Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 8 to 6 computations (25% saved)

sample1.3s (29.9%)

Results

1.2s	8256×	body	256	valid
0.0ms	3×	body	256	invalid

preprocess16.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	10	9
2	11	9
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 8 to 6 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	10	9
2	11	9

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

28.8b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	28.8b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	27.8b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 17 to 11 computations (35.3% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite43.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

527×	`pow1_binary64`
508×	`add-sqr-sqrt_binary64`
488×	`add-log-exp_binary64`
488×	`log1p-expm1-u_binary64`
488×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	122	6
2	1374	6

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

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

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

Outputs

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

simplify11.0ms (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

36 → 26

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))

eval6.0ms (0.1%)

Compiler: Compiled 208 to 159 computations (23.6% saved)

prune14.0ms (0.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	19	7	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	19	8	27

Error

0.1b

Counts

27 → 8

Alt Table

Click to see full alt table

Status	Error	Program
	33.0b	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
▶	30.5b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	29.2b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 x x)))))
▶	33.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	51.5b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
	33.3b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
✓	28.8b	(sqrt.f64 (.f64 (.f64 2 x) x))
▶	32.5b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 129 to 103 computations (20.2% saved)

localize25.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 x x)))))
✓	0.4b	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)
✓	14.3b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2))
✓	28.7b	(cbrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 58 to 34 computations (41.4% saved)

series54.0ms (1.3%)

Counts

4 → 12

Calls

12 calls:

Time	Variable		Point	Expression
46.0ms	x	@	0	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 x x)))))
1.0ms	x	@	0	(cbrt.f64 (.f64 2 (.f64 x x)))
1.0ms	x	@	inf	(cbrt.f64 (.f64 2 (.f64 x x)))
1.0ms	x	@	0	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)
1.0ms	x	@	inf	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 x x)))))

rewrite67.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

681×	`pow1_binary64`
632×	`add-log-exp_binary64`
632×	`log1p-expm1-u_binary64`
632×	`expm1-log1p-u_binary64`
613×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	39
1	206	33
2	1918	33

Stop Event

1×	node limit

Counts

4 → 91

Calls

Call 1

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

simplify12.0ms (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

103 → 66

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))

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

series2.0ms (0.1%)

Counts

1 → 0

Calls

3 calls:

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

rewrite38.0ms (0.9%)

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

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 12 to 8 computations (33.3% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite38.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

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

Outputs

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

simplify12.0ms (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	96
1	12	96
2	25	96
3	29	96
4	33	96
5	51	96
6	73	96
7	84	96
8	96	96
9	121	96

Stop Event

1×

saturated

Counts

25 → 15

Calls

Call 1

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

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

localize8.0ms (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))

rewrite44.0ms (1.1%)

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)))))))

simplify18.0ms (0.4%)

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))

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (*.f64 (sqrt.f64 2) x) 3)
	0.4b	(*.f64 (sqrt.f64 2) x)
✓	38.1b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))

Compiler

Compiled 23 to 19 computations (17.4% saved)

series6.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite52.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	170	15
2	1638	15

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

Outputs

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

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

simplify179.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	244
1	36	244
2	103	244
3	276	244
4	783	244
5	1358	244
6	2805	244
7	2927	244
8	3219	244
9	3491	244
10	3718	244
11	3949	244
12	4241	244
13	4590	244
14	5420	244
15	5945	244
16	6627	244
17	6935	244
18	7303	244
19	7633	244

Stop Event

1×	node limit

Counts

78 → 58

Calls

Call 1

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

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

eval98.0ms (2.3%)

Compiler: Compiled 2811 to 2120 computations (24.6% saved)

prune42.0ms (1%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	209	4	213
Fresh	1	1	2
Picked	1	0	1
Done	1	4	5
Total	212	9	221

Error

0.1b

Counts

221 → 9

Alt Table

Click to see full alt table

Status	Error	Program
▶	32.4b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
▶	33.3b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
▶	44.0b	(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
✓	33.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	51.5b	(cbrt.f64 (.f64 (.f64 (.f64 2 (.f64 x x)) (sqrt.f64 2)) x))
✓	30.5b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	28.8b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	32.5b	(*.f64 (sqrt.f64 2) x)
▶	29.2b	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)

Compiler

Compiled 136 to 110 computations (19.1% saved)

localize14.0ms (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)
	28.7b	(cbrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 26 to 14 computations (46.2% saved)

series5.0ms (0.1%)

Counts

2 → 12

Calls

6 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)
1.0ms	x	@	inf	(.f64 2 (.f64 x x))
1.0ms	x	@	0	(.f64 2 (.f64 x x))

rewrite65.0ms (1.6%)

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	19
1	166	13
2	1833	13

Stop Event

1×	node limit

Counts

2 → 32

Calls

Call 1

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

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

simplify180.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	84
1	11	84
2	22	84
3	43	84
4	105	84
5	329	84
6	1259	84
7	2132	84
8	2296	84
9	2480	84
10	2688	84
11	2984	84
12	3379	84
13	3860	84
14	4426	84
15	5118	84
16	5951	84
17	6343	84
18	6631	84
19	6911	84
20	6985	84
21	7019	84
22	7960	84

Stop Event

1×	node limit

Counts

44 → 34

Calls

Call 1

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

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

localize11.0ms (0.3%)

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)

series39.0ms (0.9%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
36.0ms	x	@	0	(*.f64 (pow.f64 2 1/4) x)
1.0ms	x	@	-inf	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
0.0ms	x	@	inf	(*.f64 (pow.f64 2 1/4) x)
0.0ms	x	@	-inf	(*.f64 (pow.f64 2 1/4) x)
0.0ms	x	@	inf	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

rewrite50.0ms (1.2%)

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 (0.2%)

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

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)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 2 (.f64 x x))
✓	0.1b	(.f64 (.f64 (.f64 2 (.f64 x x)) (sqrt.f64 2)) x)
✓	0.2b	(.f64 (.f64 2 (*.f64 x x)) (sqrt.f64 2))
✓	38.1b	(cbrt.f64 (.f64 (.f64 (.f64 2 (.f64 x x)) (sqrt.f64 2)) x))

Compiler

Compiled 42 to 25 computations (40.5% saved)

series29.0ms (0.7%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
23.0ms	x	@	-inf	(cbrt.f64 (.f64 (.f64 (.f64 2 (.f64 x x)) (sqrt.f64 2)) x))
2.0ms	x	@	0	(cbrt.f64 (.f64 (.f64 (.f64 2 (.f64 x x)) (sqrt.f64 2)) x))
1.0ms	x	@	inf	(cbrt.f64 (.f64 (.f64 (.f64 2 (.f64 x x)) (sqrt.f64 2)) x))
1.0ms	x	@	0	(.f64 (.f64 (.f64 2 (.f64 x x)) (sqrt.f64 2)) x)
1.0ms	x	@	0	(.f64 (.f64 2 (*.f64 x x)) (sqrt.f64 2))

rewrite98.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

769×	`pow1_binary64`
713×	`add-log-exp_binary64`
713×	`log1p-expm1-u_binary64`
713×	`expm1-log1p-u_binary64`
694×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	44
1	184	27
2	2183	27

Stop Event

1×	node limit

Counts

3 → 56

Calls

Call 1

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

Outputs

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

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

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

simplify176.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

1107×	`fma-def_binary64`
496×	`distribute-lft-neg-in_binary64`
495×	`distribute-rgt-neg-in_binary64`
468×	`associate-r_binary64`
413×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	452
1	64	452
2	175	452
3	533	452
4	1379	452
5	2217	452
6	3472	452
7	5109	452
8	6798	452
9	7785	452

Stop Event

1×	node limit

Counts

92 → 64

Calls

Call 1

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

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

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (*.f64 (sqrt.f64 2) x))
✓	0.3b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
	0.4b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 21 to 17 computations (19% saved)

series7.0ms (0.2%)

Counts

2 → 0

Calls

6 calls:

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

rewrite53.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	144	14
2	1322	14

Stop Event

1×	node limit

Counts

2 → 50

Calls

Call 1

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

Outputs

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

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

simplify155.0ms (3.7%)

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

localize27.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
✓	14.3b	(sqrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))))
✓	28.3b	(cbrt.f64 (*.f64 4 (pow.f64 x 4)))
	28.7b	(cbrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 61 to 41 computations (32.8% saved)

series22.0ms (0.5%)

Counts

3 → 12

Calls

9 calls:

Time	Variable		Point	Expression
16.0ms	x	@	0	(sqrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))))
2.0ms	x	@	0	(.f64 (sqrt.f64 (cbrt.f64 (.f64 4 (pow.f64 x 4)))) (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))))
1.0ms	x	@	0	(cbrt.f64 (*.f64 4 (pow.f64 x 4)))
1.0ms	x	@	inf	(sqrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))))
1.0ms	x	@	inf	(cbrt.f64 (*.f64 4 (pow.f64 x 4)))

rewrite64.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

875×	`pow1_binary64`
813×	`add-log-exp_binary64`
813×	`log1p-expm1-u_binary64`
813×	`expm1-log1p-u_binary64`
791×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	42
1	261	24
2	2916	24

Stop Event

1×	node limit

Counts

3 → 73

Calls

Call 1

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

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (cbrt.f64 (*.f64 x (*.f64 x 2)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (*.f64 x 2))) 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 1 (cbrt.f64 (*.f64 x (*.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (*.f64 x 2)))) (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (*.f64 x 2)))) (*.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 2) (pow.f64 (cbrt.f64 x) 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 4 (pow.f64 x 4)))) (cbrt.f64 (cbrt.f64 (*.f64 x (*.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (cbrt.f64 (*.f64 16 (pow.f64 x 8))))) (sqrt.f64 (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 4)) (sqrt.f64 (cbrt.f64 (pow.f64 x 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (*.f64 x (*.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x 2) 1/3) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (cbrt.f64 (*.f64 x (*.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 4) 1/2) (pow.f64 (cbrt.f64 (pow.f64 x 4)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 16 (pow.f64 x 8)))) 1/2) (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) (cbrt.f64 (cbrt.f64 (*.f64 x (*.f64 x 2))))) (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 4 (pow.f64 x 4)) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 4 (pow.f64 x 4))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 x 2)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (*.f64 x 2)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (cbrt.f64 (*.f64 x (*.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (*.f64 x (*.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 x (*.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (*.f64 x (*.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (*.f64 x (*.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (*.f64 x (*.f64 x 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 (*.f64 x 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (*.f64 x 2))) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.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 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))))))))

simplify15.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	164
1	17	164
2	30	164
3	34	164
4	38	164
5	56	164
6	78	164
7	89	164
8	101	164
9	126	164

Stop Event

1×

saturated

Counts

85 → 76

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 -1 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(.f64 -1 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(.f64 -1 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(.f64 -1 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 4))) x))

Outputs
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x)
(.f64 -1 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(neg.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(neg.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(neg.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 (*.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(neg.f64 (.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) x))
(.f64 (sqrt.f64 (.f64 (cbrt.f64 2) (cbrt.f64 4))) (neg.f64 x))

eval199.0ms (4.7%)

Compiler: Compiled 4170 to 3264 computations (21.7% saved)

prune51.0ms (1.2%)

Pruning

12 alts after pruning (4 fresh and 8 done)

	Pruned	Kept	Total
New	330	4	334
Fresh	0	0	0
Picked	1	0	1
Done	0	8	8
Total	331	12	343

Error

0.0b

Counts

343 → 12

Alt Table

Click to see full alt table

Status	Error	Program
✓	32.4b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
✓	33.3b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
✓	30.5b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	29.1b	(pow.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) 2)
✓	32.5b	(*.f64 (sqrt.f64 2) x)
▶	1.5b	(pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 2) 3/2)
✓	33.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	1.3b	(pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3/2)
✓	51.5b	(cbrt.f64 (.f64 (.f64 (.f64 2 (.f64 x x)) (sqrt.f64 2)) x))
✓	28.8b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	29.2b	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)
▶	1.5b	(pow.f64 (*.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 2)) 3/2)

Compiler

Compiled 105 to 86 computations (18.1% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 2 (.f64 x x))
✓	0.1b	(sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))
✓	0.5b	(pow.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) 2)
✓	27.8b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 33 to 18 computations (45.5% saved)

series4.0ms (0.1%)

Counts

3 → 12

Calls

9 calls:

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

rewrite64.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

570×	`pow1_binary64`
527×	`add-log-exp_binary64`
527×	`log1p-expm1-u_binary64`
527×	`expm1-log1p-u_binary64`
511×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	29
1	165	20
2	1598	20

Stop Event

1×	node limit

Counts

3 → 75

Calls

Call 1

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

simplify13.0ms (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

87 → 54

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))

localize17.0ms (0.4%)

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)
✓	0.5b	(cbrt.f64 (*.f64 2 x))
✓	0.6b	(cbrt.f64 x)

Compiler

Compiled 29 to 19 computations (34.5% saved)

series10.0ms (0.2%)

Counts

4 → 0

Calls

12 calls:

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

rewrite77.0ms (1.8%)

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	30
1	187	27
2	2119	27

Stop Event

1×	node limit

Counts

4 → 69

Calls

Call 1

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

69 → 69

Calls

Call 1

Inputs

Outputs

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (*.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 2)) 3/2)
✓	0.5b	(pow.f64 (cbrt.f64 x) 2)
	0.6b	(cbrt.f64 x)
✓	1.0b	(cbrt.f64 2)

Compiler

Compiled 28 to 20 computations (28.6% saved)

series5.0ms (0.1%)

Counts

3 → 0

Calls

6 calls:

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

rewrite122.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

712×	`pow1_binary64`
666×	`add-log-exp_binary64`
666×	`log1p-expm1-u_binary64`
666×	`expm1-log1p-u_binary64`
646×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	187	15
2	2018	15

Stop Event

1×	node limit

Counts

3 → 48

Calls

Call 1

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

Outputs

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

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

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

48 → 48

Calls

Call 1

Inputs

Outputs

localize19.0ms (0.5%)

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)
✓	0.4b	(*.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)

series8.0ms (0.2%)

Counts

4 → 12

Calls

12 calls:

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

rewrite77.0ms (1.8%)

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	31
1	191	29
2	2011	29

Stop Event

1×	node limit

Counts

4 → 87

Calls

Call 1

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

simplify8.0ms (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

99 → 78

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)

eval112.0ms (2.7%)

Compiler: Compiled 3313 to 2610 computations (21.2% saved)

prune39.0ms (0.9%)

Pruning

12 alts after pruning (3 fresh and 9 done)

	Pruned	Kept	Total
New	278	3	281
Fresh	0	0	0
Picked	1	0	1
Done	2	9	11
Total	281	12	293

Error

0.0b

Counts

293 → 12

Alt Table

Click to see full alt table

Status	Error	Program
	1.4b	(pow.f64 (*.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 2 1/3)) 3/2)
✓	33.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	32.4b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
✓	33.3b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
✓	1.5b	(pow.f64 (*.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 2)) 3/2)
	31.3b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) (neg.f64 x))) 2)
✓	1.3b	(pow.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x)) 3/2)
	29.1b	(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 1/4) 2)
✓	30.5b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	28.8b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	32.5b	(*.f64 (sqrt.f64 2) x)
✓	29.2b	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 3/2)

Compiler

Compiled 103 to 86 computations (16.5% saved)

regimes30.0ms (0.7%)

Counts

19 → 1

Calls

Call 1

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

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

Calls

3 calls:

10.0ms	x
8.0ms	(.f64 (.f64 2 x) x)
6.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))

Results

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

Compiler

Compiled 182 to 136 computations (25.3% saved)

regimes49.0ms (1.2%)

Counts

13 → 2

Calls

Call 1

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

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

Calls

3 calls:

17.0ms	x
14.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))
14.0ms	(.f64 (.f64 2 x) x)

Results

Error	Segments	Branch
0.4b	2	`x`
14.2b	3	`(sqrt.f64 (.f64 (.f64 2 x) x))`
14.2b	3	`(.f64 (.f64 2 x) x)`

Compiler

Compiled 113 to 84 computations (25.7% saved)

bsearch18.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
18.0ms	-2.263785011636803e-307	6.775823551664205e-305

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes25.0ms (0.6%)

Accuracy

Total -62.2b remaining (-14599.6%)

Threshold costs -62.2b (-14599.6%)

Counts

3 → 2

Calls

Call 1

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

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

Calls

3 calls:

8.0ms	(.f64 (.f64 2 x) x)
8.0ms	x
8.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))

Results

Error	Segments	Branch
0.4b	2	`x`
14.2b	3	`(sqrt.f64 (.f64 (.f64 2 x) x))`
14.2b	3	`(.f64 (.f64 2 x) x)`

Compiler

Compiled 31 to 22 computations (29% saved)

bsearch16.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
16.0ms	-2.263785011636803e-307	6.775823551664205e-305

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`*-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	21	65
1	31	65
2	38	65
3	43	65
4	46	65
5	47	65

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 -2863719920991283/12650140831706913647030959169932331690597290610258882397306334876714396222999709180747523981339820280949192366519800744461863046086612092304188337496296156870094839017285397585279181733880826021327485479904546566785125467714043293663631459728072472271300628532022423097020838413451906408261645469290375391456731733818343424) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x)))
(if (<=.f64 x -2863719920991283/12650140831706913647030959169932331690597290610258882397306334876714396222999709180747523981339820280949192366519800744461863046086612092304188337496296156870094839017285397585279181733880826021327485479904546566785125467714043293663631459728072472271300628532022423097020838413451906408261645469290375391456731733818343424) (.f64 (sqrt.f64 2) (neg.f64 x)) (.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 -2863719920991283/12650140831706913647030959169932331690597290610258882397306334876714396222999709180747523981339820280949192366519800744461863046086612092304188337496296156870094839017285397585279181733880826021327485479904546566785125467714043293663631459728072472271300628532022423097020838413451906408261645469290375391456731733818343424) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x)))
(if (<=.f64 x -2863719920991283/12650140831706913647030959169932331690597290610258882397306334876714396222999709180747523981339820280949192366519800744461863046086612092304188337496296156870094839017285397585279181733880826021327485479904546566785125467714043293663631459728072472271300628532022423097020838413451906408261645469290375391456731733818343424) (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x)))
(if (<=.f64 x -2863719920991283/12650140831706913647030959169932331690597290610258882397306334876714396222999709180747523981339820280949192366519800744461863046086612092304188337496296156870094839017285397585279181733880826021327485479904546566785125467714043293663631459728072472271300628532022423097020838413451906408261645469290375391456731733818343424) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 2) x))
(if (<=.f64 x -2863719920991283/12650140831706913647030959169932331690597290610258882397306334876714396222999709180747523981339820280949192366519800744461863046086612092304188337496296156870094839017285397585279181733880826021327485479904546566785125467714043293663631459728072472271300628532022423097020838413451906408261645469290375391456731733818343424) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 x (sqrt.f64 2)))
(if (<=.f64 x -2863719920991283/12650140831706913647030959169932331690597290610258882397306334876714396222999709180747523981339820280949192366519800744461863046086612092304188337496296156870094839017285397585279181733880826021327485479904546566785125467714043293663631459728072472271300628532022423097020838413451906408261645469290375391456731733818343424) (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))

Compiler

Compiled 46 to 36 computations (21.7% saved)

soundness10.0ms (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

Compiler

Compiled 19 to 16 computations (15.8% saved)

end39.0ms (0.9%)

Compiler: Compiled 43 to 33 computations (23.3% 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	11	164
1	17	164
2	30	164
3	34	164
4	38	164
5	56	164
6	78	164
7	89	164
8	101	164
9	126	164

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	11	164
1	17	164
2	30	164
3	34	164
4	38	164
5	56	164
6	78	164
7	89	164
8	101	164
9	126	164

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	11	164
1	17	164
2	30	164
3	34	164
4	38	164
5	56	164
6	78	164
7	89	164
8	101	164
9	126	164