Details

analyze5.0ms (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 8 to 7 computations (12.5% saved)

sample1.3s (42.5%)

Results

1.3s	8256×	body	256	valid
0.0ms	1×	body	256	infinite

Bogosity

preprocess157.0ms (5.2%)

Algorithm

2×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
617×	`cube-prod_binary64`
555×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`
442×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	9
2	23	9
3	44	9
4	108	9
5	330	9
6	1255	9
7	2129	9
8	2293	9
9	2477	9
10	2685	9
11	2984	9
12	3375	9
13	3856	9
14	4422	9
15	5110	9
16	5947	9
17	6337	9
18	6625	9
19	6903	9
20	6977	9
21	7013	9
22	7954	9
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify141.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
617×	`cube-prod_binary64`
555×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`
442×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	9
2	23	9
3	44	9
4	108	9
5	330	9
6	1255	9
7	2129	9
8	2293	9
9	2477	9
10	2685	9
11	2984	9
12	3375	9
13	3856	9
14	4422	9
15	5110	9
16	5947	9
17	6337	9
18	6625	9
19	6903	9
20	6977	9
21	7013	9
22	7954	9

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

31.1b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.1b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	29.8b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 17 to 8 computations (52.9% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite42.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

503×	`pow1_binary64`
486×	`add-sqr-sqrt_binary64`
466×	`add-log-exp_binary64`
466×	`log1p-expm1-u_binary64`
466×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	122	13
2	1367	13

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

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

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

simplify69.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

547×	`fma-neg_binary64`
507×	`distribute-rgt-in_binary64`
493×	`fma-def_binary64`
482×	`distribute-lft-in_binary64`
337×	`log-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	438
1	188	438
2	726	438
3	2397	438
4	7586	438

Stop Event

1×	node limit

Counts

60 → 44

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

eval8.0ms (0.3%)

Compiler: Compiled 346 to 260 computations (24.9% saved)

prune10.0ms (0.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	38	6	44
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	38	7	45

Error

0.1b

Counts

45 → 7

Alt Table

Click to see full alt table

Status	Error	Program
	30.8b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
▶	30.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
▶	30.7b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	33.0b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	30.2b	(*.f64 (sqrt.f64 2) x)
✓	31.1b	(sqrt.f64 (.f64 2 (.f64 x x)))
▶	33.5b	(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))

Compiler

Compiled 91 to 75 computations (17.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

series1.0ms (0%)

Counts

1 → 0

Calls

3 calls:

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

rewrite36.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

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

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

Outputs

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

simplify58.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

808×	`fma-def_binary64`
609×	`fma-neg_binary64`
524×	`log-prod_binary64`
283×	`*-commutative_binary64`
250×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	113
1	98	99
2	328	99
3	2323	99
4	5302	99
5	7601	99

Stop Event

1×	node limit

Counts

15 → 18

Calls

Call 1

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

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

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 12 to 8 computations (33.3% saved)

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))

rewrite32.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	125	6
2	1473	6

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

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

Outputs

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

simplify48.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

504×	`log-prod_binary64`
419×	`*-commutative_binary64`
327×	`distribute-rgt-in_binary64`
318×	`distribute-lft-in_binary64`
305×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	35	244
1	89	211
2	332	178
3	1748	178
4	4907	178
5	7938	128

Stop Event

1×	node limit

Counts

25 → 20

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

Outputs
(.f64 -1 (.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))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.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))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.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))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.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))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.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))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(.f64 -1 (.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))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(-.f64 0 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(-.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)
(hypot.f64 x 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)
(hypot.f64 x 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)
(hypot.f64 x 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)
(hypot.f64 x 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)
(hypot.f64 x x)
(neg.f64 (*.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) (neg.f64 x))
(neg.f64 (hypot.f64 x x))
(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)
(hypot.f64 x 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)
(hypot.f64 x 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)
(hypot.f64 x 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)
(hypot.f64 x 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)
(hypot.f64 x 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)
(hypot.f64 x x)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Compiler

Compiled 19 to 12 computations (36.8% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite35.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

597×	`pow1_binary64`
552×	`add-log-exp_binary64`
552×	`log1p-expm1-u_binary64`
552×	`expm1-log1p-u_binary64`
537×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	142	6
2	1593	6

Stop Event

1×	node limit

Counts

1 → 12

Calls

Call 1

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

Outputs

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

simplify48.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

792×	`log-prod_binary64`
549×	`fma-neg_binary64`
383×	`exp-sum_binary64`
356×	`exp-prod_binary64`
324×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	172
1	92	172
2	327	172
3	1665	172
4	4059	172
5	6073	172

Stop Event

1×	node limit

Counts

24 → 18

Calls

Call 1

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

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

localize10.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 x (sqrt.f64 2))
✓	3.0b	(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))

Compiler

Compiled 20 to 16 computations (20% saved)

series1.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite37.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

502×	`pow1_binary64`
483×	`add-sqr-sqrt_binary64`
464×	`add-log-exp_binary64`
464×	`log1p-expm1-u_binary64`
464×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	125	12
2	1284	12

Stop Event

1×	node limit

Counts

2 → 44

Calls

Call 1

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

Outputs

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

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

simplify48.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1054×	`log-prod_binary64`
469×	`associate-l_binary64`
434×	`distribute-rgt-in_binary64`
416×	`distribute-lft-in_binary64`
411×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	506
1	164	506
2	463	506
3	2882	504
4	7198	504

Stop Event

1×	node limit

Counts

68 → 36

Calls

Call 1

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

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

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.4b	(*.f64 x (sqrt.f64 2))
✓	0.6b	(cbrt.f64 (*.f64 x (sqrt.f64 2)))
✓	0.6b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

Compiler

Compiled 22 to 18 computations (18.2% saved)

series5.0ms (0.2%)

Counts

2 → 0

Calls

6 calls:

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

rewrite51.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

575×	`pow1_binary64`
543×	`add-log-exp_binary64`
542×	`log1p-expm1-u_binary64`
542×	`expm1-log1p-u_binary64`
530×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	168	14
2	1578	14

Stop Event

1×	node limit

Counts

2 → 52

Calls

Call 1

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

Outputs

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

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

simplify50.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

349×	`exp-sum_binary64`
311×	`fma-neg_binary64`
309×	`log-prod_binary64`
284×	`unswap-sqr_binary64`
255×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	107	797
1	231	682
2	748	583
3	1909	583
4	4457	583

Stop Event

1×	node limit

Counts

52 → 74

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(.f64 (.f64 x (sqrt.f64 2)) 1)
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(.f64 1 (.f64 x (sqrt.f64 2)))
(.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (sqrt.f64 2)))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (cbrt.f64 (.f64 2 (*.f64 x x)))))
(.f64 (cbrt.f64 2) (.f64 (cbrt.f64 (sqrt.f64 2)) x))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sqrt.f64 2)))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) (.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(.f64 (pow.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) 3) (pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6) 3))
(.f64 (.f64 x (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(.f64 (.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (sqrt.f64 x))
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1) (cbrt.f64 (*.f64 x (sqrt.f64 2))))
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 x)) (cbrt.f64 (sqrt.f64 2)))
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x))))) (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (pow.f64 (.f64 x (sqrt.f64 2)) 1/6)) (pow.f64 (.f64 x (sqrt.f64 2)) 1/6))
(sqrt.f64 (.f64 2 (.f64 x x)))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(-.f64 (+.f64 1 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 1)
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) 1)
(.f64 1 (cbrt.f64 (.f64 x (sqrt.f64 2))))
(*.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 2)))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/3))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6))
(.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/3) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (pow.f64 1 1/3) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(.f64 (pow.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) 1/3) (pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 1/3))
(pow.f64 (*.f64 x (sqrt.f64 2)) 1/3)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1)
(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3)
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6) 2)
(sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x))))
(log.f64 (exp.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(expm1.f64 (log1p.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(log1p.f64 (expm1.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(exp.f64 (log.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))

Outputs
(-.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)
(+.f64 1 (-.f64 (*.f64 x (sqrt.f64 2)) 1))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(*.f64 x (sqrt.f64 2))
(+.f64 1 (-.f64 (*.f64 x (sqrt.f64 2)) 1))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 (sqrt.f64 2) x)
(+.f64 1 (-.f64 (*.f64 x (sqrt.f64 2)) 1))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(.f64 (.f64 x (sqrt.f64 2)) 1)
(+.f64 1 (-.f64 (*.f64 x (sqrt.f64 2)) 1))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 x (.f64 x 2))))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 x (+.f64 x x))))
(.f64 1 (.f64 x (sqrt.f64 2)))
(+.f64 1 (-.f64 (*.f64 x (sqrt.f64 2)) 1))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 x (.f64 x 2))))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 x (+.f64 x x))))
(.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (sqrt.f64 2))))
(.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 2))))
(.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 2))))
(.f64 (cbrt.f64 (.f64 x (+.f64 x x))) (*.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 2))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (sqrt.f64 2)))
(+.f64 1 (-.f64 (*.f64 x (sqrt.f64 2)) 1))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) (.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (cbrt.f64 (.f64 2 (*.f64 x x)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 4))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) 4))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (+.f64 x x)))) 4))
(.f64 (cbrt.f64 2) (.f64 (cbrt.f64 (sqrt.f64 2)) x))
(.f64 (cbrt.f64 2) (.f64 x (cbrt.f64 (sqrt.f64 2))))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (cbrt.f64 2)))
(.f64 x (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2)))
(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))
(+.f64 1 (-.f64 (*.f64 x (sqrt.f64 2)) 1))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (sqrt.f64 2)))
(+.f64 1 (-.f64 (*.f64 x (sqrt.f64 2)) 1))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) (.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 x (.f64 x 2))))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 x (+.f64 x x))))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(+.f64 1 (-.f64 (*.f64 x (sqrt.f64 2)) 1))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 x (.f64 x 2))))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 x (+.f64 x x))))
(.f64 (pow.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) 3) (pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6) 3))
(+.f64 1 (-.f64 (*.f64 x (sqrt.f64 2)) 1))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(.f64 (.f64 x (cbrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))
(.f64 (cbrt.f64 2) (.f64 x (cbrt.f64 (sqrt.f64 2))))
(.f64 (cbrt.f64 (sqrt.f64 2)) (.f64 x (cbrt.f64 2)))
(.f64 x (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 2)))
(.f64 (.f64 x (pow.f64 2 1/4)) (pow.f64 2 1/4))
(+.f64 1 (-.f64 (*.f64 x (sqrt.f64 2)) 1))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(.f64 (.f64 (sqrt.f64 2) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))
(+.f64 1 (-.f64 (*.f64 x (sqrt.f64 2)) 1))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(.f64 (.f64 (sqrt.f64 2) (sqrt.f64 x)) (sqrt.f64 x))
(+.f64 1 (-.f64 (*.f64 x (sqrt.f64 2)) 1))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1) (cbrt.f64 (*.f64 x (sqrt.f64 2))))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 x (.f64 x 2))))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 x (+.f64 x x))))
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 x)) (cbrt.f64 (sqrt.f64 2)))
(.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (sqrt.f64 2))))
(.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 2))))
(.f64 (cbrt.f64 (.f64 x (.f64 x 2))) (.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 2))))
(.f64 (cbrt.f64 (.f64 x (+.f64 x x))) (*.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 2))))
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x))))) (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 4))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) 4))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (+.f64 x x)))) 4))
(.f64 (.f64 (cbrt.f64 (.f64 2 (.f64 x x))) (pow.f64 (.f64 x (sqrt.f64 2)) 1/6)) (pow.f64 (.f64 x (sqrt.f64 2)) 1/6))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 x (.f64 x 2))))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (*.f64 x (+.f64 x x))))
(sqrt.f64 (.f64 2 (.f64 x x)))
(+.f64 1 (-.f64 (*.f64 x (sqrt.f64 2)) 1))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(log.f64 (pow.f64 (exp.f64 x) (sqrt.f64 2)))
(+.f64 1 (-.f64 (*.f64 x (sqrt.f64 2)) 1))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3))
(+.f64 1 (-.f64 (*.f64 x (sqrt.f64 2)) 1))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))
(+.f64 1 (-.f64 (*.f64 x (sqrt.f64 2)) 1))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))
(+.f64 1 (-.f64 (*.f64 x (sqrt.f64 2)) 1))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(+.f64 1 (-.f64 (*.f64 x (sqrt.f64 2)) 1))
(+.f64 (*.f64 x (sqrt.f64 2)) 0)
(*.f64 x (sqrt.f64 2))
(-.f64 (+.f64 1 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 1)
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1))
(+.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 0)
(cbrt.f64 (*.f64 x (sqrt.f64 2)))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) 1)
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1))
(+.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 0)
(cbrt.f64 (*.f64 x (sqrt.f64 2)))
(.f64 1 (cbrt.f64 (.f64 x (sqrt.f64 2))))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1))
(+.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 0)
(cbrt.f64 (*.f64 x (sqrt.f64 2)))
(*.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 2)))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (+.f64 x x)))) (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))) (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/3))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (+.f64 x x)))) (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (+.f64 x x)))) (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x))
(*.f64 (cbrt.f64 x) (cbrt.f64 (sqrt.f64 2)))
(.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 1/6) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1))
(+.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 0)
(cbrt.f64 (*.f64 x (sqrt.f64 2)))
(.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 1/3) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (.f64 x 2)))) (cbrt.f64 (cbrt.f64 (.f64 x (sqrt.f64 2)))))
(.f64 (cbrt.f64 (cbrt.f64 (.f64 x (+.f64 x x)))) (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(.f64 (pow.f64 1 1/3) (cbrt.f64 (.f64 x (sqrt.f64 2))))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1))
(+.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 0)
(cbrt.f64 (*.f64 x (sqrt.f64 2)))
(.f64 (pow.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) 1/3) (pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 1/3))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1))
(+.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 0)
(cbrt.f64 (*.f64 x (sqrt.f64 2)))
(pow.f64 (*.f64 x (sqrt.f64 2)) 1/3)
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1))
(+.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 0)
(cbrt.f64 (*.f64 x (sqrt.f64 2)))
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1)
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1))
(+.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 0)
(cbrt.f64 (*.f64 x (sqrt.f64 2)))
(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3)
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1))
(+.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 0)
(cbrt.f64 (*.f64 x (sqrt.f64 2)))
(pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 1/6) 2)
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1))
(+.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 0)
(cbrt.f64 (*.f64 x (sqrt.f64 2)))
(sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x))))
(sqrt.f64 (cbrt.f64 (.f64 x (.f64 x 2))))
(sqrt.f64 (cbrt.f64 (*.f64 x (+.f64 x x))))
(log.f64 (exp.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1))
(+.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 0)
(cbrt.f64 (*.f64 x (sqrt.f64 2)))
(expm1.f64 (log1p.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1))
(+.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 0)
(cbrt.f64 (*.f64 x (sqrt.f64 2)))
(log1p.f64 (expm1.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1))
(+.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 0)
(cbrt.f64 (*.f64 x (sqrt.f64 2)))
(exp.f64 (log.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))
(+.f64 1 (-.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 1))
(+.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 0)
(cbrt.f64 (*.f64 x (sqrt.f64 2)))

eval57.0ms (1.9%)

Compiler: Compiled 1520 to 1186 computations (22% saved)

prune14.0ms (0.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	1	0	1
Picked	1	0	1
Done	3	2	5
Total	171	3	174

Error

Counts

174 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(hypot.f64 x x)
✓	30.2b	(*.f64 (sqrt.f64 2) x)
✓	31.1b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 16 to 11 computations (31.3% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 5 to 2 computations (60% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite67.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	60	4
2	696	4
3	7879	4

Stop Event

1×	node limit

Counts

1 → 103

Calls

Call 1

Inputs
(hypot.f64 x x)

Outputs

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

simplify18.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

41×	`*-commutative_binary64`
30×	`sqr-pow_binary64`
15×	`associate-r_binary64`
15×	`associate-l_binary64`
13×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	216	575
1	667	575

Stop Event

1×

unsound

Counts

115 → 118

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 x x) (.f64 x x))
(+.f64 (+.f64 1 (/.f64 0 0)) -1)
(+.f64 0 (/.f64 0 0))
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 0 0)) 2))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 0 0)))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))))
(+.f64 (.f64 (.f64 x x) (/.f64 0 0)) (.f64 (.f64 x x) (/.f64 0 0)))
(+.f64 (.f64 (/.f64 0 0) (.f64 x x)) (.f64 (/.f64 0 0) (.f64 x x)))
(-.f64 (+.f64 1 (/.f64 0 0)) 1)
(-.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))
(*.f64 x (+.f64 x x))
(.f64 x (.f64 (+.f64 x x) 1))
(.f64 x (.f64 (+.f64 x x) (/.f64 0 0)))
(*.f64 1 (/.f64 0 0))
(.f64 (.f64 x x) 2)
(.f64 (.f64 x x) (*.f64 (+.f64 x x) (+.f64 x x)))
(*.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x x)))
(*.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (cbrt.f64 x) 5)))
(.f64 (cbrt.f64 x) (.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 x x)))
(.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (.f64 x (cbrt.f64 x)) (*.f64 x (cbrt.f64 x))))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (+.f64 x x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
(*.f64 (sqrt.f64 x) (+.f64 (pow.f64 x 3/2) (pow.f64 x 3/2)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (+.f64 x x)))
(*.f64 (/.f64 0 0) 1)
(*.f64 (/.f64 0 0) (/.f64 0 0))
(*.f64 (/.f64 0 0) (pow.f64 1 1/3))
(*.f64 (/.f64 0 0) (pow.f64 1 1/2))
(*.f64 0 (/.f64 1 0))
(.f64 (.f64 x (cbrt.f64 x)) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(*.f64 (pow.f64 x 3/2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 2 (.f64 x x))
(.f64 2 (.f64 (*.f64 x x) (/.f64 0 0)))
(.f64 (.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 0 (pow.f64 x 4))))
(*.f64 (+.f64 x x) x)
(*.f64 (pow.f64 (cbrt.f64 x) 5) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))
(*.f64 4 (pow.f64 x 4))
(*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 (pow.f64 1 1/3) (/.f64 0 0))
(*.f64 (pow.f64 1 1/2) (/.f64 0 0))
(*.f64 (pow.f64 2 1/2) x)
(.f64 (.f64 2 (sqrt.f64 x)) (pow.f64 x 3/2))
(.f64 (.f64 (/.f64 0 0) x) (+.f64 x x))
(.f64 (.f64 (/.f64 0 0) 2) (*.f64 x x))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 2)) (*.f64 x (cbrt.f64 x)))
(.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2))
(.f64 (.f64 2 (pow.f64 x 3/2)) (sqrt.f64 x))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 5)) (cbrt.f64 x))
(/.f64 1 (/.f64 0 0))
(/.f64 1 (/.f64 (+.f64 0 (pow.f64 x 4)) (*.f64 2 (pow.f64 x 6))))
(/.f64 0 0)
(/.f64 (*.f64 2 (pow.f64 x 6)) (+.f64 0 (pow.f64 x 4)))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) (.f64 2 (pow.f64 x 6))) (.f64 (+.f64 0 (pow.f64 x 4)) (+.f64 0 (pow.f64 x 4))))
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 (.f64 0 (.f64 2 (pow.f64 x 6))) (*.f64 0 (+.f64 0 (pow.f64 x 4))))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) 0) (*.f64 (+.f64 0 (pow.f64 x 4)) 0))
(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 0 0)) 3) 1) (+.f64 (*.f64 (+.f64 1 (/.f64 0 0)) (+.f64 1 (/.f64 0 0))) (+.f64 1 (+.f64 1 (/.f64 0 0)))))
(/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 0 0)) (+.f64 1 (/.f64 0 0))) 1) (+.f64 (+.f64 1 (/.f64 0 0)) 1))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) 1) (+.f64 0 (pow.f64 x 4)))
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 0 (pow.f64 x 4)))
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
(/.f64 (.f64 (/.f64 0 0) (.f64 2 (pow.f64 x 6))) (+.f64 0 (pow.f64 x 4)))
(pow.f64 (/.f64 0 0) 1)
(pow.f64 (/.f64 0 0) 3)
(pow.f64 (/.f64 0 0) 1/3)
(pow.f64 (/.f64 0 0) 2)
(pow.f64 (/.f64 0 0) 1/2)
(pow.f64 (/.f64 0 0) 1/4)
(pow.f64 (/.f64 0 0) 1/9)
(pow.f64 (/.f64 0 0) 4)
(pow.f64 (/.f64 0 0) 9)
(pow.f64 (/.f64 0 0) 2/3)
(pow.f64 (/.f64 0 0) 6)
(pow.f64 (/.f64 0 0) 1/6)
(pow.f64 (/.f64 0 0) 3/2)
(pow.f64 (/.f64 0 0) 5/2)
(pow.f64 (/.f64 0 0) 5)
(pow.f64 (/.f64 0 0) 4/3)
(pow.f64 (E.f64) (log.f64 (/.f64 0 0)))
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (/.f64 0 0)) 2))) (cbrt.f64 (log.f64 (/.f64 0 0))))
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 0 0)))) (sqrt.f64 (log.f64 (/.f64 0 0))))
(sqrt.f64 (/.f64 0 0))
(fabs.f64 (/.f64 0 0))
(fabs.f64 (neg.f64 (/.f64 0 0)))
(log.f64 (exp.f64 (/.f64 0 0)))
(cbrt.f64 (/.f64 0 0))
(expm1.f64 (log1p.f64 (/.f64 0 0)))
(log1p.f64 (expm1.f64 (/.f64 0 0)))
(exp.f64 (log.f64 (/.f64 0 0)))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/3))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 3))
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/2))
(fma.f64 x x (*.f64 x x))
(fma.f64 1 (.f64 x x) (.f64 x x))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 x (cbrt.f64 x)) (.f64 x x))
(fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (*.f64 x x))
(fma.f64 (.f64 x (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2) (.f64 x x))
(fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (*.f64 x x))
(fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (*.f64 x x))

Outputs
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(+.f64 x x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(+.f64 x x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(+.f64 x x)
(.f64 -1 (.f64 (sqrt.f64 2) x))
(+.f64 x x)
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 x (+.f64 x x))
(+.f64 (+.f64 1 (/.f64 0 0)) -1)
-2
(+.f64 0 (/.f64 0 0))
-2
(+.f64 (log.f64 (cbrt.f64 (pow.f64 (exp.f64 (/.f64 0 0)) 2))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 0 0)))))
-2
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 0 0)))))
-2
(+.f64 (.f64 (.f64 x x) (/.f64 0 0)) (.f64 (.f64 x x) (/.f64 0 0)))
(*.f64 x (+.f64 x x))
(+.f64 (.f64 (/.f64 0 0) (.f64 x x)) (.f64 (/.f64 0 0) (.f64 x x)))
(*.f64 x (+.f64 x x))
(-.f64 (+.f64 1 (/.f64 0 0)) 1)
-2
(-.f64 (/.f64 (pow.f64 x 4) 0) (/.f64 (pow.f64 x 4) 0))
-2
(*.f64 x (+.f64 x x))
(.f64 x (.f64 (+.f64 x x) 1))
(*.f64 x (+.f64 x x))
(.f64 x (.f64 (+.f64 x x) (/.f64 0 0)))
(*.f64 x (+.f64 x x))
(*.f64 1 (/.f64 0 0))
-2
(.f64 (.f64 x x) 2)
(*.f64 x (+.f64 x x))
(.f64 (.f64 x x) (*.f64 (+.f64 x x) (+.f64 x x)))
(.f64 (.f64 x x) (*.f64 x (+.f64 x x)))
(*.f64 (cbrt.f64 x) (cbrt.f64 (+.f64 x x)))
(*.f64 (cbrt.f64 x) (+.f64 (pow.f64 (cbrt.f64 x) 5) (pow.f64 (cbrt.f64 x) 5)))
(.f64 (cbrt.f64 x) (.f64 -2 (pow.f64 (cbrt.f64 x) 5)))
(.f64 (cbrt.f64 x) (.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 x x)))
(.f64 (cbrt.f64 x) (.f64 (+.f64 x x) (pow.f64 (cbrt.f64 x) -2)))
(.f64 (pow.f64 (cbrt.f64 x) 2) (+.f64 (.f64 x (cbrt.f64 x)) (*.f64 x (cbrt.f64 x))))
(.f64 (pow.f64 (cbrt.f64 x) -2) (.f64 (+.f64 x x) (cbrt.f64 x)))
(.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (+.f64 x x)))
(.f64 (pow.f64 (cbrt.f64 x) -2) (.f64 (+.f64 x x) (cbrt.f64 x)))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x x)))
(*.f64 (sqrt.f64 x) (+.f64 (pow.f64 x 3/2) (pow.f64 x 3/2)))
(.f64 -2 (.f64 (sqrt.f64 x) (pow.f64 x 3/2)))
(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (+.f64 x x)))
(.f64 (sqrt.f64 x) (.f64 (+.f64 x x) (sqrt.f64 x)))
(*.f64 (/.f64 0 0) 1)
-2
(*.f64 (/.f64 0 0) (/.f64 0 0))
-2
(*.f64 (/.f64 0 0) (pow.f64 1 1/3))
-2
(*.f64 (/.f64 0 0) (pow.f64 1 1/2))
-2
(*.f64 0 (/.f64 1 0))
-2
(.f64 (.f64 x (cbrt.f64 x)) (+.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 (cbrt.f64 x) 2)))
(.f64 (pow.f64 (cbrt.f64 x) -2) (.f64 (+.f64 x x) (cbrt.f64 x)))
(*.f64 (pow.f64 x 3/2) (+.f64 (sqrt.f64 x) (sqrt.f64 x)))
(.f64 -2 (.f64 (sqrt.f64 x) (pow.f64 x 3/2)))
(.f64 2 (.f64 x x))
(*.f64 x (+.f64 x x))
(.f64 2 (.f64 (*.f64 x x) (/.f64 0 0)))
(*.f64 x (+.f64 x x))
(.f64 (.f64 2 (pow.f64 x 6)) (/.f64 1 (+.f64 0 (pow.f64 x 4))))
-2
(*.f64 (+.f64 x x) x)
(*.f64 x (+.f64 x x))
(*.f64 (pow.f64 (cbrt.f64 x) 5) (+.f64 (cbrt.f64 x) (cbrt.f64 x)))
(.f64 (cbrt.f64 x) (.f64 -2 (pow.f64 (cbrt.f64 x) 5)))
(*.f64 4 (pow.f64 x 4))
-2
(*.f64 (cbrt.f64 2) (pow.f64 (cbrt.f64 x) 2))
(*.f64 -2 (pow.f64 (cbrt.f64 x) -2))
(*.f64 (sqrt.f64 2) x)
(+.f64 x x)
(*.f64 (pow.f64 1 1/3) (/.f64 0 0))
-2
(*.f64 (pow.f64 1 1/2) (/.f64 0 0))
-2
(*.f64 (pow.f64 2 1/2) x)
(+.f64 x x)
(.f64 (.f64 2 (sqrt.f64 x)) (pow.f64 x 3/2))
(.f64 -2 (.f64 (sqrt.f64 x) (pow.f64 x 3/2)))
(.f64 (.f64 (/.f64 0 0) x) (+.f64 x x))
(*.f64 x (+.f64 x x))
(.f64 (.f64 (/.f64 0 0) 2) (*.f64 x x))
(*.f64 x (+.f64 x x))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 2)) (*.f64 x (cbrt.f64 x)))
(.f64 (pow.f64 (cbrt.f64 x) -2) (.f64 (+.f64 x x) (cbrt.f64 x)))
(.f64 (.f64 2 (*.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2))
(.f64 (pow.f64 (cbrt.f64 x) -2) (.f64 (+.f64 x x) (cbrt.f64 x)))
(.f64 (.f64 2 (pow.f64 x 3/2)) (sqrt.f64 x))
(.f64 -2 (.f64 (sqrt.f64 x) (pow.f64 x 3/2)))
(.f64 (.f64 2 (pow.f64 (cbrt.f64 x) 5)) (cbrt.f64 x))
(.f64 (cbrt.f64 x) (.f64 -2 (pow.f64 (cbrt.f64 x) 5)))
(/.f64 1 (/.f64 0 0))
-2
(/.f64 1 (/.f64 (+.f64 0 (pow.f64 x 4)) (*.f64 2 (pow.f64 x 6))))
-2
(/.f64 0 0)
-2
(/.f64 (*.f64 2 (pow.f64 x 6)) (+.f64 0 (pow.f64 x 4)))
-2
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) (.f64 2 (pow.f64 x 6))) (.f64 (+.f64 0 (pow.f64 x 4)) (+.f64 0 (pow.f64 x 4))))
-2
(/.f64 (cbrt.f64 (*.f64 2 (pow.f64 x 6))) (cbrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 -2 (cbrt.f64 (pow.f64 x -2)))
(/.f64 (sqrt.f64 (*.f64 2 (pow.f64 x 6))) (sqrt.f64 (+.f64 0 (pow.f64 x 4))))
(/.f64 -2 (sqrt.f64 (pow.f64 x -2)))
(/.f64 (sqrt.f64 0) (sqrt.f64 0))
-2
(/.f64 (neg.f64 (*.f64 2 (pow.f64 x 6))) (neg.f64 (+.f64 0 (pow.f64 x 4))))
-2
(/.f64 (.f64 0 (.f64 2 (pow.f64 x 6))) (*.f64 0 (+.f64 0 (pow.f64 x 4))))
-2
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) 0) (*.f64 (+.f64 0 (pow.f64 x 4)) 0))
-2
(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 0 0)) 3) 1) (+.f64 (*.f64 (+.f64 1 (/.f64 0 0)) (+.f64 1 (/.f64 0 0))) (+.f64 1 (+.f64 1 (/.f64 0 0)))))
-2
(/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 0 0)) (+.f64 1 (/.f64 0 0))) 1) (+.f64 (+.f64 1 (/.f64 0 0)) 1))
-2
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) 1) (+.f64 0 (pow.f64 x 4)))
-2
(/.f64 (.f64 (.f64 2 (pow.f64 x 6)) (/.f64 0 0)) (+.f64 0 (pow.f64 x 4)))
-2
(/.f64 (*.f64 0 (/.f64 0 0)) 0)
-2
(/.f64 (.f64 (/.f64 0 0) (.f64 2 (pow.f64 x 6))) (+.f64 0 (pow.f64 x 4)))
-2
(pow.f64 (/.f64 0 0) 1)
-2
(pow.f64 (/.f64 0 0) 3)
-2
(pow.f64 (/.f64 0 0) 1/3)
-2
(pow.f64 (/.f64 0 0) 2)
-2
(pow.f64 (/.f64 0 0) 1/2)
-2
(pow.f64 (/.f64 0 0) 1/4)
-2
(pow.f64 (/.f64 0 0) 1/9)
-2
(pow.f64 (/.f64 0 0) 4)
-2
(pow.f64 (/.f64 0 0) 9)
-2
(pow.f64 (/.f64 0 0) 2/3)
-2
(pow.f64 (/.f64 0 0) 6)
-2
(pow.f64 (/.f64 0 0) 1/6)
-2
(pow.f64 (/.f64 0 0) 3/2)
-2
(pow.f64 (/.f64 0 0) 5/2)
-2
(pow.f64 (/.f64 0 0) 5)
-2
(pow.f64 (/.f64 0 0) 4/3)
-2
(pow.f64 (E.f64) (log.f64 (/.f64 0 0)))
-2
(pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (/.f64 0 0)) 2))) (cbrt.f64 (log.f64 (/.f64 0 0))))
-2
(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (/.f64 0 0)))) (sqrt.f64 (log.f64 (/.f64 0 0))))
-2
(sqrt.f64 (/.f64 0 0))
-2
(fabs.f64 (/.f64 0 0))
-2
(fabs.f64 (neg.f64 (/.f64 0 0)))
-2
(log.f64 (exp.f64 (/.f64 0 0)))
-2
(cbrt.f64 (/.f64 0 0))
-2
(expm1.f64 (log1p.f64 (/.f64 0 0)))
-2
(log1p.f64 (expm1.f64 (/.f64 0 0)))
-2
(exp.f64 (log.f64 (/.f64 0 0)))
-2
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/3))
-2
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 3))
-2
(exp.f64 (*.f64 (log.f64 (/.f64 0 0)) 1/2))
-2
(fma.f64 x x (*.f64 x x))
(*.f64 x (+.f64 x x))
(fma.f64 1 (.f64 x x) (.f64 x x))
(fma.f64 -2 (.f64 x x) (.f64 x x))
(fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 x (cbrt.f64 x)) (.f64 x x))
(fma.f64 (pow.f64 (cbrt.f64 x) -2) (.f64 x (cbrt.f64 x)) (.f64 x x))
(fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) (*.f64 x x))
(fma.f64 (.f64 x (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2) (.f64 x x))
(fma.f64 (.f64 x (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) -2) (.f64 x x))
(fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (*.f64 x x))
(fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) (*.f64 x x))

eval19.0ms (0.6%)

Compiler: Compiled 1005 to 705 computations (29.9% saved)

prune45.0ms (1.5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	115	3	118
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	115	6	121

Error

Counts

121 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(hypot.f64 x x)
▶	56.6b	(+.f64 x x)
▶	61.0b	(.f64 (.f64 x x) 2)
✓	30.2b	(*.f64 (sqrt.f64 2) x)
✓	31.1b	(sqrt.f64 (.f64 2 (.f64 x x)))
	63.0b	-2

Compiler

Compiled 28 to 19 computations (32.1% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 11 to 5 computations (54.5% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite35.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	101	7
2	1124	7

Stop Event

1×	node limit

Counts

1 → 16

Calls

Call 1

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

Outputs

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

simplify61.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1248×	`log-prod_binary64`
456×	`fma-neg_binary64`
434×	`associate-l_binary64`
389×	`associate-+l+_binary64`
373×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	47	220
1	114	205
2	423	205
3	3180	205
4	7244	205

Stop Event

1×	node limit

Counts

28 → 22

Calls

Call 1

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

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

localize2.0ms (0.1%)

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

eval4.0ms (0.1%)

Compiler: Compiled 193 to 118 computations (38.9% saved)

prune5.0ms (0.2%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	1	1
Picked	0	1	1
Done	0	4	4
Total	22	6	28

Error

Counts

28 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(hypot.f64 x x)
✓	56.6b	(+.f64 x x)
✓	61.0b	(.f64 (.f64 x x) 2)
✓	30.2b	(*.f64 (sqrt.f64 2) x)
✓	31.1b	(sqrt.f64 (.f64 2 (.f64 x x)))
	63.0b	-2

Compiler

Compiled 28 to 19 computations (32.1% saved)

regimes26.0ms (0.9%)

Counts

12 → 1

Calls

Call 1

Inputs
-2
(+.f64 x x)
(.f64 (.f64 x x) 2)
(hypot.f64 x x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) (neg.f64 x))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)

Outputs
(hypot.f64 x x)

Calls

4 calls:

7.0ms	x
6.0ms	(pow.f64 x 2)
5.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
5.0ms	(*.f64 2 (pow.f64 x 2))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(sqrt.f64 (*.f64 2 (pow.f64 x 2)))`
0.0b	1	`(*.f64 2 (pow.f64 x 2))`
0.0b	1	`(pow.f64 x 2)`

Compiler

Compiled 80 to 59 computations (26.3% saved)

regimes4.0ms (0.1%)

Accuracy

Total -6.5b remaining (-11.5%)

Threshold costs -6.5b (-11.5%)

Counts

3 → 1

Calls

Call 1

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

Outputs
(+.f64 x x)

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
56.6b	1	`x`

Compiler

Compiled 12 to 7 computations (41.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	9

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 10 to 6 computations (40% saved)

soundness417.0ms (13.8%)

Algorithm

3×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
617×	`cube-prod_binary64`
555×	`fabs-mul_binary64`
547×	`fma-neg_binary64`
523×	`pow-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	9
2	23	9
3	44	9
4	108	9
5	330	9
6	1255	9
7	2129	9
8	2293	9
9	2477	9
10	2685	9
11	2984	9
12	3375	9
13	3856	9
14	4422	9
15	5110	9
16	5947	9
17	6337	9
18	6625	9
19	6903	9
20	6977	9
21	7013	9
22	7954	9
0	80	438
1	188	438
2	726	438
3	2397	438
4	7586	438
0	35	244
1	89	211
2	332	178
3	1748	178
4	4907	178
5	7938	128

Stop Event

1×	node limit
1×	node limit
1×	node limit

Compiler

Compiled 799 to 657 computations (17.8% saved)

end19.0ms (0.6%)

Compiler: Compiled 8 to 4 computations (50% saved)

Details

analyze5.0ms (0.2%)

sample1.3s (42.5%)

preprocess157.0ms (5.2%)

simplify141.0ms (4.7%)

eval1.0ms (0%)

prune1.0ms (0%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite42.0ms (1.4%)

simplify69.0ms (2.3%)

eval8.0ms (0.3%)

prune10.0ms (0.3%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite36.0ms (1.2%)

simplify58.0ms (1.9%)

localize6.0ms (0.2%)

series1.0ms (0%)

rewrite32.0ms (1.1%)

simplify48.0ms (1.6%)

localize8.0ms (0.3%)

series1.0ms (0%)

rewrite35.0ms (1.2%)

simplify48.0ms (1.6%)

localize10.0ms (0.3%)

series1.0ms (0%)

rewrite37.0ms (1.2%)

simplify48.0ms (1.6%)

localize10.0ms (0.3%)

series5.0ms (0.2%)

rewrite51.0ms (1.7%)

simplify50.0ms (1.7%)

eval57.0ms (1.9%)

prune14.0ms (0.4%)

localize2.0ms (0.1%)

series2.0ms (0.1%)

rewrite67.0ms (2.2%)

simplify18.0ms (0.6%)

eval19.0ms (0.6%)

prune45.0ms (1.5%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite35.0ms (1.2%)

simplify61.0ms (2%)

localize2.0ms (0.1%)

eval4.0ms (0.1%)

prune5.0ms (0.2%)

regimes26.0ms (0.9%)

regimes4.0ms (0.1%)

simplify2.0ms (0.1%)

soundness417.0ms (13.8%)

end19.0ms (0.6%)

Profiling