Details

analyze5.0ms (0.1%)

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)

sample894.0ms (16.5%)

Results

881.0ms	8256×	body	256	valid
0.0ms	2×	body	256	infinite

Bogosity

preprocess175.0ms (3.2%)

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)

simplify165.0ms (3.1%)

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

26.8b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	26.8b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	25.8b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 17 to 8 computations (52.9% saved)

series4.0ms (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	@	0	(.f64 2 (.f64 x x))
1.0ms	x	@	inf	(sqrt.f64 (.f64 2 (.f64 x x)))
1.0ms	x	@	-inf	(.f64 2 (.f64 x x))
1.0ms	x	@	inf	(.f64 2 (.f64 x x))

rewrite47.0ms (0.9%)

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))))))))

simplify84.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

60 → 40

Calls

Call 1

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

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

eval8.0ms (0.2%)

Compiler: Compiled 313 to 236 computations (24.6% saved)

prune12.0ms (0.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	33	7	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	8	41

Error

0.1b

Counts

41 → 8

Alt Table

Click to see full alt table

Status	Error	Program
	45.1b	(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
✓	26.8b	(sqrt.f64 (.f64 2 (.f64 x x)))
	33.8b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
▶	33.4b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
▶	30.1b	(*.f64 x (neg.f64 (sqrt.f64 2)))
▶	27.2b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3))
▶	33.0b	(*.f64 (sqrt.f64 2) x)
▶	33.7b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Compiler

Compiled 123 to 99 computations (19.5% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 2 (.f64 x x))
✓	0.4b	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3)
✓	25.8b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3))
✓	26.7b	(cbrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 35 to 20 computations (42.9% saved)

series11.0ms (0.2%)

Counts

3 → 12

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3))
2.0ms	x	@	0	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3)
1.0ms	x	@	0	(cbrt.f64 (.f64 2 (.f64 x x)))
1.0ms	x	@	inf	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3)
1.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3)

rewrite55.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

649×	`pow1_binary64`
612×	`add-log-exp_binary64`
611×	`log1p-expm1-u_binary64`
611×	`expm1-log1p-u_binary64`
595×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	190	22
2	1844	22

Stop Event

1×	node limit

Counts

3 → 84

Calls

Call 1

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

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

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

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

96 → 86

Calls

Call 1

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

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

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(*.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
1.0ms	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)

rewrite42.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

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

Outputs

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

15 → 15

Calls

Call 1

Inputs

Outputs

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 x (neg.f64 (sqrt.f64 2)))

Compiler

Compiled 13 to 11 computations (15.4% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite33.0ms (0.6%)

Algorithm

1×	egg-rewrite-iter-limit
1×	batch-egg-rewrite

Rules

61×	`add-sqr-sqrt_binary64`
57×	`add-exp-log_binary64`
57×	`add-log-exp_binary64`
57×	`log1p-expm1-u_binary64`
57×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	125	8
2	1470	8
0	6	8

Stop Event

1×	iter limit
1×	unsound

Counts

1 → 7

Calls

Call 1

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

Outputs

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

simplify95.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

19 → 9

Calls

Call 1

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

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

localize9.0ms (0.2%)

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)

series2.0ms (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))

rewrite98.0ms (1.8%)

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)))))))

simplify17.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

24 → 15

Calls

Call 1

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

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

localize55.0ms (1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 x (sqrt.f64 2))
✓	0.6b	(cbrt.f64 (*.f64 x (sqrt.f64 2)))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

Compiler

Compiled 22 to 18 computations (18.2% saved)

series7.0ms (0.1%)

Counts

3 → 12

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
1.0ms	x	@	0	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
1.0ms	x	@	inf	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
1.0ms	x	@	-inf	(cbrt.f64 (*.f64 x (sqrt.f64 2)))
0.0ms	x	@	inf	(cbrt.f64 (*.f64 x (sqrt.f64 2)))

rewrite55.0ms (1%)

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	20
1	168	20
2	1578	20

Stop Event

1×	node limit

Counts

3 → 64

Calls

Call 1

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

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

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	72
1	6	72

Stop Event

1×

saturated

Counts

76 → 57

Calls

Call 1

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

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

eval54.0ms (1%)

Compiler: Compiled 1986 to 1531 computations (22.9% saved)

prune28.0ms (0.5%)

Pruning

9 alts after pruning (4 fresh and 5 done)

	Pruned	Kept	Total
New	192	4	196
Fresh	2	0	2
Picked	0	1	1
Done	1	4	5
Total	195	9	204

Error

0.1b

Counts

204 → 9

Alt Table

Click to see full alt table

Status	Error	Program
▶	27.2b	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)
▶	32.9b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
▶	27.4b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3))
✓	33.4b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
✓	30.1b	(*.f64 x (neg.f64 (sqrt.f64 2)))
✓	33.0b	(*.f64 (sqrt.f64 2) x)
✓	33.7b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	26.8b	(sqrt.f64 (.f64 2 (.f64 x x)))
▶	27.0b	(sqrt.f64 (.f64 (.f64 (.f64 2 x) (cbrt.f64 (.f64 x x))) (cbrt.f64 x)))

Compiler

Compiled 77 to 61 computations (20.8% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 (.f64 2 x) (cbrt.f64 (.f64 x x))) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)
✓	25.8b	(sqrt.f64 (.f64 (.f64 (.f64 2 x) (cbrt.f64 (.f64 x x))) (cbrt.f64 x)))
✓	26.7b	(cbrt.f64 (*.f64 x x))

Compiler

Compiled 46 to 19 computations (58.7% saved)

series196.0ms (3.6%)

Counts

4 → 24

Calls

12 calls:

Time	Variable		Point	Expression
172.0ms	x	@	0	(sqrt.f64 (.f64 (.f64 (.f64 2 x) (cbrt.f64 (.f64 x x))) (cbrt.f64 x)))
15.0ms	x	@	inf	(cbrt.f64 (*.f64 x x))
2.0ms	x	@	-inf	(sqrt.f64 (.f64 (.f64 (.f64 2 x) (cbrt.f64 (.f64 x x))) (cbrt.f64 x)))
2.0ms	x	@	0	(.f64 (.f64 (.f64 2 x) (cbrt.f64 (.f64 x x))) (cbrt.f64 x))
1.0ms	x	@	-inf	(.f64 (.f64 (.f64 2 x) (cbrt.f64 (.f64 x x))) (cbrt.f64 x))

rewrite64.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

827×	`pow1_binary64`
765×	`add-log-exp_binary64`
765×	`log1p-expm1-u_binary64`
765×	`expm1-log1p-u_binary64`
743×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	200	25
2	2237	25

Stop Event

1×	node limit

Counts

4 → 80

Calls

Call 1

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

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

simplify96.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

579×	`fma-def_binary64`
578×	`distribute-lft-neg-out_binary64`
562×	`associate-l_binary64`
555×	`distribute-rgt-neg-out_binary64`
427×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	212
1	36	212
2	91	212
3	223	212
4	577	212
5	1783	212
6	2331	212
7	3686	212
8	4415	212
9	4999	212
10	6166	212

Stop Event

1×	node limit

Counts

104 → 87

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

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

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3)
	0.6b	(cbrt.f64 x)
✓	0.6b	(cbrt.f64 (*.f64 2 x))
✓	25.8b	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3))

Compiler

Compiled 39 to 26 computations (33.3% saved)

series9.0ms (0.2%)

Counts

3 → 12

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3))
1.0ms	x	@	-inf	(pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3)
1.0ms	x	@	0	(pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3)
1.0ms	x	@	inf	(pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3)
1.0ms	x	@	-inf	(cbrt.f64 (*.f64 2 x))

rewrite63.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

805×	`pow1_binary64`
754×	`add-log-exp_binary64`
753×	`log1p-expm1-u_binary64`
753×	`expm1-log1p-u_binary64`
731×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	208	22
2	2240	22

Stop Event

1×	node limit

Counts

3 → 83

Calls

Call 1

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

Outputs

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

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

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

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

95 → 86

Calls

Call 1

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

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

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 21 to 18 computations (14.3% saved)

series54.0ms (1%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
52.0ms	x	@	0	(*.f64 (pow.f64 2 1/4) x)
1.0ms	x	@	inf	(*.f64 (pow.f64 2 1/4) x)
0.0ms	x	@	-inf	(*.f64 (pow.f64 2 1/4) x)
0.0ms	x	@	inf	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
0.0ms	x	@	0	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

rewrite172.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 22

Calls

Call 1

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

Outputs

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	72
1	6	72

Stop Event

1×

saturated

Counts

34 → 23

Calls

Call 1

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

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

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(.f64 2 (.f64 x x))
✓	0.4b	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)
	26.7b	(cbrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 26 to 14 computations (46.2% saved)

series4.0ms (0.1%)

Counts

1 → 0

Calls

3 calls:

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

rewrite50.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

645×	`pow1_binary64`
606×	`add-log-exp_binary64`
606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
591×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	166	6
2	1833	6

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

Inputs
(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

20 → 20

Calls

Call 1

Inputs

Outputs

eval94.0ms (1.7%)

Compiler: Compiled 3240 to 2222 computations (31.4% saved)

prune88.0ms (1.6%)

Pruning

12 alts after pruning (5 fresh and 7 done)

	Pruned	Kept	Total
New	268	5	273
Fresh	0	0	0
Picked	0	1	1
Done	2	6	8
Total	270	12	282

Error

0.1b

Counts

282 → 12

Alt Table

Click to see full alt table

Status	Error	Program
▶	1.4b	(pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2) 3/2)
▶	33.8b	(.f64 (pow.f64 2 1/4) (pow.f64 (.f64 (sqrt.f64 x) (pow.f64 2 1/8)) 2))
✓	33.4b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
▶	26.9b	(pow.f64 (pow.f64 (.f64 x (.f64 x 2)) 1/4) 2)
✓	27.2b	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)
✓	32.9b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
▶	1.3b	(pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3/2)
✓	33.7b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	36.7b	(cbrt.f64 (pow.f64 (.f64 x (.f64 x 2)) 3/2))
✓	30.1b	(*.f64 x (neg.f64 (sqrt.f64 2)))
✓	33.0b	(*.f64 (sqrt.f64 2) x)
✓	26.8b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 157 to 131 computations (16.6% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 29 to 19 computations (34.5% saved)

series6.0ms (0.1%)

Counts

2 → 0

Calls

6 calls:

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

rewrite79.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

755×	`pow1_binary64`
706×	`add-log-exp_binary64`
706×	`log1p-expm1-u_binary64`
706×	`expm1-log1p-u_binary64`
685×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	21
1	187	18
2	2119	18

Stop Event

1×	node limit

Counts

2 → 28

Calls

Call 1

Inputs
(pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3/2)
(.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x))

Outputs

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

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

28 → 28

Calls

Call 1

Inputs

Outputs

localize20.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (.f64 x (.f64 x 2)) 3/2)
✓	35.7b	(cbrt.f64 (pow.f64 (.f64 x (.f64 x 2)) 3/2))

Compiler

Compiled 27 to 19 computations (29.6% saved)

series18.0ms (0.3%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	x	@	inf	(pow.f64 (.f64 x (.f64 x 2)) 3/2)
8.0ms	x	@	0	(pow.f64 (.f64 x (.f64 x 2)) 3/2)
0.0ms	x	@	-inf	(pow.f64 (.f64 x (.f64 x 2)) 3/2)
0.0ms	x	@	0	(cbrt.f64 (pow.f64 (.f64 x (.f64 x 2)) 3/2))
0.0ms	x	@	inf	(cbrt.f64 (pow.f64 (.f64 x (.f64 x 2)) 3/2))

rewrite65.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

701×	`pow1_binary64`
657×	`add-log-exp_binary64`
657×	`log1p-expm1-u_binary64`
657×	`expm1-log1p-u_binary64`
641×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	168	15
2	1908	15

Stop Event

1×	node limit

Counts

2 → 45

Calls

Call 1

Inputs
(cbrt.f64 (pow.f64 (.f64 x (.f64 x 2)) 3/2))
(pow.f64 (.f64 x (.f64 x 2)) 3/2)

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

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

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Rules

712×	`times-frac_binary64`
504×	`associate-l_binary64`
405×	`fma-def_binary64`
320×	`unswap-sqr_binary64`
277×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	272
1	67	248
2	167	200
3	328	200
4	627	200
5	1483	200
6	3906	200

Stop Event

1×	node limit

Counts

69 → 52

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))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 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))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 3/2) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 3/2) (pow.f64 x 3))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 3/2) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 3/2) (pow.f64 x 3))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 3/2) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 3/2) (pow.f64 x 3))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 3/2) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 3/2) (pow.f64 x 3))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 3/2) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 3/2) (pow.f64 x 3))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 3/2) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 3/2) (pow.f64 x 3))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 3/2) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 3/2) (pow.f64 x 3))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 3/2) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 3/2) (pow.f64 x 3))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 3/2) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 3/2) (pow.f64 x 3))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 3/2) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 3/2) (pow.f64 x 3))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 3/2) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 3/2) (pow.f64 x 3))
(exp.f64 (.f64 3/2 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 3/2) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 3/2) (pow.f64 x 3))

localize16.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (pow.f64 (.f64 x (.f64 x 2)) 1/4) 2)
✓	26.5b	(pow.f64 (.f64 x (.f64 x 2)) 1/4)

Compiler

Compiled 28 to 20 computations (28.6% saved)

series4.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(pow.f64 (.f64 x (.f64 x 2)) 1/4)
1.0ms	x	@	inf	(pow.f64 (pow.f64 (.f64 x (.f64 x 2)) 1/4) 2)
1.0ms	x	@	inf	(pow.f64 (.f64 x (.f64 x 2)) 1/4)
1.0ms	x	@	0	(pow.f64 (pow.f64 (.f64 x (.f64 x 2)) 1/4) 2)
0.0ms	x	@	-inf	(pow.f64 (pow.f64 (.f64 x (.f64 x 2)) 1/4) 2)

rewrite173.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

702×	`pow1_binary64`
653×	`add-log-exp_binary64`
653×	`log1p-expm1-u_binary64`
653×	`expm1-log1p-u_binary64`
636×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	176	14
2	1957	14

Stop Event

1×	node limit

Counts

2 → 48

Calls

Call 1

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

Outputs

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

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

simplify52.0ms (1%)

Algorithm

1×	egg-herbie

Rules

660×	`associate-l_binary64`
648×	`associate-r_binary64`
605×	`unswap-sqr_binary64`
318×	`fma-def_binary64`
227×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	28	420
1	72	372
2	180	276
3	494	216
4	1297	180
5	5963	180

Stop Event

1×	node limit

Counts

72 → 55

Calls

Call 1

Inputs
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x)))))) 2)
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x)))))) 2)

Outputs
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x)))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x))))
(pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2)))
(*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2))
(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x)))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2))) 2)
(pow.f64 (*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2)) 2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(*.f64 x (sqrt.f64 2))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x)))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2))) 2)
(pow.f64 (*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2)) 2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(*.f64 x (sqrt.f64 2))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x)))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2))) 2)
(pow.f64 (*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2)) 2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(*.f64 x (sqrt.f64 2))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 2 (log.f64 x))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x)))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2))) 2)
(pow.f64 (*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2)) 2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(*.f64 x (sqrt.f64 2))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x)))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2))) 2)
(pow.f64 (*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2)) 2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(*.f64 x (sqrt.f64 2))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x)))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2))) 2)
(pow.f64 (*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2)) 2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(*.f64 x (sqrt.f64 2))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x)))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2))) 2)
(pow.f64 (*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2)) 2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(*.f64 x (sqrt.f64 2))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 1 x)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x)))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2))) 2)
(pow.f64 (*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2)) 2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(*.f64 x (sqrt.f64 2))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x)))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2))) 2)
(pow.f64 (*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2)) 2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(*.f64 x (sqrt.f64 2))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x)))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2))) 2)
(pow.f64 (*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2)) 2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(*.f64 x (sqrt.f64 2))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x)))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2))) 2)
(pow.f64 (*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2)) 2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(*.f64 x (sqrt.f64 2))
(pow.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 2) (.f64 -2 (log.f64 (/.f64 -1 x)))))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 2) (*.f64 2 (log.f64 x)))) 2)
(pow.f64 (pow.f64 (exp.f64 1/4) (fma.f64 2 (log.f64 x) (log.f64 2))) 2)
(pow.f64 (*.f64 (pow.f64 2 1/4) (pow.f64 x 1/2)) 2)
(sqrt.f64 (.f64 2 (.f64 x x)))
(*.f64 x (sqrt.f64 2))

localize30.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2) 3/2)
	0.5b	(*.f64 x (sqrt.f64 2))
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	0.6b	(cbrt.f64 (*.f64 x (sqrt.f64 2)))

Compiler

Compiled 31 to 26 computations (16.1% saved)

series14.0ms (0.3%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	(pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2) 3/2)
4.0ms	x	@	inf	(pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2) 3/2)
3.0ms	x	@	0	(pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2) 3/2)
1.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2)
1.0ms	x	@	0	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2)

rewrite69.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

652×	`pow1_binary64`
616×	`add-log-exp_binary64`
615×	`log1p-expm1-u_binary64`
615×	`expm1-log1p-u_binary64`
600×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	191	15
2	2011	15

Stop Event

1×	node limit

Counts

2 → 50

Calls

Call 1

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

Outputs

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

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

simplify26.0ms (0.5%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

50 → 50

Calls

Call 1

Inputs

Outputs

localize34.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (pow.f64 2 1/4) (pow.f64 (.f64 (sqrt.f64 x) (pow.f64 2 1/8)) 2))
✓	0.1b	(*.f64 (sqrt.f64 x) (pow.f64 2 1/8))
✓	0.3b	(pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8)) 2)

Compiler

Compiled 39 to 31 computations (20.5% saved)

series11.0ms (0.2%)

Counts

3 → 12

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8)) 2)
2.0ms	x	@	0	(pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8)) 2)
2.0ms	x	@	-inf	(.f64 (pow.f64 2 1/4) (pow.f64 (.f64 (sqrt.f64 x) (pow.f64 2 1/8)) 2))
1.0ms	x	@	inf	(pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8)) 2)
1.0ms	x	@	-inf	(*.f64 (sqrt.f64 x) (pow.f64 2 1/8))

rewrite92.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

853×	`pow1_binary64`
791×	`add-log-exp_binary64`
791×	`log1p-expm1-u_binary64`
791×	`expm1-log1p-u_binary64`
768×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	39
1	234	22
2	2435	22

Stop Event

1×	node limit

Counts

3 → 50

Calls

Call 1

Inputs
(pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8)) 2)
(*.f64 (sqrt.f64 x) (pow.f64 2 1/8))
(.f64 (pow.f64 2 1/4) (pow.f64 (.f64 (sqrt.f64 x) (pow.f64 2 1/8)) 2))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 x (pow.f64 4 1/8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (pow.f64 4 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 2 1/8) (*.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (pow.f64 2 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8)) (*.f64 (sqrt.f64 x) (pow.f64 2 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (pow.f64 4 1/8)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 4 1/8) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (pow.f64 4 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (*.f64 x (sqrt.f64 2)))) (cbrt.f64 (*.f64 x (pow.f64 4 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (pow.f64 4 1/8))) (cbrt.f64 (*.f64 x (*.f64 x (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (pow.f64 4 1/8))) (*.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8))) (*.f64 (sqrt.f64 x) (pow.f64 2 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 2 1/16) (pow.f64 x 1/4)) (*.f64 (*.f64 (pow.f64 2 1/16) (pow.f64 x 1/4)) (*.f64 (sqrt.f64 x) (pow.f64 2 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8)) (*.f64 (pow.f64 2 1/16) (pow.f64 x 1/4))) (*.f64 (pow.f64 2 1/16) (pow.f64 x 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8)) (sqrt.f64 x)) (pow.f64 2 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8)) (cbrt.f64 (*.f64 x (pow.f64 4 1/8)))) (cbrt.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 x) (pow.f64 4 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (pow.f64 4 1/8)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (pow.f64 4 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (pow.f64 4 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (pow.f64 4 1/8))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (pow.f64 4 1/8)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 2 1/16) (pow.f64 x 1/4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 x (pow.f64 4 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 x)) (pow.f64 2 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3/2) (pow.f64 2 3/8)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 2 3/8) (pow.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 x) (pow.f64 2 1/8))))))))

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

simplify172.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

946×	`fma-def_binary64`
507×	`cube-prod_binary64`
439×	`distribute-rgt-neg-in_binary64`
429×	`fma-neg_binary64`
339×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	72
1	25	72
2	78	72
3	166	72
4	613	72
5	1281	72
6	2436	72
7	3799	72
8	4964	72
9	7212	72

Stop Event

1×

unsound

Counts

62 → 52

Calls

Call 1

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

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

eval301.0ms (5.6%)

Compiler: Compiled 3567 to 2832 computations (20.6% saved)

prune88.0ms (1.6%)

Pruning

13 alts after pruning (1 fresh and 12 done)

	Pruned	Kept	Total
New	307	1	308
Fresh	0	0	0
Picked	0	1	1
Done	0	11	11
Total	307	13	320

Error

0.1b

Counts

320 → 13

Alt Table

Click to see full alt table

Status	Error	Program
	1.5b	(pow.f64 (*.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 2)) 3/2)
✓	36.7b	(cbrt.f64 (pow.f64 (.f64 x (.f64 x 2)) 3/2))
✓	1.4b	(pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2) 3/2)
✓	33.8b	(.f64 (pow.f64 2 1/4) (pow.f64 (.f64 (sqrt.f64 x) (pow.f64 2 1/8)) 2))
✓	33.4b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
✓	26.9b	(pow.f64 (pow.f64 (.f64 x (.f64 x 2)) 1/4) 2)
✓	27.2b	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)
✓	32.9b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
✓	1.3b	(pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3/2)
✓	33.7b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	30.1b	(*.f64 x (neg.f64 (sqrt.f64 2)))
✓	33.0b	(*.f64 (sqrt.f64 2) x)
✓	26.8b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 115 to 96 computations (16.5% saved)

regimes79.0ms (1.5%)

Counts

19 → 1

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 x (neg.f64 (sqrt.f64 2)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(cbrt.f64 (pow.f64 (.f64 x (.f64 x 2)) 3/2))
(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)
(pow.f64 (pow.f64 (.f64 x (.f64 x 2)) 1/4) 2)
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
(pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3/2)
(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3))
(sqrt.f64 (.f64 (.f64 (.f64 2 x) (cbrt.f64 (.f64 x x))) (cbrt.f64 x)))
(.f64 (cbrt.f64 (.f64 x (sqrt.f64 2))) (cbrt.f64 (.f64 2 (.f64 x x))))
(pow.f64 (*.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 2)) 3/2)
(pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2) 3/2)
(sqrt.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3))
(.f64 (pow.f64 2 1/4) (pow.f64 (.f64 (sqrt.f64 x) (pow.f64 2 1/8)) 2))

Outputs
(pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3/2)

Calls

4 calls:

23.0ms	x
17.0ms	(*.f64 2 (pow.f64 x 2))
14.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
14.0ms	(pow.f64 x 2)

Results

Error	Segments	Branch
1.3b	1	`x`
1.3b	1	`(sqrt.f64 (*.f64 2 (pow.f64 x 2)))`
1.3b	1	`(*.f64 2 (pow.f64 x 2))`
1.3b	1	`(pow.f64 x 2)`

Compiler

Compiled 178 to 134 computations (24.7% saved)

regimes162.0ms (3%)

Counts

11 → 2

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 x (neg.f64 (sqrt.f64 2)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(cbrt.f64 (pow.f64 (.f64 x (.f64 x 2)) 3/2))
(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)
(pow.f64 (pow.f64 (.f64 x (.f64 x 2)) 1/4) 2)
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)

Outputs
(*.f64 x (neg.f64 (sqrt.f64 2)))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

Calls

4 calls:

60.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
52.0ms	(pow.f64 x 2)
28.0ms	(*.f64 2 (pow.f64 x 2))
15.0ms	x

Results

Error	Segments	Branch
0.4b	2	`x`
12.5b	3	`(sqrt.f64 (*.f64 2 (pow.f64 x 2)))`
12.5b	3	`(*.f64 2 (pow.f64 x 2))`
12.5b	3	`(pow.f64 x 2)`

Compiler

Compiled 96 to 75 computations (21.9% saved)

bsearch16.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
16.0ms	-1.355249987510172e-301	1.0402395157782813e-300

Compiler

Compiled 11 to 9 computations (18.2% saved)

regimes73.0ms (1.3%)

Counts

8 → 2

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 2) x)
(*.f64 x (neg.f64 (sqrt.f64 2)))
(sqrt.f64 (.f64 2 (.f64 x x)))
(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(cbrt.f64 (pow.f64 (.f64 x (.f64 x 2)) 3/2))
(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)
(pow.f64 (pow.f64 (.f64 x (.f64 x 2)) 1/4) 2)

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

Calls

4 calls:

33.0ms	(*.f64 2 (pow.f64 x 2))
13.0ms	x
12.0ms	(pow.f64 x 2)
12.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))

Results

Error	Segments	Branch
0.4b	2	`x`
12.5b	3	`(sqrt.f64 (*.f64 2 (pow.f64 x 2)))`
12.5b	3	`(*.f64 2 (pow.f64 x 2))`
12.5b	3	`(pow.f64 x 2)`

Compiler

Compiled 73 to 55 computations (24.7% saved)

bsearch17.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
17.0ms	-1.355249987510172e-301	1.0402395157782813e-300

Compiler

Compiled 11 to 9 computations (18.2% saved)

regimes45.0ms (0.8%)

Accuracy

Total -62.2b remaining (-13722.5%)

Threshold costs -62.2b (-13722.5%)

Counts

4 → 2

Calls

Call 1

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

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

Calls

4 calls:

19.0ms	(sqrt.f64 (*.f64 2 (pow.f64 x 2)))
8.0ms	(*.f64 2 (pow.f64 x 2))
8.0ms	(pow.f64 x 2)
7.0ms	x

Results

Error	Segments	Branch
0.5b	2	`x`
12.5b	3	`(sqrt.f64 (*.f64 2 (pow.f64 x 2)))`
12.5b	3	`(*.f64 2 (pow.f64 x 2))`
12.5b	3	`(pow.f64 x 2)`

Compiler

Compiled 41 to 32 computations (22% saved)

bsearch17.0ms (0.3%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
16.0ms	-1.355249987510172e-301	1.0402395157782813e-300

Compiler

Compiled 11 to 9 computations (18.2% saved)

simplify34.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	92
1	39	92
2	46	92
3	51	92
4	54	92
5	55	92

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3/2)
(if (<=.f64 x -1634989090363761/12064114410120881697684249086315471354100504503497011563593230129923244688987454586741947156276531487416450850028801674329627080999958126358211839195533902044386710183415792069701368078118158360793576698212191168580174892152827542937880954483101341506291035205862448784848059094859987648259778470316291228729945882624) (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) x)))
(if (<=.f64 x -1634989090363761/12064114410120881697684249086315471354100504503497011563593230129923244688987454586741947156276531487416450850028801674329627080999958126358211839195533902044386710183415792069701368078118158360793576698212191168580174892152827542937880954483101341506291035205862448784848059094859987648259778470316291228729945882624) (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x)))
(if (<=.f64 x -1634989090363761/12064114410120881697684249086315471354100504503497011563593230129923244688987454586741947156276531487416450850028801674329627080999958126358211839195533902044386710183415792069701368078118158360793576698212191168580174892152827542937880954483101341506291035205862448784848059094859987648259778470316291228729945882624) (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) x)

Outputs
(pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3/2)
(if (<=.f64 x -1634989090363761/12064114410120881697684249086315471354100504503497011563593230129923244688987454586741947156276531487416450850028801674329627080999958126358211839195533902044386710183415792069701368078118158360793576698212191168580174892152827542937880954483101341506291035205862448784848059094859987648259778470316291228729945882624) (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 (pow.f64 2 1/4) (*.f64 (pow.f64 2 1/4) x)))
(if (<=.f64 x -1634989090363761/12064114410120881697684249086315471354100504503497011563593230129923244688987454586741947156276531487416450850028801674329627080999958126358211839195533902044386710183415792069701368078118158360793576698212191168580174892152827542937880954483101341506291035205862448784848059094859987648259778470316291228729945882624) (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 (pow.f64 2 1/4) (*.f64 x (pow.f64 2 1/4))))
(if (<=.f64 x -1634989090363761/12064114410120881697684249086315471354100504503497011563593230129923244688987454586741947156276531487416450850028801674329627080999958126358211839195533902044386710183415792069701368078118158360793576698212191168580174892152827542937880954483101341506291035205862448784848059094859987648259778470316291228729945882624) (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x)))
(if (<=.f64 x -1634989090363761/12064114410120881697684249086315471354100504503497011563593230129923244688987454586741947156276531487416450850028801674329627080999958126358211839195533902044386710183415792069701368078118158360793576698212191168580174892152827542937880954483101341506291035205862448784848059094859987648259778470316291228729945882624) (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 2) x))
(if (<=.f64 x -1634989090363761/12064114410120881697684249086315471354100504503497011563593230129923244688987454586741947156276531487416450850028801674329627080999958126358211839195533902044386710183415792069701368078118158360793576698212191168580174892152827542937880954483101341506291035205862448784848059094859987648259778470316291228729945882624) (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))

Compiler

Compiled 65 to 52 computations (20% saved)

soundness570.0ms (10.5%)

Algorithm

3×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
1082×	`sqr-pow_binary64`
964×	`fma-def_binary64`
617×	`cube-prod_binary64`
617×	`cube-prod_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	9	164
1	20	164
2	43	164
3	83	164
4	205	164
5	632	164
6	988	164
7	1635	164
8	2038	164
9	2907	164
10	3744	164
11	4611	164
12	5738	164
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
1×	node limit
1×	node limit

Compiler

Compiled 53 to 43 computations (18.9% saved)

end48.0ms (0.9%)

Compiler: Compiled 61 to 48 computations (21.3% saved)

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

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

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