
7	1905	7
8	3263	7
9	4212	7
10	5004	7
11	6030	7
12	6918	7
13	7857	7
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)

simplify146.0ms (4%)

Algorithm

1×	egg-herbie

Rules

2476×	`fma-def`
1806×	`distribute-lft-out`
1312×	`count-2`
1058×	`hypot-def`
976×	`sqr-pow`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	14	7
2	35	7
3	59	7
4	122	7
5	306	7
6	1067	7
7	1905	7
8	3263	7
9	4212	7
10	5004	7
11	6030	7
12	6918	7
13	7857	7

Stop Event

1×	node limit

Counts

1 → 3

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 18 to 12 computations (33.3% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	2	3
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	2	4

Error

0.01%

Counts

4 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.02%	(hypot.f64 x x)
▶	41.32%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 11 to 7 computations (36.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.01%	(.f64 2 (.f64 x x))
✓	39.85%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 17 to 8 computations (52.9% saved)

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite196.0ms (5.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1372×	`add-sqr-sqrt`
1354×	`*-un-lft-identity`
1256×	`add-cube-cbrt`
1246×	`add-cbrt-cube`
1234×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	30
1	159	24
2	1829	24

Stop Event

1×	node limit

Counts

2 → 36

Calls

Call 1

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

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

simplify167.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

1326×	`distribute-lft-in`
1310×	`distribute-rgt-in`
1040×	`associate-+r+`
954×	`associate-+l+`
876×	`fma-def`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	816
1	201	816
2	880	816
3	2375	688

Stop Event

1×	node limit

Counts

60 → 46

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))
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(*.f64 x (sqrt.f64 2))
(.f64 (.f64 x (sqrt.f64 2)) 1)
(.f64 1 (.f64 x (sqrt.f64 2)))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (pow.f64 1 1/2) (.f64 x (sqrt.f64 2)))
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4)) 1/2) (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/2))
(.f64 (pow.f64 (.f64 2 x) 1/2) (sqrt.f64 x))
(pow.f64 (.f64 2 (.f64 x x)) 1/2)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(fabs.f64 (*.f64 x (sqrt.f64 2)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(-.f64 (+.f64 1 (.f64 2 (.f64 x x))) 1)
(pow.f64 (.f64 2 (.f64 x x)) 1)
(pow.f64 (*.f64 x (sqrt.f64 2)) 2)
(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3)
(pow.f64 (*.f64 (pow.f64 x 4) 4) 1/2)
(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 3) 1/3)
(sqrt.f64 (*.f64 (pow.f64 x 4) 4))
(log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 2))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 x x)) 3))
(expm1.f64 (log1p.f64 (.f64 2 (.f64 x x))))
(exp.f64 (log.f64 (.f64 2 (.f64 x x))))
(log1p.f64 (expm1.f64 (.f64 2 (.f64 x x))))

Outputs
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.f64 (sqrt.f64 2) x))
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.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))
(*.f64 2 (pow.f64 x 2))
(.f64 2 (.f64 x x))
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 (.f64 x (sqrt.f64 2)) 1)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 1 (.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (pow.f64 1 1/2) (.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 4)) 1/2) (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/2))
(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (pow.f64 (.f64 2 x) 1/2) (sqrt.f64 x))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 2 x)))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(*.f64 (sqrt.f64 (+.f64 x x)) (sqrt.f64 x))
(pow.f64 (.f64 2 (.f64 x x)) 1/2)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(pow.f64 (*.f64 x (sqrt.f64 2)) 1)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3) 1/3)
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(fabs.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(*.f64 (sqrt.f64 2) x)
(hypot.f64 x x)
(-.f64 (+.f64 1 (.f64 2 (.f64 x x))) 1)
(.f64 2 (.f64 x x))
(pow.f64 (.f64 2 (.f64 x x)) 1)
(.f64 2 (.f64 x x))
(pow.f64 (*.f64 x (sqrt.f64 2)) 2)
(.f64 2 (.f64 x x))
(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3)
(.f64 2 (.f64 x x))
(pow.f64 (*.f64 (pow.f64 x 4) 4) 1/2)
(.f64 2 (.f64 x x))
(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 3) 1/3)
(.f64 2 (.f64 x x))
(sqrt.f64 (*.f64 (pow.f64 x 4) 4))
(.f64 2 (.f64 x x))
(log.f64 (pow.f64 (pow.f64 (exp.f64 x) x) 2))
(.f64 2 (.f64 x x))
(cbrt.f64 (pow.f64 (.f64 2 (.f64 x x)) 3))
(.f64 2 (.f64 x x))
(expm1.f64 (log1p.f64 (.f64 2 (.f64 x x))))
(.f64 2 (.f64 x x))
(exp.f64 (log.f64 (.f64 2 (.f64 x x))))
(.f64 2 (.f64 x x))
(log1p.f64 (expm1.f64 (.f64 2 (.f64 x x))))
(.f64 2 (.f64 x x))

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.02%	(hypot.f64 x x)

Compiler

Compiled 5 to 2 computations (60% saved)

series2.0ms (0%)

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)
0.0ms	x	@	0	(hypot.f64 x x)

rewrite47.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

918×	`associate-r`
744×	`add-sqr-sqrt`
738×	`*-un-lft-identity`
696×	`pow1`
682×	`add-cube-cbrt`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	80	7
2	916	7

Stop Event

1×	node limit

Counts

1 → 36

Calls

Call 1

Inputs
(hypot.f64 x x)

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

Outputs

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

simplify122.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1144×	`distribute-lft-in`
1118×	`associate-r`
1046×	`distribute-rgt-in`
928×	`associate-l`
836×	`*-commutative`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	88	1038
1	194	864
2	596	854
3	3338	854
4	7923	854

Stop Event

1×	node limit

Counts

48 → 50

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 (+.f64 (hypot.f64 x x) 1) 1)
(*.f64 (hypot.f64 x x) 1)
(*.f64 1 (hypot.f64 x x))
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (hypot.f64 x x))))
(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
(.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(.f64 (cbrt.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (hypot.f64 x x))))
(.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (*.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))))) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(.f64 (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x))) (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x))))
(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))))
(.f64 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
(pow.f64 (hypot.f64 x x) 1)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(pow.f64 (*.f64 x (+.f64 x x)) 1/2)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(log.f64 (exp.f64 (hypot.f64 x x)))
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(exp.f64 (log.f64 (hypot.f64 x x)))
(log1p.f64 (expm1.f64 (hypot.f64 x 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))
(-.f64 (+.f64 (hypot.f64 x x) 1) 1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(*.f64 (hypot.f64 x x) 1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(*.f64 1 (hypot.f64 x x))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(*.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (hypot.f64 x x)))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(*.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (hypot.f64 x x)))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (hypot.f64 x x))))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (hypot.f64 x x))))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(.f64 (cbrt.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (hypot.f64 x x))))
(.f64 (cbrt.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))))
(.f64 (cbrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4))))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4))))
(.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(.f64 (sqrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
(*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 5/2))
(.f64 (.f64 (sqrt.f64 (hypot.f64 x x)) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (*.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x))))) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)))
(.f64 (cbrt.f64 (.f64 (hypot.f64 x x) (cbrt.f64 (hypot.f64 x x)))) (*.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))))
(.f64 (cbrt.f64 (hypot.f64 x x)) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4))))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (cbrt.f64 (hypot.f64 x x)) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 4))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (sqrt.f64 (cbrt.f64 (hypot.f64 x x)))) (sqrt.f64 (cbrt.f64 (hypot.f64 x x))))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
(.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
(.f64 (.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x))))
(.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
(.f64 (.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x))) (*.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) (cbrt.f64 (hypot.f64 x x))))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(.f64 (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))) (*.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))))
(.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
(.f64 (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))) (*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
(.f64 (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2) (.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) (cbrt.f64 (sqrt.f64 (hypot.f64 x x)))))
(pow.f64 (hypot.f64 x x) 1)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (cbrt.f64 (hypot.f64 x x)) 3)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (pow.f64 (hypot.f64 x x) 3) 1/3)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(pow.f64 (*.f64 x (+.f64 x x)) 1/2)
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(sqrt.f64 (*.f64 x (+.f64 x x)))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(log.f64 (exp.f64 (hypot.f64 x x)))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(expm1.f64 (log1p.f64 (hypot.f64 x x)))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(exp.f64 (log.f64 (hypot.f64 x x)))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)
(log1p.f64 (expm1.f64 (hypot.f64 x x)))
(+.f64 (hypot.f64 x x) 0)
(hypot.f64 x x)

eval17.0ms (0.5%)

Compiler: Compiled 1015 to 464 computations (54.3% saved)

prune10.0ms (0.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	94	4	98

Error

Counts

98 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	41.29%	(pow.f64 (*.f64 x (+.f64 x x)) 1/2)
✓	0.02%	(hypot.f64 x x)
▶	46.43%	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	41.32%	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 25 to 17 computations (32% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.73%	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 12 to 8 computations (33.3% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite51.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1266×	`add-sqr-sqrt`
1248×	`*-un-lft-identity`
1162×	`add-cube-cbrt`
1148×	`add-cbrt-cube`
1134×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	162	11
2	1917	11

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

simplify69.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1082×	`*-commutative`
878×	`log-prod`
650×	`distribute-lft-in`
648×	`distribute-rgt-in`
646×	`distribute-lft-out`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	37	463
1	90	397
2	331	331
3	1789	331
4	4954	331
5	7952	331

Stop Event

1×	node limit

Counts

25 → 19

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))
(-.f64 0 (*.f64 (sqrt.f64 2) x))
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(neg.f64 (*.f64 (sqrt.f64 2) x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))

Outputs
(.f64 -1 (.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))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.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))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.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))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.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))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.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))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 -1 (.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))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(-.f64 0 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 2)))
(-.f64 (+.f64 1 (*.f64 (sqrt.f64 2) x)) 1)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (*.f64 (sqrt.f64 2) x) 1)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(pow.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3) 1/3)
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.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)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 2)) x))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)
(log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))
(+.f64 1 (-.f64 (*.f64 (sqrt.f64 2) x) 1))
(+.f64 (*.f64 (sqrt.f64 2) x) 0)
(*.f64 (sqrt.f64 2) x)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	39.84%	(pow.f64 (*.f64 x (+.f64 x x)) 1/2)

Compiler

Compiled 18 to 6 computations (66.7% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite49.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1076×	`add-sqr-sqrt`
1056×	`*-un-lft-identity`
1004×	`pow1`
998×	`add-cube-cbrt`
988×	`add-cbrt-cube`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	158	7
2	2138	7

Stop Event

1×	node limit

Counts

1 → 76

Calls

Call 1

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

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

simplify35.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

80×	`*-commutative`
36×	`distribute-lft-in`
24×	`distribute-rgt-in`
24×	`associate-l`
22×	`associate-/l*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	430
1	472	430

Stop Event

1×

unsound

Counts

88 → 93

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 x x)
(+.f64 (+.f64 x x) (+.f64 x x))
(+.f64 (.f64 x x) (.f64 x x))
(+.f64 (.f64 (.f64 x x) 1) (.f64 (.f64 x x) 1))
(-.f64 (+.f64 1 (+.f64 x x)) 1)
(-.f64 (/.f64 (.f64 x x) 0) (/.f64 (.f64 x x) 0))
(*.f64 x (+.f64 x x))
(*.f64 x 2)
(*.f64 (+.f64 x x) x)
(*.f64 (+.f64 x x) (+.f64 x x))
(*.f64 (+.f64 x x) 1)
(*.f64 (+.f64 x x) (sqrt.f64 x))
(*.f64 (+.f64 x x) (cbrt.f64 x))
(.f64 (+.f64 x x) (.f64 x x))
(*.f64 (+.f64 x x) (pow.f64 x 3))
(*.f64 (+.f64 x x) (pow.f64 x 1/4))
(*.f64 1 (+.f64 x x))
(*.f64 (sqrt.f64 x) (+.f64 x x))
(*.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 (cbrt.f64 x) (+.f64 x x))
(.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 (*.f64 x x))))
(.f64 (cbrt.f64 (.f64 x x)) (+.f64 x x))
(.f64 (cbrt.f64 (.f64 x x)) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))
(.f64 (.f64 x x) (+.f64 x x))
(*.f64 2 x)
(*.f64 2 (+.f64 x x))
(.f64 2 (.f64 x x))
(*.f64 0 (/.f64 1 0))
(*.f64 (pow.f64 x 3) (+.f64 x x))
(.f64 (.f64 2 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x 0)))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (+.f64 x x))
(*.f64 (sqrt.f64 2) (sqrt.f64 x))
(*.f64 (cbrt.f64 (sqrt.f64 x)) (+.f64 x x))
(*.f64 (cbrt.f64 2) (cbrt.f64 x))
(.f64 4 (.f64 x x))
(.f64 (.f64 (+.f64 x x) 2) x)
(.f64 (.f64 (+.f64 x x) (cbrt.f64 (*.f64 x x))) (cbrt.f64 x))
(.f64 (.f64 2 (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 2 (cbrt.f64 (*.f64 x x))) (cbrt.f64 x))
(*.f64 (pow.f64 x 1/4) (+.f64 x x))
(*.f64 (pow.f64 (+.f64 x x) 1/8) (pow.f64 (+.f64 x x) 1/8))
(*.f64 (pow.f64 1 1/2) (+.f64 x x))
(*.f64 (pow.f64 1 1/4) (+.f64 x x))
(*.f64 (pow.f64 2 1/2) (sqrt.f64 x))
(/.f64 1 (+.f64 x x))
(/.f64 1 (/.f64 (fma.f64 x x 0) (*.f64 2 (pow.f64 x 3))))
(/.f64 0 0)
(/.f64 (*.f64 2 (pow.f64 x 3)) (fma.f64 x x 0))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x 0)))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 3))) (cbrt.f64 (fma.f64 x x 0)))
(/.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)))
(/.f64 (.f64 (+.f64 x x) (.f64 2 (pow.f64 x 3))) (fma.f64 x x 0))
(/.f64 (.f64 x (.f64 2 (pow.f64 x 3))) (fma.f64 x x 0))
(/.f64 (*.f64 0 (+.f64 x x)) 0)
(/.f64 (.f64 (.f64 2 (pow.f64 x 3)) (+.f64 x x)) (fma.f64 x x 0))
(/.f64 (*.f64 0 x) 0)
(/.f64 (.f64 (.f64 2 (pow.f64 x 3)) x) (fma.f64 x x 0))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))) 0)
(/.f64 (+.f64 (pow.f64 (.f64 x x) 3) (pow.f64 (.f64 x x) 3)) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (*.f64 x x)))))
(/.f64 (.f64 0 (.f64 2 (pow.f64 x 3))) (*.f64 0 (fma.f64 x x 0)))
(/.f64 (.f64 (.f64 2 (pow.f64 x 3)) 0) (*.f64 (fma.f64 x x 0) 0))
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 3))) (neg.f64 (fma.f64 x x 0)))
(sqrt.f64 (+.f64 x x))
(fabs.f64 (+.f64 x x))
(log.f64 (pow.f64 (exp.f64 2) x))
(cbrt.f64 (+.f64 x x))
(expm1.f64 (log1p.f64 (+.f64 x x)))
(hypot.f64 x x)
(hypot.f64 (sqrt.f64 x) (sqrt.f64 x))
(exp.f64 (log.f64 (+.f64 x x)))
(log1p.f64 (expm1.f64 (+.f64 x x)))
(fma.f64 x x (*.f64 x x))
(fma.f64 1 x x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) x)
(fma.f64 (cbrt.f64 (*.f64 x x)) (cbrt.f64 x) x)

Outputs
(*.f64 (sqrt.f64 2) x)
-2
(*.f64 (sqrt.f64 2) x)
-2
(*.f64 (sqrt.f64 2) x)
-2
(*.f64 (sqrt.f64 2) x)
-2
(*.f64 (sqrt.f64 2) x)
-2
(*.f64 (sqrt.f64 2) x)
-2
(*.f64 (sqrt.f64 2) x)
-2
(*.f64 (sqrt.f64 2) x)
-2
(.f64 -1 (.f64 (sqrt.f64 2) x))
-2
(.f64 -1 (.f64 (sqrt.f64 2) x))
-2
(.f64 -1 (.f64 (sqrt.f64 2) x))
-2
(.f64 -1 (.f64 (sqrt.f64 2) x))
-2
(+.f64 x x)
-2
(+.f64 (+.f64 x x) (+.f64 x x))
-2
(+.f64 (.f64 x x) (.f64 x x))
-2
(+.f64 (.f64 (.f64 x x) 1) (.f64 (.f64 x x) 1))
-2
(-.f64 (+.f64 1 (+.f64 x x)) 1)
-2
(-.f64 (/.f64 (.f64 x x) 0) (/.f64 (.f64 x x) 0))
-2
(*.f64 x (+.f64 x x))
-2
(*.f64 x 2)
-2
(*.f64 (+.f64 x x) x)
-2
(*.f64 (+.f64 x x) (+.f64 x x))
-2
(*.f64 (+.f64 x x) 1)
-2
(*.f64 (+.f64 x x) (sqrt.f64 x))
(*.f64 -2 (sqrt.f64 x))
(*.f64 (+.f64 x x) (cbrt.f64 x))
(*.f64 -2 (cbrt.f64 x))
(.f64 (+.f64 x x) (.f64 x x))
-2
(*.f64 (+.f64 x x) (pow.f64 x 3))
-2
(*.f64 (+.f64 x x) (pow.f64 x 1/4))
(*.f64 -2 (pow.f64 x 1/4))
(*.f64 1 (+.f64 x x))
-2
(*.f64 (sqrt.f64 x) (+.f64 x x))
(*.f64 -2 (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 -2 (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 (cbrt.f64 x) (+.f64 x x))
(*.f64 -2 (cbrt.f64 x))
(.f64 (cbrt.f64 x) (+.f64 (cbrt.f64 (.f64 x x)) (cbrt.f64 (*.f64 x x))))
(.f64 -2 (.f64 (cbrt.f64 x) (cbrt.f64 -2)))
(.f64 (cbrt.f64 (.f64 x x)) (+.f64 x x))
(*.f64 -2 (cbrt.f64 -2))
(.f64 (cbrt.f64 (.f64 x x)) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))
(.f64 -2 (.f64 (cbrt.f64 x) (cbrt.f64 -2)))
(.f64 (.f64 x x) (+.f64 x x))
-2
(*.f64 2 x)
-2
(*.f64 2 (+.f64 x x))
-2
(.f64 2 (.f64 x x))
-2
(*.f64 0 (/.f64 1 0))
-2
(*.f64 (pow.f64 x 3) (+.f64 x x))
-2
(.f64 (.f64 2 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x 0)))
-2
(*.f64 (sqrt.f64 (sqrt.f64 x)) (+.f64 x x))
(*.f64 -2 (sqrt.f64 (sqrt.f64 x)))
(*.f64 (sqrt.f64 2) (sqrt.f64 x))
(*.f64 -2 (sqrt.f64 x))
(*.f64 (cbrt.f64 (sqrt.f64 x)) (+.f64 x x))
(*.f64 -2 (cbrt.f64 (sqrt.f64 x)))
(*.f64 (cbrt.f64 2) (cbrt.f64 x))
(*.f64 (cbrt.f64 x) (cbrt.f64 -2))
(.f64 4 (.f64 x x))
-2
(.f64 (.f64 (+.f64 x x) 2) x)
-2
(.f64 (.f64 (+.f64 x x) (cbrt.f64 (*.f64 x x))) (cbrt.f64 x))
(.f64 -2 (.f64 (cbrt.f64 x) (cbrt.f64 -2)))
(.f64 (.f64 2 (sqrt.f64 x)) (sqrt.f64 x))
(.f64 -2 (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 (.f64 2 (cbrt.f64 (*.f64 x x))) (cbrt.f64 x))
(.f64 -2 (.f64 (cbrt.f64 x) (cbrt.f64 -2)))
(*.f64 (pow.f64 x 1/4) (+.f64 x x))
(*.f64 -2 (pow.f64 x 1/4))
(*.f64 (pow.f64 (+.f64 x x) 1/8) (pow.f64 (+.f64 x x) 1/8))
-2
(*.f64 (pow.f64 1 1/2) (+.f64 x x))
-2
(*.f64 (pow.f64 1 1/4) (+.f64 x x))
-2
(*.f64 (pow.f64 2 1/2) (sqrt.f64 x))
(*.f64 -2 (sqrt.f64 x))
(/.f64 1 (+.f64 x x))
-2
(/.f64 1 (/.f64 (fma.f64 x x 0) (*.f64 2 (pow.f64 x 3))))
-2
(/.f64 0 0)
-2
(/.f64 (*.f64 2 (pow.f64 x 3)) (fma.f64 x x 0))
-2
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x 0)))
-2
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
-2
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 3))) (cbrt.f64 (fma.f64 x x 0)))
(/.f64 (cbrt.f64 -2) (cbrt.f64 -2))
(/.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)))
-2
(/.f64 (.f64 (+.f64 x x) (.f64 2 (pow.f64 x 3))) (fma.f64 x x 0))
-2
(/.f64 (.f64 x (.f64 2 (pow.f64 x 3))) (fma.f64 x x 0))
-2
(/.f64 (*.f64 0 (+.f64 x x)) 0)
-2
(/.f64 (.f64 (.f64 2 (pow.f64 x 3)) (+.f64 x x)) (fma.f64 x x 0))
-2
(/.f64 (*.f64 0 x) 0)
-2
(/.f64 (.f64 (.f64 2 (pow.f64 x 3)) x) (fma.f64 x x 0))
-2
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))) 0)
-2
(/.f64 (+.f64 (pow.f64 (.f64 x x) 3) (pow.f64 (.f64 x x) 3)) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (*.f64 x x)))))
-2
(/.f64 (.f64 0 (.f64 2 (pow.f64 x 3))) (*.f64 0 (fma.f64 x x 0)))
-2
(/.f64 (.f64 (.f64 2 (pow.f64 x 3)) 0) (*.f64 (fma.f64 x x 0) 0))
-2
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 3))) (neg.f64 (fma.f64 x x 0)))
-2
(sqrt.f64 (+.f64 x x))
-2
(fabs.f64 (+.f64 x x))
-2
(log.f64 (pow.f64 (exp.f64 2) x))
(*.f64 x (log.f64 -2))
(cbrt.f64 (+.f64 x x))
(cbrt.f64 -2)
(expm1.f64 (log1p.f64 (+.f64 x x)))
-2
(hypot.f64 x x)
(hypot.f64 (sqrt.f64 x) (sqrt.f64 x))
(exp.f64 (log.f64 (+.f64 x x)))
-2
(log1p.f64 (expm1.f64 (+.f64 x x)))
-2
(fma.f64 x x (*.f64 x x))
-2
(fma.f64 1 x x)
(+.f64 -2 x)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) x)
(fma.f64 (cbrt.f64 (*.f64 x x)) (cbrt.f64 x) x)
(fma.f64 (cbrt.f64 -2) (cbrt.f64 x) x)

eval17.0ms (0.5%)

Compiler: Compiled 800 to 425 computations (46.9% saved)

prune18.0ms (0.5%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	104	8	112
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	104	12	116

Error

Counts

116 → 12

Alt Table

Click to see full alt table

Status	Error	Program
✓	41.29%	(pow.f64 (*.f64 x (+.f64 x x)) 1/2)
✓	0.02%	(hypot.f64 x x)
▶	97.18%	(/.f64 1 (+.f64 x x))
	92.78%	(-.f64 (+.f64 1 (+.f64 x x)) 1)
▶	89.3%	(+.f64 x x)
▶	94.67%	(+.f64 -2 x)
	94.36%	(*.f64 (+.f64 x x) (+.f64 x x))
▶	94.4%	(*.f64 (+.f64 x x) x)
✓	46.43%	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	94.36%	(.f64 4 (.f64 x x))
✓	41.32%	(sqrt.f64 (.f64 2 (.f64 x x)))
	98.31%	-2

Compiler

Compiled 111 to 69 computations (37.8% saved)

localize2.0ms (0.1%)

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

localize2.0ms (0.1%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.02%	(.f64 4 (.f64 x x))

Compiler

Compiled 11 to 5 computations (54.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(.f64 4 (.f64 x x))
0.0ms	x	@	inf	(.f64 4 (.f64 x x))
0.0ms	x	@	-inf	(.f64 4 (.f64 x x))

rewrite55.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1052×	`add-sqr-sqrt`
1038×	`*-un-lft-identity`
986×	`pow1`
968×	`add-cube-cbrt`
960×	`add-cbrt-cube`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	122	13
2	1389	13

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

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

Outputs

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

simplify239.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

1554×	`distribute-rgt-in`
1526×	`distribute-lft-in`
1288×	`log-prod`
850×	`associate-r`
768×	`associate-+r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	299
1	91	299
2	343	299
3	2105	299

Stop Event

1×	node limit

Counts

23 → 14

Calls

Call 1

Inputs
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(-.f64 (+.f64 1 (.f64 4 (.f64 x x))) 1)
(pow.f64 (.f64 4 (.f64 x x)) 1)
(pow.f64 (*.f64 x 2) 2)
(pow.f64 (cbrt.f64 (.f64 4 (.f64 x x))) 3)
(pow.f64 (pow.f64 (.f64 4 (.f64 x x)) 3) 1/3)
(sqrt.f64 (*.f64 16 (pow.f64 x 4)))
(log.f64 (pow.f64 (exp.f64 4) (*.f64 x x)))
(cbrt.f64 (pow.f64 (.f64 4 (.f64 x x)) 3))
(expm1.f64 (log1p.f64 (.f64 4 (.f64 x x))))
(exp.f64 (log.f64 (.f64 4 (.f64 x x))))
(log1p.f64 (expm1.f64 (.f64 4 (.f64 x x))))

Outputs
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(-.f64 (+.f64 1 (.f64 4 (.f64 x x))) 1)
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(pow.f64 (.f64 4 (.f64 x x)) 1)
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(pow.f64 (*.f64 x 2) 2)
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(pow.f64 (cbrt.f64 (.f64 4 (.f64 x x))) 3)
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(pow.f64 (pow.f64 (.f64 4 (.f64 x x)) 3) 1/3)
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(sqrt.f64 (*.f64 16 (pow.f64 x 4)))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(log.f64 (pow.f64 (exp.f64 4) (*.f64 x x)))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(cbrt.f64 (pow.f64 (.f64 4 (.f64 x x)) 3))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(expm1.f64 (log1p.f64 (.f64 4 (.f64 x x))))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(exp.f64 (log.f64 (.f64 4 (.f64 x x))))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(log1p.f64 (expm1.f64 (.f64 4 (.f64 x x))))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))

localize4.0ms (0.1%)

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

localize4.0ms (0.1%)

Compiler: Compiled 11 to 5 computations (54.5% saved)

eval2.0ms (0.1%)

Compiler: Compiled 96 to 62 computations (35.4% saved)

prune5.0ms (0.1%)

Pruning

12 alts after pruning (4 fresh and 8 done)

	Pruned	Kept	Total
New	12	2	14
Fresh	1	2	3
Picked	0	1	1
Done	1	7	8
Total	14	12	26

Error

Counts

26 → 12

Alt Table

Click to see full alt table

Status	Error	Program
✓	41.29%	(pow.f64 (*.f64 x (+.f64 x x)) 1/2)
✓	0.02%	(hypot.f64 x x)
✓	97.18%	(/.f64 1 (+.f64 x x))
▶	92.78%	(-.f64 (+.f64 1 (+.f64 x x)) 1)
▶	95.05%	(-.f64 (+.f64 1 (.f64 4 (.f64 x x))) 1)
✓	89.3%	(+.f64 x x)
✓	94.67%	(+.f64 -2 x)
✓	94.4%	(*.f64 (+.f64 x x) x)
✓	46.43%	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	94.36%	(.f64 x (.f64 4 x))
✓	41.32%	(sqrt.f64 (.f64 2 (.f64 x x)))
	98.31%	-2

Compiler

Compiled 71 to 49 computations (31% saved)

localize230.0ms (6.3%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.01%	(+.f64 1 (.f64 4 (.f64 x x)))
	0.02%	(.f64 4 (.f64 x x))
✓	1.82%	(-.f64 (+.f64 1 (.f64 4 (.f64 x x))) 1)

Compiler

Compiled 28 to 16 computations (42.9% saved)

series1.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(-.f64 (+.f64 1 (.f64 4 (.f64 x x))) 1)
0.0ms	x	@	0	(-.f64 (+.f64 1 (.f64 4 (.f64 x x))) 1)
0.0ms	x	@	inf	(+.f64 1 (.f64 4 (.f64 x x)))
0.0ms	x	@	0	(+.f64 1 (.f64 4 (.f64 x x)))
0.0ms	x	@	-inf	(-.f64 (+.f64 1 (.f64 4 (.f64 x x))) 1)

rewrite71.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1832×	`add-sqr-sqrt`
1810×	`*-un-lft-identity`
1706×	`add-cube-cbrt`
1696×	`add-cbrt-cube`
188×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	44
1	198	28
2	2617	28

Stop Event

1×	node limit

Counts

2 → 87

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (.f64 4 (.f64 x x))) 1)
(+.f64 1 (.f64 4 (.f64 x x)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (fma.f64 4 (*.f64 x x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (fma.f64 4 (*.f64 x x) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (*.f64 x 2) 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 4 (*.f64 x x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 4 (*.f64 x x) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (fma.f64 4 (*.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 x 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 4 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x x) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x 2) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 2) (*.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 x 4)) (*.f64 (cbrt.f64 (*.f64 x x)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 x 2) 2)) (cbrt.f64 (*.f64 (pow.f64 x 4) 16)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 16)) (cbrt.f64 (pow.f64 (*.f64 x 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 4 x) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 2) -1) (/.f64 1 (+.f64 (pow.f64 (*.f64 x 2) 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 2) (+.f64 (pow.f64 (*.f64 x 2) 2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 4 (cbrt.f64 (pow.f64 x 4))) (cbrt.f64 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 4 x) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 4 x) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 4 x) (cbrt.f64 (*.f64 x x))) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (hypot.f64 1 (*.f64 x 2)) 1) (-.f64 (hypot.f64 1 (*.f64 x 2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (*.f64 x 2) 2) 2) (+.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 2) (+.f64 (pow.f64 (*.f64 x 2) 2) 2)) (+.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 2) -1) (+.f64 (pow.f64 (*.f64 x 2) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 2) -1) (-.f64 (fma.f64 4 (*.f64 x x) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 2) (+.f64 (pow.f64 (*.f64 x 2) 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 2) (-.f64 1 (*.f64 (fma.f64 4 (*.f64 x x) 1) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (fma.f64 4 (*.f64 x x) -1) (fma.f64 4 (*.f64 x x) -1))) (-.f64 1 (fma.f64 4 (*.f64 x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (fma.f64 4 (*.f64 x x) -1) 3)) (+.f64 1 (-.f64 (*.f64 (fma.f64 4 (*.f64 x x) -1) (fma.f64 4 (*.f64 x x) -1)) (fma.f64 4 (*.f64 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 2) -1)) (neg.f64 (+.f64 (pow.f64 (*.f64 x 2) 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 2) (+.f64 (pow.f64 (*.f64 x 2) 2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x 2) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (*.f64 x 2) 2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 (*.f64 x x) 3) 64) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 x 4) 16))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 x 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 x 2) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 x x) 3) 64))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 x 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (pow.f64 (*.f64 x 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 x 2) 2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 x 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 4 (*.f64 x x) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 1 (*.f64 x 2)) (hypot.f64 1 (*.f64 x 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (*.f64 x x) 1)) 2) (cbrt.f64 (fma.f64 4 (*.f64 x x) 1)) -1)))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (pow.f64 (*.f64 x 2) 2) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (+.f64 1 (*.f64 -4 (*.f64 x x)))) (/.f64 (*.f64 (pow.f64 x 4) 16) (+.f64 1 (*.f64 -4 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 4 (*.f64 x x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 4 (*.f64 x x) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (*.f64 x 2)) (hypot.f64 1 (*.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 1 (*.f64 x 2)) (*.f64 (hypot.f64 1 (*.f64 x 2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 4 (*.f64 x x) 1)) (pow.f64 (cbrt.f64 (fma.f64 4 (*.f64 x x) 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (*.f64 x x) 1)) 2) (cbrt.f64 (fma.f64 4 (*.f64 x x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (*.f64 x x) 1)) 2) (*.f64 (cbrt.f64 (fma.f64 4 (*.f64 x x) 1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (*.f64 (pow.f64 x 4) 16)) (/.f64 1 (+.f64 1 (*.f64 -4 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (*.f64 (pow.f64 (*.f64 x x) 3) 64)) (/.f64 1 (+.f64 1 (+.f64 (*.f64 (pow.f64 x 4) 16) (*.f64 -4 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (*.f64 -4 (*.f64 x x))) (-.f64 1 (*.f64 (pow.f64 x 4) 16))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (+.f64 (*.f64 (pow.f64 x 4) 16) (*.f64 -4 (*.f64 x x)))) (+.f64 1 (*.f64 (pow.f64 (*.f64 x x) 3) 64))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (*.f64 (pow.f64 x 4) 16)) (+.f64 1 (*.f64 -4 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (*.f64 (pow.f64 (*.f64 x x) 3) 64)) (+.f64 1 (+.f64 (*.f64 (pow.f64 x 4) 16) (*.f64 -4 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (*.f64 (pow.f64 (*.f64 x x) 3) 64)) (+.f64 (*.f64 (pow.f64 x 4) 16) (+.f64 1 (*.f64 -4 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1 (*.f64 (pow.f64 x 4) 16)) 1) (+.f64 1 (*.f64 -4 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 1 (*.f64 (pow.f64 (*.f64 x x) 3) 64)) 1) (+.f64 1 (+.f64 (*.f64 (pow.f64 x 4) 16) (*.f64 -4 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (pow.f64 x 4) 16) 1) (fma.f64 4 (*.f64 x x) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (*.f64 (pow.f64 x 4) 16))) (neg.f64 (+.f64 1 (*.f64 -4 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (*.f64 (pow.f64 (*.f64 x x) 3) 64))) (neg.f64 (+.f64 1 (+.f64 (*.f64 (pow.f64 x 4) 16) (*.f64 -4 (*.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 4 (*.f64 x x) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 1 (*.f64 x 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 4 (*.f64 x x) 1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 4 (*.f64 x x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 4 (*.f64 x x) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 4 (*.f64 x x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (pow.f64 (*.f64 x 2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log1p.f64 (pow.f64 (*.f64 x 2) 2)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 4 (*.f64 x x) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 (*.f64 x 2) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 4 (*.f64 x x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 4 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x 2) (*.f64 x 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (*.f64 (pow.f64 x 4) 16)) (cbrt.f64 (pow.f64 (*.f64 x 2) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 4 x) x 1)))))

simplify96.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1344×	`fma-def`
1120×	`associate-/r/`
1054×	`associate-/l/`
984×	`associate--l-`
622×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	2889
1	420	2623
2	1555	2601
3	6410	2601

Stop Event

1×	node limit

Counts

111 → 118

Calls

Call 1

Inputs
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
(*.f64 4 (pow.f64 x 2))
1
(+.f64 (*.f64 4 (pow.f64 x 2)) 1)
(+.f64 (*.f64 4 (pow.f64 x 2)) 1)
(+.f64 (*.f64 4 (pow.f64 x 2)) 1)
(*.f64 4 (pow.f64 x 2))
(+.f64 1 (*.f64 4 (pow.f64 x 2)))
(+.f64 1 (*.f64 4 (pow.f64 x 2)))
(+.f64 1 (*.f64 4 (pow.f64 x 2)))
(*.f64 4 (pow.f64 x 2))
(+.f64 1 (*.f64 4 (pow.f64 x 2)))
(+.f64 1 (*.f64 4 (pow.f64 x 2)))
(+.f64 1 (*.f64 4 (pow.f64 x 2)))
(+.f64 1 (fma.f64 4 (*.f64 x x) -1))
(+.f64 1 (.f64 (fma.f64 4 (.f64 x x) -1) 1))
(+.f64 (pow.f64 (*.f64 x 2) 2) 0)
(+.f64 (fma.f64 4 (*.f64 x x) 1) -1)
(+.f64 (fma.f64 4 (*.f64 x x) -1) 1)
(+.f64 -1 (fma.f64 4 (*.f64 x x) 1))
(.f64 1 (pow.f64 (.f64 x 2) 2))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(.f64 (.f64 x x) 4)
(.f64 (pow.f64 (.f64 x 2) 2) 1)
(.f64 (.f64 x 2) (*.f64 x 2))
(.f64 (cbrt.f64 (pow.f64 x 4)) (.f64 (cbrt.f64 (*.f64 x x)) 4))
(.f64 (cbrt.f64 (pow.f64 (.f64 x 2) 2)) (cbrt.f64 (*.f64 (pow.f64 x 4) 16)))
(.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 16)) (cbrt.f64 (pow.f64 (*.f64 x 2) 2)))
(.f64 (.f64 4 x) x)
(.f64 (+.f64 (pow.f64 (fma.f64 4 (.f64 x x) 1) 2) -1) (/.f64 1 (+.f64 (pow.f64 (*.f64 x 2) 2) 2)))
(.f64 (+.f64 (pow.f64 (fma.f64 4 (.f64 x x) 1) 3) -1) (/.f64 1 (+.f64 (pow.f64 (fma.f64 4 (.f64 x x) 1) 2) (+.f64 (pow.f64 (.f64 x 2) 2) 2))))
(.f64 (.f64 4 (cbrt.f64 (pow.f64 x 4))) (cbrt.f64 (*.f64 x x)))
(.f64 (.f64 (*.f64 4 x) 1) x)
(.f64 (.f64 (*.f64 4 x) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 (.f64 4 x) (cbrt.f64 (.f64 x x))) (cbrt.f64 x))
(.f64 (+.f64 (hypot.f64 1 (.f64 x 2)) 1) (-.f64 (hypot.f64 1 (*.f64 x 2)) 1))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (.f64 x 2) 2) 2) (+.f64 (pow.f64 (fma.f64 4 (.f64 x x) 1) 2) -1)))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (fma.f64 4 (.f64 x x) 1) 2) (+.f64 (pow.f64 (.f64 x 2) 2) 2)) (+.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 3) -1)))
(/.f64 (+.f64 (pow.f64 (fma.f64 4 (.f64 x x) 1) 2) -1) (+.f64 (pow.f64 (.f64 x 2) 2) 2))
(/.f64 (+.f64 (pow.f64 (fma.f64 4 (.f64 x x) 1) 2) -1) (-.f64 (fma.f64 4 (.f64 x x) 1) -1))
(/.f64 (+.f64 (pow.f64 (fma.f64 4 (.f64 x x) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 4 (.f64 x x) 1) 2) (+.f64 (pow.f64 (*.f64 x 2) 2) 2)))
(/.f64 (+.f64 (pow.f64 (fma.f64 4 (.f64 x x) 1) 3) -1) (+.f64 (pow.f64 (fma.f64 4 (.f64 x x) 1) 2) (-.f64 1 (.f64 (fma.f64 4 (.f64 x x) 1) -1))))
(/.f64 (-.f64 1 (.f64 (fma.f64 4 (.f64 x x) -1) (fma.f64 4 (.f64 x x) -1))) (-.f64 1 (fma.f64 4 (.f64 x x) -1)))
(/.f64 (+.f64 1 (pow.f64 (fma.f64 4 (.f64 x x) -1) 3)) (+.f64 1 (-.f64 (.f64 (fma.f64 4 (.f64 x x) -1) (fma.f64 4 (.f64 x x) -1)) (fma.f64 4 (*.f64 x x) -1))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 4 (.f64 x x) 1) 2) -1)) (neg.f64 (+.f64 (pow.f64 (.f64 x 2) 2) 2)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 4 (.f64 x x) 1) 3) -1)) (neg.f64 (+.f64 (pow.f64 (fma.f64 4 (.f64 x x) 1) 2) (+.f64 (pow.f64 (*.f64 x 2) 2) 2))))
(pow.f64 (pow.f64 (*.f64 x 2) 2) 1)
(pow.f64 (*.f64 x 2) 2)
(pow.f64 (cbrt.f64 (pow.f64 (*.f64 x 2) 2)) 3)
(pow.f64 (.f64 (pow.f64 (.f64 x x) 3) 64) 1/3)
(sqrt.f64 (*.f64 (pow.f64 x 4) 16))
(log.f64 (exp.f64 (pow.f64 (*.f64 x 2) 2)))
(log.f64 (+.f64 1 (expm1.f64 (pow.f64 (*.f64 x 2) 2))))
(cbrt.f64 (.f64 (pow.f64 (.f64 x x) 3) 64))
(expm1.f64 (log1p.f64 (pow.f64 (*.f64 x 2) 2)))
(exp.f64 (log.f64 (pow.f64 (*.f64 x 2) 2)))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 x 2) 2)) 1))
(log1p.f64 (expm1.f64 (pow.f64 (*.f64 x 2) 2)))
(fma.f64 1 (fma.f64 4 (*.f64 x x) 1) -1)
(fma.f64 (hypot.f64 1 (.f64 x 2)) (hypot.f64 1 (.f64 x 2)) -1)
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (.f64 x x) 1)) 2) (cbrt.f64 (fma.f64 4 (.f64 x x) 1)) -1)
(-.f64 (+.f64 (pow.f64 (*.f64 x 2) 2) 2) 1)
(-.f64 (/.f64 1 (+.f64 1 (.f64 -4 (.f64 x x)))) (/.f64 (.f64 (pow.f64 x 4) 16) (+.f64 1 (.f64 -4 (*.f64 x x)))))
(.f64 1 (fma.f64 4 (.f64 x x) 1))
(.f64 (fma.f64 4 (.f64 x x) 1) 1)
(.f64 (hypot.f64 1 (.f64 x 2)) (hypot.f64 1 (*.f64 x 2)))
(.f64 (hypot.f64 1 (.f64 x 2)) (.f64 (hypot.f64 1 (.f64 x 2)) 1))
(.f64 (cbrt.f64 (fma.f64 4 (.f64 x x) 1)) (pow.f64 (cbrt.f64 (fma.f64 4 (*.f64 x x) 1)) 2))
(.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (.f64 x x) 1)) 2) (cbrt.f64 (fma.f64 4 (*.f64 x x) 1)))
(.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (.f64 x x) 1)) 2) (.f64 (cbrt.f64 (fma.f64 4 (.f64 x x) 1)) 1))
(.f64 (-.f64 1 (.f64 (pow.f64 x 4) 16)) (/.f64 1 (+.f64 1 (.f64 -4 (.f64 x x)))))
(.f64 (+.f64 1 (.f64 (pow.f64 (.f64 x x) 3) 64)) (/.f64 1 (+.f64 1 (+.f64 (.f64 (pow.f64 x 4) 16) (.f64 -4 (.f64 x x))))))
(/.f64 1 (/.f64 (+.f64 1 (.f64 -4 (.f64 x x))) (-.f64 1 (*.f64 (pow.f64 x 4) 16))))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (.f64 (pow.f64 x 4) 16) (.f64 -4 (.f64 x x)))) (+.f64 1 (.f64 (pow.f64 (*.f64 x x) 3) 64))))
(/.f64 (-.f64 1 (.f64 (pow.f64 x 4) 16)) (+.f64 1 (.f64 -4 (*.f64 x x))))
(/.f64 (+.f64 1 (.f64 (pow.f64 (.f64 x x) 3) 64)) (+.f64 1 (+.f64 (.f64 (pow.f64 x 4) 16) (.f64 -4 (*.f64 x x)))))
(/.f64 (+.f64 1 (.f64 (pow.f64 (.f64 x x) 3) 64)) (+.f64 (.f64 (pow.f64 x 4) 16) (+.f64 1 (.f64 -4 (*.f64 x x)))))
(/.f64 (.f64 (-.f64 1 (.f64 (pow.f64 x 4) 16)) 1) (+.f64 1 (.f64 -4 (.f64 x x))))
(/.f64 (.f64 (+.f64 1 (.f64 (pow.f64 (.f64 x x) 3) 64)) 1) (+.f64 1 (+.f64 (.f64 (pow.f64 x 4) 16) (.f64 -4 (.f64 x x)))))
(/.f64 (-.f64 (.f64 (pow.f64 x 4) 16) 1) (fma.f64 4 (.f64 x x) -1))
(/.f64 (neg.f64 (-.f64 1 (.f64 (pow.f64 x 4) 16))) (neg.f64 (+.f64 1 (.f64 -4 (*.f64 x x)))))
(/.f64 (neg.f64 (+.f64 1 (.f64 (pow.f64 (.f64 x x) 3) 64))) (neg.f64 (+.f64 1 (+.f64 (.f64 (pow.f64 x 4) 16) (.f64 -4 (*.f64 x x))))))
(pow.f64 (fma.f64 4 (*.f64 x x) 1) 1)
(pow.f64 (hypot.f64 1 (*.f64 x 2)) 2)
(pow.f64 (cbrt.f64 (fma.f64 4 (*.f64 x x) 1)) 3)
(pow.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 3) 1/3)
(sqrt.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 2))
(log.f64 (exp.f64 (fma.f64 4 (*.f64 x x) 1)))
(log.f64 (+.f64 1 (expm1.f64 (fma.f64 4 (*.f64 x x) 1))))
(cbrt.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 3))
(expm1.f64 (log1p.f64 (fma.f64 4 (*.f64 x x) 1)))
(exp.f64 (log1p.f64 (pow.f64 (*.f64 x 2) 2)))
(exp.f64 (.f64 (log1p.f64 (pow.f64 (.f64 x 2) 2)) 1))
(log1p.f64 (expm1.f64 (fma.f64 4 (*.f64 x x) 1)))
(fma.f64 1 (pow.f64 (*.f64 x 2) 2) 1)
(fma.f64 4 (*.f64 x x) 1)
(fma.f64 (*.f64 x x) 4 1)
(fma.f64 (.f64 x 2) (.f64 x 2) 1)
(fma.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 16)) (cbrt.f64 (pow.f64 (.f64 x 2) 2)) 1)
(fma.f64 (*.f64 4 x) x 1)

Outputs
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
1
(+.f64 (*.f64 4 (pow.f64 x 2)) 1)
(fma.f64 4 (*.f64 x x) 1)
(+.f64 (*.f64 4 (pow.f64 x 2)) 1)
(fma.f64 4 (*.f64 x x) 1)
(+.f64 (*.f64 4 (pow.f64 x 2)) 1)
(fma.f64 4 (*.f64 x x) 1)
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(+.f64 1 (*.f64 4 (pow.f64 x 2)))
(fma.f64 4 (*.f64 x x) 1)
(+.f64 1 (*.f64 4 (pow.f64 x 2)))
(fma.f64 4 (*.f64 x x) 1)
(+.f64 1 (*.f64 4 (pow.f64 x 2)))
(fma.f64 4 (*.f64 x x) 1)
(*.f64 4 (pow.f64 x 2))
(.f64 4 (.f64 x x))
(+.f64 1 (*.f64 4 (pow.f64 x 2)))
(fma.f64 4 (*.f64 x x) 1)
(+.f64 1 (*.f64 4 (pow.f64 x 2)))
(fma.f64 4 (*.f64 x x) 1)
(+.f64 1 (*.f64 4 (pow.f64 x 2)))
(fma.f64 4 (*.f64 x x) 1)
(+.f64 1 (fma.f64 4 (*.f64 x x) -1))
(.f64 4 (.f64 x x))
(+.f64 1 (.f64 (fma.f64 4 (.f64 x x) -1) 1))
(.f64 4 (.f64 x x))
(+.f64 (pow.f64 (*.f64 x 2) 2) 0)
(.f64 4 (.f64 x x))
(+.f64 (fma.f64 4 (*.f64 x x) 1) -1)
(.f64 4 (.f64 x x))
(+.f64 (fma.f64 4 (*.f64 x x) -1) 1)
(.f64 4 (.f64 x x))
(+.f64 -1 (fma.f64 4 (*.f64 x x) 1))
(.f64 4 (.f64 x x))
(.f64 1 (pow.f64 (.f64 x 2) 2))
(.f64 4 (.f64 x x))
(.f64 4 (.f64 x x))
(.f64 x (.f64 4 x))
(.f64 4 (.f64 x x))
(.f64 (.f64 x x) 4)
(.f64 4 (.f64 x x))
(.f64 (pow.f64 (.f64 x 2) 2) 1)
(.f64 4 (.f64 x x))
(.f64 (.f64 x 2) (*.f64 x 2))
(.f64 4 (.f64 x x))
(.f64 (cbrt.f64 (pow.f64 x 4)) (.f64 (cbrt.f64 (*.f64 x x)) 4))
(.f64 (cbrt.f64 (pow.f64 x 4)) (.f64 4 (cbrt.f64 (*.f64 x x))))
(.f64 4 (.f64 (cbrt.f64 (pow.f64 x 4)) (cbrt.f64 (*.f64 x x))))
(.f64 (cbrt.f64 (pow.f64 (.f64 x 2) 2)) (cbrt.f64 (*.f64 (pow.f64 x 4) 16)))
(.f64 (cbrt.f64 (.f64 4 (.f64 x x))) (cbrt.f64 (.f64 (pow.f64 x 4) 16)))
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(pow.f64 (fma.f64 4 (*.f64 x x) 1) 1)
(fma.f64 4 (*.f64 x x) 1)
(pow.f64 (hypot.f64 1 (*.f64 x 2)) 2)
(fma.f64 4 (*.f64 x x) 1)
(pow.f64 (cbrt.f64 (fma.f64 4 (*.f64 x x) 1)) 3)
(fma.f64 4 (*.f64 x x) 1)
(pow.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 3) 1/3)
(fma.f64 4 (*.f64 x x) 1)
(sqrt.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 2))
(fma.f64 4 (*.f64 x x) 1)
(log.f64 (exp.f64 (fma.f64 4 (*.f64 x x) 1)))
(fma.f64 4 (*.f64 x x) 1)
(log.f64 (+.f64 1 (expm1.f64 (fma.f64 4 (*.f64 x x) 1))))
(fma.f64 4 (*.f64 x x) 1)
(cbrt.f64 (pow.f64 (fma.f64 4 (*.f64 x x) 1) 3))
(fma.f64 4 (*.f64 x x) 1)
(expm1.f64 (log1p.f64 (fma.f64 4 (*.f64 x x) 1)))
(fma.f64 4 (*.f64 x x) 1)
(exp.f64 (log1p.f64 (pow.f64 (*.f64 x 2) 2)))
(exp.f64 (log1p.f64 (.f64 4 (.f64 x x))))
(exp.f64 (.f64 (log1p.f64 (pow.f64 (.f64 x 2) 2)) 1))
(exp.f64 (log1p.f64 (.f64 4 (.f64 x x))))
(log1p.f64 (expm1.f64 (fma.f64 4 (*.f64 x x) 1)))
(fma.f64 4 (*.f64 x x) 1)
(fma.f64 1 (pow.f64 (*.f64 x 2) 2) 1)
(fma.f64 4 (*.f64 x x) 1)
(fma.f64 4 (*.f64 x x) 1)
(fma.f64 (*.f64 x x) 4 1)
(fma.f64 4 (*.f64 x x) 1)
(fma.f64 (.f64 x 2) (.f64 x 2) 1)
(fma.f64 4 (*.f64 x x) 1)
(fma.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 16)) (cbrt.f64 (pow.f64 (.f64 x 2) 2)) 1)
(fma.f64 (cbrt.f64 (.f64 (pow.f64 x 4) 16)) (cbrt.f64 (.f64 4 (*.f64 x x))) 1)
(fma.f64 (cbrt.f64 (.f64 4 (.f64 x x))) (cbrt.f64 (*.f64 (pow.f64 x 4) 16)) 1)
(fma.f64 (*.f64 4 x) x 1)
(fma.f64 4 (*.f64 x x) 1)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.45%	(-.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
0.0ms	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)

rewrite132.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1526×	`add-sqr-sqrt`
1506×	`*-un-lft-identity`
1422×	`add-cube-cbrt`
1414×	`add-cbrt-cube`
168×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	165	7
2	2559	7

Stop Event

1×	node limit

Counts

1 → 96

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

simplify58.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

78×	`*-commutative`
46×	`distribute-lft-in`
44×	`+-commutative`
40×	`distribute-rgt-in`
30×	`associate-/l*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	222	410
1	804	410

Stop Event

1×

unsound

Counts

108 → 108

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)
(+.f64 1 (fma.f64 2 x -1))
(+.f64 1 (*.f64 (fma.f64 2 x -1) 1))
(+.f64 x x)
(+.f64 (+.f64 x x) 0)
(+.f64 (+.f64 x x) (+.f64 (+.f64 x x) (*.f64 -2 x)))
(+.f64 (+.f64 x x) (*.f64 (fma.f64 2 x -1) (+.f64 x x)))
(+.f64 (fma.f64 2 x 1) -1)
(+.f64 (+.f64 1 x) (+.f64 x -1))
(+.f64 (+.f64 1 x) (-.f64 x 1))
(+.f64 (fma.f64 2 x -1) 1)
(+.f64 -1 (fma.f64 2 x 1))
(+.f64 (.f64 x (+.f64 x x)) (.f64 x (+.f64 x x)))
(+.f64 (.f64 (+.f64 x x) x) (.f64 (+.f64 x x) x))
(+.f64 (.f64 (fma.f64 2 x 1) (+.f64 x x)) (.f64 -1 (+.f64 x x)))
(+.f64 (.f64 (+.f64 x x) (fma.f64 2 x 1)) (.f64 (+.f64 x x) -1))
(*.f64 1 (+.f64 x x))
(*.f64 x 2)
(*.f64 (+.f64 x x) 1)
(*.f64 (+.f64 x x) (+.f64 x x))
(*.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))
(*.f64 2 x)
(.f64 2 (.f64 x (+.f64 x x)))
(*.f64 0 (/.f64 1 0))
(*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (/.f64 1 (+.f64 (+.f64 x x) 2)))
(.f64 (.f64 2 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x 0)))
(*.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))))
(*.f64 (sqrt.f64 2) (sqrt.f64 x))
(*.f64 (cbrt.f64 2) (cbrt.f64 x))
(.f64 4 (.f64 x x))
(*.f64 8 (pow.f64 x 3))
(.f64 (.f64 (+.f64 x x) 2) x)
(.f64 (.f64 2 (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(*.f64 (+.f64 (hypot.f64 1 (+.f64 x x)) 1) (-.f64 (hypot.f64 1 (+.f64 x x)) 1))
(*.f64 (pow.f64 (+.f64 x x) 3/2) (pow.f64 (+.f64 x x) 3/2))
(/.f64 1 (+.f64 x x))
(/.f64 1 (/.f64 (fma.f64 x x 0) (*.f64 2 (pow.f64 x 3))))
(/.f64 1 (/.f64 (+.f64 (+.f64 x x) 2) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)))
(/.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)))
(/.f64 0 0)
(/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 (+.f64 x x) 2))
(/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (-.f64 (fma.f64 2 x 1) -1))
(/.f64 (*.f64 2 (pow.f64 x 3)) (fma.f64 x x 0))
(/.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)))
(/.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))))
(/.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))))
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (sqrt.f64 (+.f64 (+.f64 x x) 2)))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x 0)))
(/.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))))
(/.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (cbrt.f64 (+.f64 (+.f64 x x) 2)))
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 3))) (cbrt.f64 (fma.f64 x x 0)))
(/.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))))
(/.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)))
(/.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)))
(/.f64 (*.f64 (+.f64 x x) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (+.f64 (+.f64 x x) 2))
(/.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)))
(/.f64 (.f64 (+.f64 x x) (.f64 2 (pow.f64 x 3))) (fma.f64 x x 0))
(/.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 x x)) (+.f64 (+.f64 x x) 2))
(/.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)))
(/.f64 (*.f64 0 (+.f64 x x)) 0)
(/.f64 (.f64 (.f64 2 (pow.f64 x 3)) (+.f64 x x)) (fma.f64 x x 0))
(/.f64 (-.f64 1 (*.f64 (fma.f64 2 x -1) (fma.f64 2 x -1))) (-.f64 1 (fma.f64 2 x -1)))
(/.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))))
(/.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))))
(/.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)))
(/.f64 (.f64 0 (.f64 2 (pow.f64 x 3))) (*.f64 0 (fma.f64 x x 0)))
(/.f64 (.f64 (.f64 2 (pow.f64 x 3)) 0) (*.f64 (fma.f64 x x 0) 0))
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 3))) (neg.f64 (fma.f64 x x 0)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (neg.f64 (+.f64 (+.f64 x x) 2)))
(/.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))))
(/.f64 (pow.f64 (*.f64 2 (pow.f64 x 3)) 3) (pow.f64 (fma.f64 x x 0) 3))
(pow.f64 (+.f64 x x) 1)
(pow.f64 (+.f64 x x) 2)
(pow.f64 (+.f64 x x) 3)
(pow.f64 (+.f64 x x) 1/2)
(pow.f64 (+.f64 x x) 1/3)
(sqrt.f64 (+.f64 x x))
(fabs.f64 (+.f64 x x))
(log.f64 (pow.f64 (exp.f64 2) x))
(log.f64 (+.f64 1 (expm1.f64 (+.f64 x x))))
(cbrt.f64 (+.f64 x x))
(expm1.f64 (log1p.f64 (+.f64 x x)))
(hypot.f64 (sqrt.f64 x) (sqrt.f64 x))
(exp.f64 (log.f64 (+.f64 x x)))
(exp.f64 (*.f64 (log.f64 (+.f64 x x)) 1))
(exp.f64 (*.f64 (log.f64 (+.f64 x x)) 3))
(log1p.f64 (expm1.f64 (+.f64 x x)))
(fma.f64 1 x x)
(fma.f64 1 (fma.f64 2 x 1) -1)
(fma.f64 (hypot.f64 1 (+.f64 x x)) (hypot.f64 1 (+.f64 x x)) -1)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) x)
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 2 x 1)) 2) (cbrt.f64 (fma.f64 2 x 1)) -1)
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) x)

Outputs
(*.f64 2 x)
-3
(*.f64 2 x)
-3
(*.f64 2 x)
-3
(*.f64 2 x)
-3
(*.f64 2 x)
-3
(*.f64 2 x)
-3
(*.f64 2 x)
-3
(*.f64 2 x)
-3
(*.f64 2 x)
-3
(*.f64 2 x)
-3
(*.f64 2 x)
-3
(*.f64 2 x)
-3
(+.f64 1 (fma.f64 2 x -1))
-3
(+.f64 1 (*.f64 (fma.f64 2 x -1) 1))
-3
(+.f64 x x)
-3
(+.f64 (+.f64 x x) 0)
-3
(+.f64 (+.f64 x x) (+.f64 (+.f64 x x) (*.f64 -2 x)))
-3
(+.f64 (+.f64 x x) (*.f64 (fma.f64 2 x -1) (+.f64 x x)))
-3
(+.f64 (fma.f64 2 x 1) -1)
-3
(+.f64 (+.f64 1 x) (+.f64 x -1))
-3
(+.f64 (+.f64 1 x) (-.f64 x 1))
-3
(+.f64 (fma.f64 2 x -1) 1)
-3
(+.f64 -1 (fma.f64 2 x 1))
-3
(+.f64 (.f64 x (+.f64 x x)) (.f64 x (+.f64 x x)))
-3
(+.f64 (.f64 (+.f64 x x) x) (.f64 (+.f64 x x) x))
-3
(+.f64 (.f64 (fma.f64 2 x 1) (+.f64 x x)) (.f64 -1 (+.f64 x x)))
-3
(+.f64 (.f64 (+.f64 x x) (fma.f64 2 x 1)) (.f64 (+.f64 x x) -1))
-3
(*.f64 1 (+.f64 x x))
-3
(*.f64 x 2)
-3
(*.f64 (+.f64 x x) 1)
-3
(*.f64 (+.f64 x x) (+.f64 x x))
-3
(*.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 -3 (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(*.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(.f64 -3 (.f64 (pow.f64 (cbrt.f64 x) -3) (cbrt.f64 x)))
(*.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))
(.f64 -3 (.f64 (pow.f64 (cbrt.f64 x) -3) (cbrt.f64 x)))
(*.f64 2 x)
-3
(.f64 2 (.f64 x (+.f64 x x)))
-3
(*.f64 0 (/.f64 1 0))
-3
(*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (/.f64 1 (+.f64 (+.f64 x x) 2)))
-3
(.f64 (.f64 2 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x 0)))
-3
(*.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))))
-3
(*.f64 (sqrt.f64 2) (sqrt.f64 x))
(*.f64 -3 (sqrt.f64 x))
(*.f64 (cbrt.f64 2) (cbrt.f64 x))
(*.f64 -3 (cbrt.f64 x))
(.f64 4 (.f64 x x))
-3
(*.f64 8 (pow.f64 x 3))
-3
(.f64 (.f64 (+.f64 x x) 2) x)
-3
(.f64 (.f64 2 (sqrt.f64 x)) (sqrt.f64 x))
(.f64 -3 (.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(.f64 -3 (.f64 (pow.f64 (cbrt.f64 x) -3) (cbrt.f64 x)))
(*.f64 (+.f64 (hypot.f64 1 (+.f64 x x)) 1) (-.f64 (hypot.f64 1 (+.f64 x x)) 1))
(*.f64 (+.f64 -3 (hypot.f64 -3 -3)) (+.f64 -3 (hypot.f64 -3 -3)))
(*.f64 (pow.f64 (+.f64 x x) 3/2) (pow.f64 (+.f64 x x) 3/2))
-3
(/.f64 1 (+.f64 x x))
-3
(/.f64 1 (/.f64 (fma.f64 x x 0) (*.f64 2 (pow.f64 x 3))))
-3
(/.f64 1 (/.f64 (+.f64 (+.f64 x x) 2) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)))
-3
(/.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)))
-3
(/.f64 0 0)
-3
(/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 (+.f64 x x) 2))
-3
(/.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (-.f64 (fma.f64 2 x 1) -1))
-3
(/.f64 (*.f64 2 (pow.f64 x 3)) (fma.f64 x x 0))
-3
(/.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)))
-3
(/.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))))
-3
(/.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))))
-3
(/.f64 (sqrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (sqrt.f64 (+.f64 (+.f64 x x) 2)))
-3
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
-3
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 3))) (sqrt.f64 (fma.f64 x x 0)))
(/.f64 -3 (sqrt.f64 (fma.f64 x x -3)))
(/.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))))
-3
(/.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (cbrt.f64 (+.f64 (+.f64 x x) 2)))
-3
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 3))) (cbrt.f64 (fma.f64 x x 0)))
(/.f64 -3 (cbrt.f64 (fma.f64 x x -3)))
(/.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))))
-3
(/.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)))
-3
(/.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)))
-3
(/.f64 (*.f64 (+.f64 x x) (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (+.f64 (+.f64 x x) 2))
-3
(/.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)))
-3
(/.f64 (.f64 (+.f64 x x) (.f64 2 (pow.f64 x 3))) (fma.f64 x x 0))
-3
(/.f64 (*.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1) (+.f64 x x)) (+.f64 (+.f64 x x) 2))
-3
(/.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)))
-3
(/.f64 (*.f64 0 (+.f64 x x)) 0)
-3
(/.f64 (.f64 (.f64 2 (pow.f64 x 3)) (+.f64 x x)) (fma.f64 x x 0))
-3
(/.f64 (-.f64 1 (*.f64 (fma.f64 2 x -1) (fma.f64 2 x -1))) (-.f64 1 (fma.f64 2 x -1)))
-3
(/.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))))
-3
(/.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))))
-3
(/.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)))
-3
(/.f64 (.f64 0 (.f64 2 (pow.f64 x 3))) (*.f64 0 (fma.f64 x x 0)))
-3
(/.f64 (.f64 (.f64 2 (pow.f64 x 3)) 0) (*.f64 (fma.f64 x x 0) 0))
-3
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 3))) (neg.f64 (fma.f64 x x 0)))
-3
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 2 x 1) 2) -1)) (neg.f64 (+.f64 (+.f64 x x) 2)))
-3
(/.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))))
-3
(/.f64 (pow.f64 (*.f64 2 (pow.f64 x 3)) 3) (pow.f64 (fma.f64 x x 0) 3))
(/.f64 -3 (pow.f64 (fma.f64 x x -3) -3))
(pow.f64 (+.f64 x x) 1)
-3
(pow.f64 (+.f64 x x) 2)
-3
(pow.f64 (+.f64 x x) 3)
-3
(pow.f64 (+.f64 x x) 1/2)
-3
(pow.f64 (+.f64 x x) 1/3)
-3
(sqrt.f64 (+.f64 x x))
-3
(fabs.f64 (+.f64 x x))
-3
(log.f64 (pow.f64 (exp.f64 2) x))
-3
(log.f64 (+.f64 1 (expm1.f64 (+.f64 x x))))
-3
(cbrt.f64 (+.f64 x x))
-3
(expm1.f64 (log1p.f64 (+.f64 x x)))
-3
(hypot.f64 (sqrt.f64 x) (sqrt.f64 x))
(exp.f64 (log.f64 (+.f64 x x)))
-3
(exp.f64 (*.f64 (log.f64 (+.f64 x x)) 1))
-3
(exp.f64 (*.f64 (log.f64 (+.f64 x x)) 3))
-3
(log1p.f64 (expm1.f64 (+.f64 x x)))
-3
(fma.f64 1 x x)
(+.f64 x -3)
(fma.f64 1 (fma.f64 2 x 1) -1)
-3
(fma.f64 (hypot.f64 1 (+.f64 x x)) (hypot.f64 1 (+.f64 x x)) -1)
(fma.f64 (hypot.f64 -3 -3) (hypot.f64 -3 -3) -3)
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) x)
(fma.f64 (pow.f64 (cbrt.f64 (fma.f64 2 x 1)) 2) (cbrt.f64 (fma.f64 2 x 1)) -1)
-3
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) x)
(fma.f64 (pow.f64 (cbrt.f64 x) -3) (cbrt.f64 x) x)

eval67.0ms (1.8%)

Compiler: Compiled 3078 to 2169 computations (29.5% saved)

prune69.0ms (1.9%)

Pruning

13 alts after pruning (3 fresh and 10 done)

	Pruned	Kept	Total
New	238	2	240
Fresh	0	1	1
Picked	0	1	1
Done	1	9	10
Total	239	13	252

Error

Counts

252 → 13

Alt Table

Click to see full alt table

Status	Error	Program
✓	41.29%	(pow.f64 (*.f64 x (+.f64 x x)) 1/2)
✓	0.02%	(hypot.f64 x x)
✓	92.78%	(-.f64 (+.f64 1 (+.f64 x x)) 1)
✓	95.05%	(-.f64 (+.f64 1 (.f64 4 (.f64 x x))) 1)
	96.17%	(-.f64 1 1)
	92.78%	(+.f64 (+.f64 1 x) (-.f64 x 1))
✓	89.3%	(+.f64 x x)
✓	94.67%	(+.f64 -2 x)
✓	94.4%	(*.f64 (+.f64 x x) x)
✓	46.43%	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	94.36%	(.f64 x (.f64 4 x))
✓	41.32%	(sqrt.f64 (.f64 2 (.f64 x x)))
	98.31%	-2

Compiler

Compiled 77 to 55 computations (28.6% saved)

regimes41.0ms (1.1%)

Counts

17 → 1

Calls

Call 1

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

Outputs
(hypot.f64 x x)

Calls

4 calls:

18.0ms	x
7.0ms	(pow.f64 x 2)
6.0ms	(+.f64 (pow.f64 x 2) (pow.f64 x 2))
6.0ms	(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))

Results

Error	Segments	Branch
0.02%	1	`x`
0.02%	1	`(sqrt.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 2)))`
0.02%	1	`(+.f64 (pow.f64 x 2) (pow.f64 x 2))`
0.02%	1	`(pow.f64 x 2)`

Compiler

Compiled 113 to 67 computations (40.7% saved)

regimes60.0ms (1.6%)

Counts

12 → 2

Calls

Call 1

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

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

Calls

1 calls:

58.0ms

Results

Error	Segments	Branch
87.61%	2	`x`

Compiler

Compiled 63 to 34 computations (46% saved)

bsearch30.0ms (0.8%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
30.0ms	-4.267435684838857e-308	4.968818317836703e-303

Results

29.0ms

144×

body

256

valid

Compiler

Compiled 121 to 82 computations (32.2% saved)

regimes5.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(+.f64 x x)

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
89.3%	1	`x`

Compiler

Compiled 13 to 9 computations (30.8% saved)

regimes4.0ms (0.1%)

Accuracy

Total -2.4b remaining (-4%)

Threshold costs -2.4b (-4%)

Counts

2 → 1

Calls

Call 1

Inputs
-2
(+.f64 -2 x)

Outputs
(+.f64 -2 x)

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
94.67%	1	`x`

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative`
2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	51
1	18	51

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(hypot.f64 x x)
(if (<=.f64 x -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784) (.f64 4 (.f64 x x)) (+.f64 x x))
(+.f64 x x)
(+.f64 -2 x)
-2

Outputs
(hypot.f64 x x)
(if (<=.f64 x -101201126653655/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784) (.f64 4 (.f64 x x)) (+.f64 x x))
(+.f64 x x)
(+.f64 -2 x)
(+.f64 x -2)
-2

Compiler

Compiled 27 to 17 computations (37% saved)

soundness396.0ms (10.9%)

Algorithm

1×	egg-herbie

Rules

2476×	`fma-def`
1806×	`distribute-lft-out`
1312×	`count-2`
1058×	`hypot-def`
976×	`sqr-pow`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	14	7
2	35	7
3	59	7
4	122	7
5	306	7
6	1067	7
7	1905	7
8	3263	7
9	4212	7
10	5004	7
11	6030	7
12	6918	7
13	7857	7

Stop Event

1×	node limit

Compiler

Compiled 28 to 15 computations (46.4% saved)

end38.0ms (1.1%)

Compiler: Compiled 23 to 12 computations (47.8% saved)

Details

analyze7.0ms (0.2%)

sample866.0ms (23.8%)

preprocess153.0ms (4.2%)

simplify146.0ms (4%)

eval1.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.2%)

series2.0ms (0.1%)

rewrite196.0ms (5.4%)

simplify167.0ms (4.6%)

localize2.0ms (0.1%)

series2.0ms (0%)

rewrite47.0ms (1.3%)

simplify122.0ms (3.3%)

eval17.0ms (0.5%)

prune10.0ms (0.3%)

localize7.0ms (0.2%)

series1.0ms (0%)

rewrite51.0ms (1.4%)

simplify69.0ms (1.9%)

localize8.0ms (0.2%)

series0.0ms (0%)

rewrite49.0ms (1.4%)

simplify35.0ms (0.9%)

eval17.0ms (0.5%)

prune18.0ms (0.5%)

localize2.0ms (0.1%)

localize2.0ms (0.1%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite55.0ms (1.5%)

simplify239.0ms (6.6%)

localize4.0ms (0.1%)

localize4.0ms (0.1%)

eval2.0ms (0.1%)

prune5.0ms (0.1%)

localize230.0ms (6.3%)

localize9.0ms (0.2%)

series1.0ms (0%)

rewrite71.0ms (1.9%)

simplify96.0ms (2.7%)

localize6.0ms (0.2%)

series1.0ms (0%)

rewrite132.0ms (3.6%)

simplify58.0ms (1.6%)

eval67.0ms (1.8%)

prune69.0ms (1.9%)

regimes41.0ms (1.1%)

regimes60.0ms (1.6%)

bsearch30.0ms (0.8%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

simplify6.0ms (0.2%)

soundness396.0ms (10.9%)

end38.0ms (1.1%)

Profiling