Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 8 to 6 computations (25% saved)

sample1.1s (35.9%)

Results

1.1s	8256×	body	256	valid
0.0ms	2×	body	256	invalid

preprocess15.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	9	9
2	12	9
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 8 to 6 computations (25% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	9	9
2	12	9

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

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

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

eval0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

28.7b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	28.7b	(sqrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	27.9b	(sqrt.f64 (.f64 2 (.f64 x x)))
✓	27.9b	(sqrt.f64 (.f64 2 (.f64 x x)))

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite37.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	122	6
2	1363	6

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

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

Outputs

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

simplify121.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

36 → 26

Calls

Call 1

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

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

eval6.0ms (0.2%)

Compiler: Compiled 201 to 158 computations (21.4% saved)

prune8.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	21	5	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	21	6	27

Error

0.1b

Counts

27 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	28.7b	(sqrt.f64 (.f64 2 (.f64 x x)))
▶	33.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	32.8b	(pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3)
▶	30.4b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	32.4b	(*.f64 x (sqrt.f64 2))
▶	33.3b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)

Compiler

Compiled 77 to 63 computations (18.2% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

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))

rewrite36.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	125	6
2	1472	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 exp.f64 (log.f64 (.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))))))

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

simplify13.0ms (0.4%)

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))

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite31.0ms (1%)

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 x (sqrt.f64 2))

Outputs

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

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

27 → 16

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)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series2.0ms (0.1%)

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))

rewrite51.0ms (1.6%)

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	1591	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 (*.f64 x (*.f64 2 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 x (*.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 exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))))))

simplify15.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

248×	`fma-def_binary64`
23×	`distribute-rgt-in_binary64`
21×	`sub-neg_binary64`
20×	`associate-l_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	118	100
5	166	100
6	238	100
7	275	100
8	321	100
9	498	100
10	526	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))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -1) (sqrt.f64 -2))))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 -2))))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) x))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -1) (sqrt.f64 -2))))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 -2))))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) x))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -1) (sqrt.f64 -2))))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 -2))))
(.f64 -1 (.f64 (sqrt.f64 -1) (*.f64 (sqrt.f64 -2) x)))
(neg.f64 (.f64 (.f64 (sqrt.f64 -1) (sqrt.f64 -2)) x))
(neg.f64 (.f64 x (.f64 (sqrt.f64 -1) (sqrt.f64 -2))))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 -2))))

localize7.0ms (0.2%)

Local error

Found 6 expressions with local error:

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

series6.0ms (0.2%)

Counts

2 → 0

Calls

6 calls:

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

rewrite50.0ms (1.6%)

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	1321	14

Stop Event

1×	node limit

Counts

2 → 50

Calls

Call 1

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

Outputs

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

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

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

localize5.0ms (0.2%)

Local error

Found 6 expressions with local error:

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

series5.0ms (0.2%)

Counts

2 → 0

Calls

6 calls:

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

rewrite44.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 52

Calls

Call 1

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

Outputs

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

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

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

52 → 52

Calls

Call 1

Inputs

Outputs

eval53.0ms (1.7%)

Compiler: Compiled 1720 to 1387 computations (19.4% saved)

prune27.0ms (0.8%)

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	177	3	180
Fresh	0	0	0
Picked	1	0	1
Done	0	5	5
Total	178	8	186

Error

0.1b

Counts

186 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	28.7b	(sqrt.f64 (.f64 2 (.f64 x x)))
✓	33.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	32.4b	(*.f64 x (sqrt.f64 2))
▶	32.4b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
▶	33.3b	(.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))
✓	33.3b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
✓	30.4b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	29.0b	(pow.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) 2)

Compiler

Compiled 74 to 61 computations (17.6% saved)

localize6.0ms (0.2%)

Local error

Found 6 expressions with local error:

New	Error	Program
	27.9b	(sqrt.f64 (.f64 2 (.f64 x x)))
	0.5b	(pow.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) 2)
	0.1b	(sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))
✓	0.1b	(sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x))))
✓	0.5b	(pow.f64 (sqrt.f64 (sqrt.f64 (.f64 2 (.f64 x x)))) 2)
	27.9b	(sqrt.f64 (.f64 2 (.f64 x x)))

series3.0ms (0.1%)

Counts

2 → 0

Calls

6 calls:

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

rewrite50.0ms (1.6%)

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	20
1	165	14
2	1593	14

Stop Event

1×	node limit

Counts

2 → 47

Calls

Call 1

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (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 exp.f64 (log.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)))))))))

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

47 → 47

Calls

Call 1

Inputs

Outputs

localize11.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.2b	(.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))
	0.2b	(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/4))
	0.1b	(sqrt.f64 (*.f64 x (sqrt.f64 2)))
	0.0b	(pow.f64 (*.f64 x (sqrt.f64 2)) 1/4)
	0.1b	(sqrt.f64 (*.f64 x (sqrt.f64 2)))
✓	0.2b	(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/4))
✓	0.2b	(.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))
	0.4b	(*.f64 x (sqrt.f64 2))

series87.0ms (2.7%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
34.0ms	x	@	inf	(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/4))
28.0ms	x	@	0	(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/4))
22.0ms	x	@	-inf	(.f64 (sqrt.f64 (.f64 x (sqrt.f64 2))) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/4))
2.0ms	x	@	-inf	(.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))
1.0ms	x	@	0	(.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))

rewrite102.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

746×	`pow1_binary64`
695×	`add-log-exp_binary64`
695×	`log1p-expm1-u_binary64`
695×	`expm1-log1p-u_binary64`
677×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	49
1	210	15
2	2321	15

Stop Event

1×	node limit

Counts

2 → 27

Calls

Call 1

Inputs

(*.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))

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

Outputs

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

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

simplify52.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-def_binary64`
678×	`log-prod_binary64`
404×	`associate-+l+_binary64`
373×	`associate-+r+_binary64`
369×	`unswap-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	348
1	100	324
2	282	284
3	709	260
4	2244	232
5	7570	232

Stop Event

1×	node limit

Counts

51 → 34

Calls

Call 1

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

Outputs
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(*.f64 (sqrt.f64 2) x)
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (pow.f64 (sqrt.f64 -1) 2) x)))
(*.f64 (sqrt.f64 2) x)
(exp.f64 (.f64 1/4 (+.f64 (.f64 3 (log.f64 x)) (log.f64 (pow.f64 (sqrt.f64 2) 3)))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (*.f64 3 (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 2 (sqrt.f64 2)) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 (sqrt.f64 2) x) 3/4)
(exp.f64 (.f64 1/4 (+.f64 (.f64 3 (log.f64 x)) (log.f64 (pow.f64 (sqrt.f64 2) 3)))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (*.f64 3 (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 2 (sqrt.f64 2)) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 (sqrt.f64 2) x) 3/4)
(exp.f64 (.f64 1/4 (+.f64 (.f64 3 (log.f64 x)) (log.f64 (pow.f64 (sqrt.f64 2) 3)))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (*.f64 3 (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 2 (sqrt.f64 2)) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 (sqrt.f64 2) x) 3/4)
(exp.f64 (.f64 1/4 (+.f64 (.f64 3 (log.f64 x)) (log.f64 (pow.f64 (sqrt.f64 2) 3)))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (*.f64 3 (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 2 (sqrt.f64 2)) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 (sqrt.f64 2) x) 3/4)
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (sqrt.f64 2) 3)) (.f64 -3 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (*.f64 3 (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 2 (sqrt.f64 2)) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 (sqrt.f64 2) x) 3/4)
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (sqrt.f64 2) 3)) (.f64 -3 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (*.f64 3 (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 2 (sqrt.f64 2)) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 (sqrt.f64 2) x) 3/4)
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (sqrt.f64 2) 3)) (.f64 -3 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (*.f64 3 (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 2 (sqrt.f64 2)) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 (sqrt.f64 2) x) 3/4)
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (sqrt.f64 2) 3)) (.f64 -3 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (*.f64 3 (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 2 (sqrt.f64 2)) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 (sqrt.f64 2) x) 3/4)
(.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1 (pow.f64 (sqrt.f64 2) 3))) (.f64 -3 (log.f64 (/.f64 -1 x)))))) (sqrt.f64 -1))
(.f64 (sqrt.f64 -1) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (neg.f64 (pow.f64 (sqrt.f64 2) 3))) (.f64 -3 (log.f64 (/.f64 -1 x))))))
(.f64 (sqrt.f64 -1) (pow.f64 (exp.f64 1/4) (fma.f64 -3 (log.f64 (/.f64 -1 x)) (log.f64 (.f64 (sqrt.f64 2) -2)))))
(.f64 (sqrt.f64 -1) (.f64 (pow.f64 (*.f64 (sqrt.f64 2) -2) 1/4) (pow.f64 (/.f64 -1 x) -3/4)))
(.f64 (sqrt.f64 -1) (pow.f64 (neg.f64 (.f64 -1 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))) 1/4))
(.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1 (pow.f64 (sqrt.f64 2) 3))) (.f64 -3 (log.f64 (/.f64 -1 x)))))) (sqrt.f64 -1))
(.f64 (sqrt.f64 -1) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (neg.f64 (pow.f64 (sqrt.f64 2) 3))) (.f64 -3 (log.f64 (/.f64 -1 x))))))
(.f64 (sqrt.f64 -1) (pow.f64 (exp.f64 1/4) (fma.f64 -3 (log.f64 (/.f64 -1 x)) (log.f64 (.f64 (sqrt.f64 2) -2)))))
(.f64 (sqrt.f64 -1) (.f64 (pow.f64 (*.f64 (sqrt.f64 2) -2) 1/4) (pow.f64 (/.f64 -1 x) -3/4)))
(.f64 (sqrt.f64 -1) (pow.f64 (neg.f64 (.f64 -1 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))) 1/4))
(.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1 (pow.f64 (sqrt.f64 2) 3))) (.f64 -3 (log.f64 (/.f64 -1 x)))))) (sqrt.f64 -1))
(.f64 (sqrt.f64 -1) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (neg.f64 (pow.f64 (sqrt.f64 2) 3))) (.f64 -3 (log.f64 (/.f64 -1 x))))))
(.f64 (sqrt.f64 -1) (pow.f64 (exp.f64 1/4) (fma.f64 -3 (log.f64 (/.f64 -1 x)) (log.f64 (.f64 (sqrt.f64 2) -2)))))
(.f64 (sqrt.f64 -1) (.f64 (pow.f64 (*.f64 (sqrt.f64 2) -2) 1/4) (pow.f64 (/.f64 -1 x) -3/4)))
(.f64 (sqrt.f64 -1) (pow.f64 (neg.f64 (.f64 -1 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))) 1/4))
(.f64 (exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1 (pow.f64 (sqrt.f64 2) 3))) (.f64 -3 (log.f64 (/.f64 -1 x)))))) (sqrt.f64 -1))
(.f64 (sqrt.f64 -1) (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (neg.f64 (pow.f64 (sqrt.f64 2) 3))) (.f64 -3 (log.f64 (/.f64 -1 x))))))
(.f64 (sqrt.f64 -1) (pow.f64 (exp.f64 1/4) (fma.f64 -3 (log.f64 (/.f64 -1 x)) (log.f64 (.f64 (sqrt.f64 2) -2)))))
(.f64 (sqrt.f64 -1) (.f64 (pow.f64 (*.f64 (sqrt.f64 2) -2) 1/4) (pow.f64 (/.f64 -1 x) -3/4)))
(.f64 (sqrt.f64 -1) (pow.f64 (neg.f64 (.f64 -1 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))) 1/4))

localize5.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series20.0ms (0.6%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
18.0ms	x	@	0	(*.f64 (pow.f64 2 1/4) x)
1.0ms	x	@	inf	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
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	@	0	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

rewrite47.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 22

Calls

Call 1

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

Outputs

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

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

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)

eval78.0ms (2.4%)

Compiler: Compiled 2959 to 2491 computations (15.8% saved)

prune29.0ms (0.9%)

Pruning

10 alts after pruning (4 fresh and 6 done)

	Pruned	Kept	Total
New	196	4	200
Fresh	0	0	0
Picked	0	1	1
Done	2	5	7
Total	198	10	208

Error

0.1b

Counts

208 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	28.7b	(sqrt.f64 (.f64 2 (.f64 x x)))
✓	33.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	32.4b	(*.f64 x (sqrt.f64 2))
✓	32.4b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
✓	30.4b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	31.4b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) (neg.f64 x))) 2)
✓	33.3b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
▶	40.9b	(.f64 (sqrt.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 3/2)) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/4))
▶	29.0b	(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 1/4) 2)
▶	28.9b	(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 x (*.f64 x (sqrt.f64 2)))))

Compiler

Compiled 90 to 75 computations (16.7% saved)

localize17.0ms (0.5%)

Local error

Found 8 expressions with local error:

New	Error	Program
	27.9b	(sqrt.f64 (.f64 x (.f64 x (sqrt.f64 2))))
	0.4b	(*.f64 x (sqrt.f64 2))
	0.3b	(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 x (*.f64 x (sqrt.f64 2)))))
	0.2b	(.f64 x (.f64 x (sqrt.f64 2)))
✓	0.2b	(.f64 x (.f64 x (sqrt.f64 2)))
✓	0.3b	(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 x (*.f64 x (sqrt.f64 2)))))
	0.4b	(*.f64 x (sqrt.f64 2))
✓	27.9b	(sqrt.f64 (.f64 x (.f64 x (sqrt.f64 2))))

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite56.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

754×	`pow1_binary64`
700×	`add-log-exp_binary64`
700×	`log1p-expm1-u_binary64`
700×	`expm1-log1p-u_binary64`
684×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	207	22
2	2281	22

Stop Event

1×	node limit

Counts

3 → 53

Calls

Call 1

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

Outputs

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

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

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

simplify80.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

696×	`distribute-lft-neg-in_binary64`
690×	`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	270	388
4	1137	388
5	2159	388
6	3827	388
7	5279	388
8	6612	388
9	7452	388

Stop Event

1×	node limit

Counts

89 → 62

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 (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)))
(*.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))

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

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	28.7b	(pow.f64 (.f64 2 (.f64 x x)) 1/4)
	0.5b	(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 1/4) 2)
✓	0.5b	(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 1/4) 2)
✓	28.7b	(pow.f64 (.f64 2 (.f64 x x)) 1/4)

series38.0ms (1.2%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
28.0ms	x	@	inf	(pow.f64 (.f64 2 (.f64 x x)) 1/4)
8.0ms	x	@	0	(pow.f64 (.f64 2 (.f64 x x)) 1/4)
1.0ms	x	@	inf	(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 1/4) 2)
1.0ms	x	@	0	(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 1/4) 2)
0.0ms	x	@	-inf	(pow.f64 (.f64 2 (.f64 x x)) 1/4)

rewrite45.0ms (1.4%)

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	1914	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 (*.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 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 exp.f64 (log.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 -.f64 (+.f64 1 (*.f64 x (sqrt.f64 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (sqrt.f64 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) (sqrt.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (sqrt.f64 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (sqrt.f64 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (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 (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 (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 exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))))))

simplify53.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

592×	`unswap-sqr_binary64`
546×	`associate-l_binary64`
495×	`associate-r_binary64`
393×	`associate-/l*_binary64`
318×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	28	420
1	72	372
2	180	276
3	478	216
4	1280	180
5	4960	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))

localize9.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.4b	(*.f64 x (sqrt.f64 2))
	0.2b	(.f64 (sqrt.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 3/2)) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/4))
	0.2b	(pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)
	0.0b	(pow.f64 (*.f64 x (sqrt.f64 2)) 1/4)
✓	0.2b	(pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)
✓	0.2b	(.f64 (sqrt.f64 (pow.f64 (.f64 x (sqrt.f64 2)) 3/2)) (pow.f64 (*.f64 x (sqrt.f64 2)) 1/4))
	0.4b	(*.f64 x (sqrt.f64 2))
✓	7.7b	(sqrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/2))

series67.0ms (2.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
13.0ms	x	@	-inf	(pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)
13.0ms	x	@	0	(pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)
11.0ms	x	@	-inf	(sqrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/2))
10.0ms	x	@	inf	(pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)
10.0ms	x	@	0	(sqrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/2))

rewrite58.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

895×	`pow1_binary64`
837×	`add-log-exp_binary64`
837×	`log1p-expm1-u_binary64`
837×	`expm1-log1p-u_binary64`
814×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	38
1	236	24
2	2600	24

Stop Event

1×	node limit

Counts

3 → 65

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)) (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)) (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/8) (pow.f64 (*.f64 x (sqrt.f64 2)) 3/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) (sqrt.f64 (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) (pow.f64 (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 x 3/2)) (sqrt.f64 (pow.f64 2 3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 2) 3/4) (pow.f64 x 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 3/4) (pow.f64 (*.f64 x (sqrt.f64 2)) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) 3/4) (pow.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 3/4) (pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (pow.f64 (*.f64 x (sqrt.f64 2)) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 x 3/2) 1/2) (pow.f64 (pow.f64 2 3/4) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/4) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 9/4) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/8) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 9/4))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 x (sqrt.f64 2))) 3/4))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)))))))

((#(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 (cbrt.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)) 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 cbrt.f64 (*.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 9/4) (pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 1/4) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (pow.f64 (*.f64 x (sqrt.f64 2)) 1/4) 3) (pow.f64 (*.f64 x (sqrt.f64 2)) 9/4)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (*.f64 2 (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 2 (sqrt.f64 2)) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))))))

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

simplify37.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

464×	`unswap-sqr_binary64`
437×	`associate-l_binary64`
428×	`associate-r_binary64`
374×	`associate-+l+_binary64`
363×	`exp-sum_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	50	508
1	139	496
2	389	424
3	956	352
4	2500	316

Stop Event

1×	node limit

Counts

101 → 76

Calls

Call 1

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

Outputs
(exp.f64 (.f64 1/4 (+.f64 (.f64 3 (log.f64 x)) (log.f64 (pow.f64 (sqrt.f64 2) 3)))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (log.f64 (pow.f64 (sqrt.f64 2) 3))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 2) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)
(exp.f64 (.f64 1/4 (+.f64 (.f64 3 (log.f64 x)) (log.f64 (pow.f64 (sqrt.f64 2) 3)))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (log.f64 (pow.f64 (sqrt.f64 2) 3))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 2) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)
(exp.f64 (.f64 1/4 (+.f64 (.f64 3 (log.f64 x)) (log.f64 (pow.f64 (sqrt.f64 2) 3)))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (log.f64 (pow.f64 (sqrt.f64 2) 3))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 2) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)
(exp.f64 (.f64 1/4 (+.f64 (.f64 3 (log.f64 x)) (log.f64 (pow.f64 (sqrt.f64 2) 3)))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (log.f64 (pow.f64 (sqrt.f64 2) 3))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 2) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (sqrt.f64 2) 3)) (.f64 -3 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (log.f64 (pow.f64 (sqrt.f64 2) 3))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 2) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (sqrt.f64 2) 3)) (.f64 -3 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (log.f64 (pow.f64 (sqrt.f64 2) 3))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 2) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (sqrt.f64 2) 3)) (.f64 -3 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (log.f64 (pow.f64 (sqrt.f64 2) 3))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 2) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (pow.f64 (sqrt.f64 2) 3)) (.f64 -3 (log.f64 (/.f64 1 x))))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (log.f64 (pow.f64 (sqrt.f64 2) 3))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 2) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1 (pow.f64 (sqrt.f64 2) 3))) (*.f64 -3 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (log.f64 (pow.f64 (sqrt.f64 2) 3))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 2) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1 (pow.f64 (sqrt.f64 2) 3))) (*.f64 -3 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (log.f64 (pow.f64 (sqrt.f64 2) 3))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 2) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1 (pow.f64 (sqrt.f64 2) 3))) (*.f64 -3 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (log.f64 (pow.f64 (sqrt.f64 2) 3))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 2) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)
(exp.f64 (.f64 1/4 (+.f64 (log.f64 (.f64 -1 (pow.f64 (sqrt.f64 2) 3))) (*.f64 -3 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 1/4) (fma.f64 3 (log.f64 x) (log.f64 (pow.f64 (sqrt.f64 2) 3))))
(pow.f64 (exp.f64 1/4) (*.f64 3 (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2)))))
(.f64 (pow.f64 (.f64 (sqrt.f64 2) 2) 1/4) (pow.f64 x 3/4))
(*.f64 (pow.f64 x 3/4) (pow.f64 (sqrt.f64 2) 3/4))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/4)
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 -1) x)))
(.f64 (neg.f64 (sqrt.f64 2)) (.f64 x (sqrt.f64 -1)))
(.f64 (.f64 x (sqrt.f64 -1)) (neg.f64 (sqrt.f64 2)))
(.f64 x (.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 -1))))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 2))))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 -1) x)))
(.f64 (neg.f64 (sqrt.f64 2)) (.f64 x (sqrt.f64 -1)))
(.f64 (.f64 x (sqrt.f64 -1)) (neg.f64 (sqrt.f64 2)))
(.f64 x (.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 -1))))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 2))))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 -1) x)))
(.f64 (neg.f64 (sqrt.f64 2)) (.f64 x (sqrt.f64 -1)))
(.f64 (.f64 x (sqrt.f64 -1)) (neg.f64 (sqrt.f64 2)))
(.f64 x (.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 -1))))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 2))))
(.f64 -1 (.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 -1) x)))
(.f64 (neg.f64 (sqrt.f64 2)) (.f64 x (sqrt.f64 -1)))
(.f64 (.f64 x (sqrt.f64 -1)) (neg.f64 (sqrt.f64 2)))
(.f64 x (.f64 (sqrt.f64 2) (neg.f64 (sqrt.f64 -1))))
(.f64 x (.f64 (sqrt.f64 -1) (neg.f64 (sqrt.f64 2))))
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2))))
(*.f64 (pow.f64 (sqrt.f64 2) 3/2) (pow.f64 x 3/2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2))))
(*.f64 (pow.f64 (sqrt.f64 2) 3/2) (pow.f64 x 3/2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2))))
(*.f64 (pow.f64 (sqrt.f64 2) 3/2) (pow.f64 x 3/2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)
(exp.f64 (*.f64 3/2 (+.f64 (log.f64 (sqrt.f64 2)) (log.f64 x))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2))))
(*.f64 (pow.f64 (sqrt.f64 2) 3/2) (pow.f64 x 3/2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2))))
(*.f64 (pow.f64 (sqrt.f64 2) 3/2) (pow.f64 x 3/2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2))))
(*.f64 (pow.f64 (sqrt.f64 2) 3/2) (pow.f64 x 3/2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2))))
(*.f64 (pow.f64 (sqrt.f64 2) 3/2) (pow.f64 x 3/2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (log.f64 (sqrt.f64 2)))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2))))
(*.f64 (pow.f64 (sqrt.f64 2) 3/2) (pow.f64 x 3/2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 2))) (*.f64 -1 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2))))
(*.f64 (pow.f64 (sqrt.f64 2) 3/2) (pow.f64 x 3/2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 2))) (*.f64 -1 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2))))
(*.f64 (pow.f64 (sqrt.f64 2) 3/2) (pow.f64 x 3/2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 2))) (*.f64 -1 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2))))
(*.f64 (pow.f64 (sqrt.f64 2) 3/2) (pow.f64 x 3/2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)
(exp.f64 (.f64 3/2 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 2))) (*.f64 -1 (log.f64 (/.f64 -1 x))))))
(pow.f64 (exp.f64 3/2) (+.f64 (log.f64 x) (log.f64 (sqrt.f64 2))))
(*.f64 (pow.f64 (sqrt.f64 2) 3/2) (pow.f64 x 3/2))
(pow.f64 (*.f64 x (sqrt.f64 2)) 3/2)

localize5.0ms (0.2%)

Local error

Found 6 expressions with local error:

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

series6.0ms (0.2%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	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)

rewrite40.0ms (1.2%)

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	1723	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 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 (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 exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))))))

((#(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 exp.f64 (log.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))))))))

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

eval119.0ms (3.7%)

Compiler: Compiled 3966 to 3348 computations (15.6% saved)

prune64.0ms (2%)

Pruning

10 alts after pruning (2 fresh and 8 done)

	Pruned	Kept	Total
New	308	2	310
Fresh	0	0	0
Picked	0	1	1
Done	2	7	9
Total	310	10	320

Error

0.0b

Counts

320 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	28.7b	(sqrt.f64 (.f64 2 (.f64 x x)))
✓	33.2b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
✓	32.4b	(*.f64 x (sqrt.f64 2))
✓	32.4b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
✓	30.4b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	31.4b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) (neg.f64 x))) 2)
	32.5b	(*.f64 (pow.f64 (pow.f64 2 1/4) 2) x)
✓	33.3b	(pow.f64 (sqrt.f64 (*.f64 x (sqrt.f64 2))) 2)
	30.4b	(.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 (.f64 x (pow.f64 2 1/4))))
✓	29.0b	(pow.f64 (pow.f64 (.f64 2 (.f64 x x)) 1/4) 2)

Compiler

Compiled 82 to 69 computations (15.9% saved)

regimes123.0ms (3.9%)

Counts

15 → 2

Calls

Call 1

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

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

Calls

7 calls:

23.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
18.0ms	x
18.0ms	(.f64 2 (.f64 x x))
15.0ms	(*.f64 x x)
15.0ms	(*.f64 x x)

Results

Error	Segments	Branch
0.4b	2	`x`
13.4b	3	`(sqrt.f64 (.f64 2 (.f64 x x)))`
13.4b	3	`(sqrt.f64 (.f64 2 (.f64 x x)))`
13.4b	3	`(.f64 2 (.f64 x x))`
13.4b	3	`(.f64 2 (.f64 x x))`
13.4b	3	`(*.f64 x x)`
13.4b	3	`(*.f64 x x)`

Compiler

Compiled 169 to 130 computations (23.1% saved)

bsearch17.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
17.0ms	-5.614315514990902e-303	1.5525248639476563e-306

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes40.0ms (1.2%)

Accuracy

Total -62.0b remaining (-14843.2%)

Threshold costs -62.0b (-14843.2%)

Counts

4 → 2

Calls

Call 1

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

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

Calls

4 calls:

14.0ms	(.f64 2 (.f64 x x))
9.0ms	x
8.0ms	(sqrt.f64 (.f64 2 (.f64 x x)))
7.0ms	(*.f64 x x)

Results

Error	Segments	Branch
0.4b	2	`x`
13.4b	3	`(sqrt.f64 (.f64 2 (.f64 x x)))`
13.4b	3	`(.f64 2 (.f64 x x))`
13.4b	3	`(*.f64 x x)`

Compiler

Compiled 42 to 30 computations (28.6% saved)

bsearch16.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
16.0ms	-5.614315514990902e-303	1.5525248639476563e-306

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify4.0ms (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	26	51
2	33	51
3	38	51
4	41	51
5	42	51

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 x -8669663322542973/1544206644495472857303583883048380333324864576447617480139933456630175320190394187102969236003396030389305708803686614314192266367994640173851115417028339461681498903477221384921775113999124270181577817371160469578262386195561925496048762173836971712805252506350393444460551564142078418977251644200485277277433072975872) (*.f64 (sqrt.f64 2) (neg.f64 x)) (*.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x)))

(if (<=.f64 x -8669663322542973/1544206644495472857303583883048380333324864576447617480139933456630175320190394187102969236003396030389305708803686614314192266367994640173851115417028339461681498903477221384921775113999124270181577817371160469578262386195561925496048762173836971712805252506350393444460551564142078418977251644200485277277433072975872) (*.f64 (sqrt.f64 2) (neg.f64 x)) (*.f64 x (sqrt.f64 2)))

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

Outputs
(if (<=.f64 x -8669663322542973/1544206644495472857303583883048380333324864576447617480139933456630175320190394187102969236003396030389305708803686614314192266367994640173851115417028339461681498903477221384921775113999124270181577817371160469578262386195561925496048762173836971712805252506350393444460551564142078418977251644200485277277433072975872) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x)))
(if (<=.f64 x -8669663322542973/1544206644495472857303583883048380333324864576447617480139933456630175320190394187102969236003396030389305708803686614314192266367994640173851115417028339461681498903477221384921775113999124270181577817371160469578262386195561925496048762173836971712805252506350393444460551564142078418977251644200485277277433072975872) (neg.f64 (.f64 x (sqrt.f64 2))) (.f64 (sqrt.f64 (*.f64 x 2)) (sqrt.f64 x)))
(if (<=.f64 x -8669663322542973/1544206644495472857303583883048380333324864576447617480139933456630175320190394187102969236003396030389305708803686614314192266367994640173851115417028339461681498903477221384921775113999124270181577817371160469578262386195561925496048762173836971712805252506350393444460551564142078418977251644200485277277433072975872) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 x (sqrt.f64 2)))
(if (<=.f64 x -8669663322542973/1544206644495472857303583883048380333324864576447617480139933456630175320190394187102969236003396030389305708803686614314192266367994640173851115417028339461681498903477221384921775113999124270181577817371160469578262386195561925496048762173836971712805252506350393444460551564142078418977251644200485277277433072975872) (neg.f64 (.f64 x (sqrt.f64 2))) (.f64 x (sqrt.f64 2)))
(*.f64 x (sqrt.f64 2))

end47.0ms (1.5%)

Stop Event

1×

fuel

Compiler

Compiled 70 to 54 computations (22.9% saved)

Iter	Nodes	Cost
0	12	100
1	21	100
2	53	100
3	104	100
4	118	100
5	166	100
6	238	100
7	275	100
8	321	100
9	498	100
10	526	100

Iter	Nodes	Cost
0	12	100
1	21	100
2	53	100
3	104	100
4	118	100
5	166	100
6	238	100
7	275	100
8	321	100
9	498	100
10	526	100

Details

analyze3.0ms (0.1%)

sample1.1s (35.9%)

preprocess15.0ms (0.5%)

simplify6.0ms (0.2%)

eval0.0ms (0%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series2.0ms (0.1%)

rewrite37.0ms (1.2%)

simplify121.0ms (3.8%)

eval6.0ms (0.2%)

prune8.0ms (0.3%)

localize5.0ms (0.1%)

series1.0ms (0%)

rewrite36.0ms (1.1%)

simplify13.0ms (0.4%)

localize3.0ms (0.1%)

series1.0ms (0%)

rewrite31.0ms (1%)

simplify7.0ms (0.2%)

localize5.0ms (0.1%)

series2.0ms (0.1%)

rewrite51.0ms (1.6%)

simplify15.0ms (0.5%)

localize7.0ms (0.2%)

series6.0ms (0.2%)

rewrite50.0ms (1.6%)

simplify7.0ms (0.2%)

localize5.0ms (0.2%)

series5.0ms (0.2%)

rewrite44.0ms (1.4%)

simplify6.0ms (0.2%)

eval53.0ms (1.7%)

prune27.0ms (0.8%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite50.0ms (1.6%)

simplify6.0ms (0.2%)

localize11.0ms (0.3%)

series87.0ms (2.7%)

rewrite102.0ms (3.2%)

simplify52.0ms (1.6%)

localize5.0ms (0.1%)

series20.0ms (0.6%)

rewrite47.0ms (1.5%)

simplify7.0ms (0.2%)

eval78.0ms (2.4%)

prune29.0ms (0.9%)

localize17.0ms (0.5%)

series4.0ms (0.1%)

rewrite56.0ms (1.8%)

simplify80.0ms (2.5%)

localize7.0ms (0.2%)

series38.0ms (1.2%)

rewrite45.0ms (1.4%)

simplify53.0ms (1.7%)

localize9.0ms (0.3%)

series67.0ms (2.1%)

rewrite58.0ms (1.8%)

simplify37.0ms (1.2%)

localize5.0ms (0.2%)

series6.0ms (0.2%)

rewrite40.0ms (1.2%)

simplify6.0ms (0.2%)

eval119.0ms (3.7%)

prune64.0ms (2%)

regimes123.0ms (3.9%)

bsearch17.0ms (0.5%)

regimes40.0ms (1.2%)

bsearch16.0ms (0.5%)

simplify4.0ms (0.1%)

end47.0ms (1.5%)

Profiling

Iter	Nodes	Cost
0	12	100
1	21	100
2	53	100
3	104	100
4	118	100
5	166	100
6	238	100
7	275	100
8	321	100
9	498	100
10	526	100