Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 8 to 6 computations (25% saved)

sample1.3s (31.6%)

Results

1.2s	8256×	body	256	valid
0.0ms	2×	body	256	infinite

Bogosity

preprocess18.0ms (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 (0.2%)

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)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	27.7b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 17 to 11 computations (35.3% saved)

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite42.0ms (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)))))))

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

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))

eval14.0ms (0.3%)

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

prune18.0ms (0.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	20	6	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	7	27

Error

0.1b

Counts

27 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	28.4b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
▶	28.2b	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
▶	35.5b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	28.8b	(sqrt.f64 (.f64 (.f64 2 x) x))
▶	27.7b	(*.f64 (sqrt.f64 2) x)
	29.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 x x)))))
▶	28.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Compiler

Compiled 113 to 89 computations (21.2% saved)

localize10.0ms (0.3%)

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)

series3.0ms (0.1%)

Counts

1 → 0

Calls

3 calls:

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

rewrite52.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

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

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

Outputs

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

simplify12.0ms (0.3%)

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

localize15.0ms (0.4%)

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))

rewrite39.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

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

Outputs

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

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))

localize9.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 12 computations (36.8% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite45.0ms (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)))))))

simplify24.0ms (0.6%)

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
	0.4b	(*.f64 (sqrt.f64 2) x)
✓	0.6b	(cbrt.f64 (*.f64 (sqrt.f64 2) x))
✓	0.7b	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)

Compiler

Compiled 22 to 18 computations (18.2% saved)

series11.0ms (0.3%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	x	@	0	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
2.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
1.0ms	x	@	inf	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
1.0ms	x	@	-inf	(cbrt.f64 (*.f64 (sqrt.f64 2) x))
0.0ms	x	@	inf	(cbrt.f64 (*.f64 (sqrt.f64 2) x))

rewrite51.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 52

Calls

Call 1

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

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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

52 → 52

Calls

Call 1

Inputs

Outputs

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (*.f64 (sqrt.f64 2) x))
✓	0.3b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
	0.4b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 21 to 17 computations (19% saved)

series6.0ms (0.1%)

Counts

2 → 0

Calls

6 calls:

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

rewrite45.0ms (1.1%)

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))))))))

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

50 → 50

Calls

Call 1

Inputs

Outputs

eval48.0ms (1.2%)

Compiler: Compiled 1702 to 1385 computations (18.6% saved)

prune25.0ms (0.6%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	173	4	177
Fresh	1	0	1
Picked	1	0	1
Done	1	4	5
Total	176	8	184

Error

0.1b

Counts

184 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	27.7b	(*.f64 (sqrt.f64 2) x)
▶	27.7b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
▶	29.3b	(pow.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3)
▶	29.1b	(pow.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) 2)
✓	28.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	28.3b	(pow.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x)) 3)
✓	35.5b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	28.8b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize12.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 21 to 18 computations (14.3% saved)

series55.0ms (1.3%)

Counts

2 → 12

Calls

6 calls:

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

rewrite47.0ms (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) x)
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

Outputs

((#(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)))))))

((#(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))))))))

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)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	0.1b	(sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x))))
✓	0.7b	(pow.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3)
✓	28.5b	(cbrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 34 to 19 computations (44.1% saved)

series34.0ms (0.8%)

Counts

4 → 12

Calls

12 calls:

Time	Variable		Point	Expression
22.0ms	x	@	0	(pow.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3)
6.0ms	x	@	inf	(.f64 2 (.f64 x x))
1.0ms	x	@	inf	(pow.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3)
1.0ms	x	@	0	(cbrt.f64 (.f64 2 (.f64 x x)))
1.0ms	x	@	-inf	(pow.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3)

rewrite68.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

702×	`pow1_binary64`
659×	`add-log-exp_binary64`
658×	`log1p-expm1-u_binary64`
658×	`expm1-log1p-u_binary64`
641×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	39
1	189	30
2	1997	30

Stop Event

1×	node limit

Counts

4 → 90

Calls

Call 1

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

simplify173.0ms (4.2%)

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

102 → 92

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))

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 2 (.f64 x x))
✓	0.2b	(sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))
✓	0.5b	(pow.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) 2)
✓	27.7b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 33 to 18 computations (45.5% saved)

series5.0ms (0.1%)

Counts

3 → 12

Calls

9 calls:

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

rewrite57.0ms (1.4%)

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))

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)
✓	0.7b	(pow.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x)) 3)

Compiler

Compiled 25 to 19 computations (24% saved)

series4.0ms (0.1%)

Counts

3 → 0

Calls

9 calls:

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

rewrite65.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

708×	`pow1_binary64`
664×	`add-log-exp_binary64`
663×	`log1p-expm1-u_binary64`
663×	`expm1-log1p-u_binary64`
644×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	188	17
2	1959	17

Stop Event

1×	node limit

Counts

3 → 59

Calls

Call 1

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

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

59 → 59

Calls

Call 1

Inputs

Outputs

eval209.0ms (5.1%)

Compiler: Compiled 2702 to 2158 computations (20.1% saved)

prune37.0ms (0.9%)

Pruning

12 alts after pruning (5 fresh and 7 done)

	Pruned	Kept	Total
New	238	5	243
Fresh	0	0	0
Picked	0	1	1
Done	1	6	7
Total	239	12	251

Error

0.0b

Counts

251 → 12

Alt Table

Click to see full alt table

Status	Error	Program
✓	27.7b	(*.f64 (sqrt.f64 2) x)
✓	27.7b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
✓	29.3b	(pow.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3)
▶	36.3b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) (neg.f64 x))) 2)
▶	29.0b	(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 (*.f64 x x) (sqrt.f64 2))))
▶	1.4b	(pow.f64 (fabs.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3)
✓	28.3b	(pow.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x)) 3)
▶	29.1b	(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 1/4) 2)
✓	35.5b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	28.8b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	28.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	1.4b	(pow.f64 (sqrt.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x))) 3)

Compiler

Compiled 157 to 131 computations (16.6% saved)

localize28.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x))
	0.6b	(cbrt.f64 x)
✓	0.6b	(cbrt.f64 (*.f64 2 x))
✓	0.7b	(pow.f64 (sqrt.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x))) 3)

Compiler

Compiled 38 to 25 computations (34.2% saved)

series6.0ms (0.2%)

Counts

3 → 0

Calls

9 calls:

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

rewrite82.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

809×	`pow1_binary64`
757×	`add-log-exp_binary64`
756×	`log1p-expm1-u_binary64`
756×	`expm1-log1p-u_binary64`
735×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	208	24
2	2216	24

Stop Event

1×	node limit

Counts

3 → 65

Calls

Call 1

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

Outputs

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

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

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

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

65 → 65

Calls

Call 1

Inputs

Outputs

localize16.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(.f64 2 (.f64 x x))
✓	0.5b	(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 1/4) 2)
✓	28.4b	(pow.f64 (.f64 2 (.f64 x x)) 1/4)

Compiler

Compiled 28 to 16 computations (42.9% saved)

series172.0ms (4.2%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
153.0ms	x	@	-inf	(pow.f64 (.f64 2 (.f64 x x)) 1/4)
9.0ms	x	@	0	(pow.f64 (.f64 2 (.f64 x x)) 1/4)
8.0ms	x	@	inf	(pow.f64 (.f64 2 (.f64 x x)) 1/4)
1.0ms	x	@	0	(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 1/4) 2)
1.0ms	x	@	inf	(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 1/4) 2)

rewrite51.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

665×	`pow1_binary64`
619×	`add-log-exp_binary64`
619×	`log1p-expm1-u_binary64`
619×	`expm1-log1p-u_binary64`
601×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	176	14
2	1945	14

Stop Event

1×	node limit

Counts

2 → 48

Calls

Call 1

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

Outputs

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

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

simplify53.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×	node limit

Counts

72 → 54

Calls

Call 1

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

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

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (*.f64 (sqrt.f64 2) (neg.f64 x)))
✓	0.2b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) (neg.f64 x))) 2)
	0.4b	(*.f64 (sqrt.f64 2) (neg.f64 x))

Compiler

Compiled 26 to 18 computations (30.8% saved)

series5.0ms (0.1%)

Counts

2 → 0

Calls

6 calls:

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

rewrite55.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

523×	`pow1_binary64`
505×	`add-sqr-sqrt_binary64`
486×	`add-log-exp_binary64`
485×	`log1p-expm1-u_binary64`
485×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	169	14
2	1725	14

Stop Event

1×	node limit

Counts

2 → 55

Calls

Call 1

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

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

55 → 55

Calls

Call 1

Inputs

Outputs

localize17.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 (*.f64 x x) (sqrt.f64 2))))
✓	0.3b	(.f64 (.f64 x x) (sqrt.f64 2))
✓	27.8b	(sqrt.f64 (.f64 (.f64 x x) (sqrt.f64 2)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

series5.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite66.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

795×	`pow1_binary64`
736×	`add-log-exp_binary64`
736×	`log1p-expm1-u_binary64`
736×	`expm1-log1p-u_binary64`
716×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	207	22
2	2269	22

Stop Event

1×	node limit

Counts

3 → 51

Calls

Call 1

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

Outputs

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

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

simplify126.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

706×	`distribute-lft-neg-in_binary64`
689×	`distribute-rgt-neg-in_binary64`
598×	`fma-def_binary64`
454×	`unswap-sqr_binary64`
441×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	388
1	37	388
2	95	388
3	272	388
4	1146	388
5	2190	388
6	3858	388
7	5310	388
8	6649	388
9	7473	388

Stop Event

1×	node limit

Counts

87 → 60

Calls

Call 1

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

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

localize19.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 x (sqrt.f64 2))
✓	0.6b	(cbrt.f64 (*.f64 x (sqrt.f64 2)))
✓	0.7b	(pow.f64 (fabs.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3)

Compiler

Compiled 29 to 24 computations (17.2% saved)

series5.0ms (0.1%)

Counts

3 → 24

Calls

9 calls:

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

rewrite58.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

610×	`pow1_binary64`
576×	`add-log-exp_binary64`
575×	`log1p-expm1-u_binary64`
575×	`expm1-log1p-u_binary64`
563×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	34
1	188	20
2	2061	20

Stop Event

1×	node limit

Counts

3 → 67

Calls

Call 1

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

Outputs

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

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

simplify112.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

1513×	`fma-def_binary64`
338×	`sqr-pow_binary64`
335×	`distribute-lft-neg-in_binary64`
334×	`distribute-rgt-neg-in_binary64`
320×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	340
1	48	300
2	99	192
3	271	192
4	1179	192
5	2206	192
6	3229	192
7	4259	192
8	5852	192
9	7907	192

Stop Event

1×	node limit

Counts

91 → 64

Calls

Call 1

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

eval210.0ms (5.1%)

Compiler: Compiled 3965 to 3147 computations (20.6% saved)

prune61.0ms (1.5%)

Pruning

10 alts after pruning (3 fresh and 7 done)

	Pruned	Kept	Total
New	343	3	346
Fresh	0	0	0
Picked	1	0	1
Done	4	7	11
Total	348	10	358

Error

0.0b

Counts

358 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	27.7b	(*.f64 (sqrt.f64 2) x)
✓	29.3b	(pow.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3)
✓	28.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	31.3b	(exp.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 x x)))))
✓	29.1b	(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 1/4) 2)
✓	35.5b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	28.8b	(sqrt.f64 (.f64 (.f64 2 x) x))
	35.5b	(.f64 (pow.f64 2 1/4) (.f64 x (neg.f64 (sqrt.f64 (sqrt.f64 2)))))
	27.7b	(*.f64 (pow.f64 (pow.f64 2 1/4) 2) x)
✓	36.3b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) (neg.f64 x))) 2)

Compiler

Compiled 83 to 68 computations (18.1% saved)

regimes64.0ms (1.6%)

Counts

19 → 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 (pow.f64 (pow.f64 2 1/4) 2) x)
(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
(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))
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(exp.f64 (log.f64 (sqrt.f64 (.f64 2 (.f64 x x)))))
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) (neg.f64 x))) 2)
(pow.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3)
(pow.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) 2)
(.f64 (pow.f64 2 1/4) (.f64 x (neg.f64 (sqrt.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 (*.f64 x x) (sqrt.f64 2))))
(pow.f64 (fabs.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3)
(pow.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x)) 3)
(pow.f64 (sqrt.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x))) 3)
(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 x x)))))

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

Calls

3 calls:

18.0ms	x
7.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))
7.0ms	(.f64 (.f64 2 x) x)

Results

Error	Segments	Branch
0.3b	2	`x`
1.4b	1	`(sqrt.f64 (.f64 (.f64 2 x) x))`
1.4b	1	`(.f64 (.f64 2 x) x)`

Compiler

Compiled 175 to 132 computations (24.6% saved)

bsearch62.0ms (1.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
61.0ms	-8.071019112801398e-297	1.229338635343958e-286

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes27.0ms (0.7%)

Accuracy

Total -62.3b remaining (-14917.3%)

Threshold costs -62.3b (-14917.3%)

Counts

4 → 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 (pow.f64 (pow.f64 2 1/4) 2) x)

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

Calls

3 calls:

10.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))
8.0ms	(.f64 (.f64 2 x) x)
7.0ms	x

Results

Error	Segments	Branch
0.4b	2	`x`
12.2b	3	`(sqrt.f64 (.f64 (.f64 2 x) x))`
12.2b	3	`(.f64 (.f64 2 x) x)`

Compiler

Compiled 38 to 28 computations (26.3% saved)

bsearch16.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
16.0ms	-8.071019112801398e-297	1.229338635343958e-286

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-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	16	51
1	25	51
2	32	51
3	37	51
4	40	51
5	41	51

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs

(if (<=.f64 x -5942974730414331/736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140822066036736) (*.f64 (sqrt.f64 2) (neg.f64 x)) (*.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x)))

(if (<=.f64 x -5942974730414331/736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140822066036736) (*.f64 (sqrt.f64 2) (neg.f64 x)) (*.f64 (sqrt.f64 2) x))

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

Outputs
(if (<=.f64 x -5942974730414331/736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140822066036736) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x)))
(if (<=.f64 x -5942974730414331/736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140822066036736) (neg.f64 (.f64 x (sqrt.f64 2))) (.f64 (sqrt.f64 (*.f64 x 2)) (sqrt.f64 x)))
(if (<=.f64 x -5942974730414331/736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140822066036736) (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 (sqrt.f64 (*.f64 x 2)) (sqrt.f64 x)))
(if (<=.f64 x -5942974730414331/736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140822066036736) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 2) x))
(if (<=.f64 x -5942974730414331/736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140822066036736) (neg.f64 (.f64 x (sqrt.f64 2))) (.f64 x (sqrt.f64 2)))
(if (<=.f64 x -5942974730414331/736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140822066036736) (.f64 x (neg.f64 (sqrt.f64 2))) (.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))

Compiler

Compiled 36 to 28 computations (22.2% saved)

soundness12.0ms (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

Compiler

Compiled 19 to 16 computations (15.8% saved)

end30.0ms (0.7%)

Compiler: Compiled 34 to 26 computations (23.5% saved)

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

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

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