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)

sample851.0ms (27.3%)

Results

838.0ms	8256×	body	256	valid
0.0ms	2×	body	256	invalid

preprocess16.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 8 to 6 computations (25% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

31.6b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.6b	(sqrt.f64 (.f64 (.f64 2 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
	30.5b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	30.5b	(sqrt.f64 (.f64 (.f64 2 x) x))

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite36.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

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

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

Outputs

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

simplify12.0ms (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	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 208 to 159 computations (23.6% saved)

prune9.0ms (0.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

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

Error

0.1b

Counts

27 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	32.1b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
▶	31.7b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	31.2b	(*.f64 (sqrt.f64 2) x)
✓	31.6b	(sqrt.f64 (.f64 (.f64 2 x) x))
	31.9b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 x x)))))
▶	31.9b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	52.4b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))

Compiler

Compiled 113 to 89 computations (21.2% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series1.0ms (0%)

Counts

1 → 0

Calls

3 calls:

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

rewrite30.0ms (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 (sqrt.f64 2) x)

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

Outputs

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

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

15 → 15

Calls

Call 1

Inputs

Outputs

localize4.0ms (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 log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 2) x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 2) x)))))))

simplify11.0ms (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))

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))

rewrite39.0ms (1.3%)

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

localize6.0ms (0.2%)

Local error

Found 6 expressions with local error:

New	Error	Program
	41.4b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))
	0.4b	(*.f64 (sqrt.f64 2) x)
	0.2b	(pow.f64 (*.f64 (sqrt.f64 2) x) 3)
✓	0.2b	(pow.f64 (*.f64 (sqrt.f64 2) x) 3)
	0.4b	(*.f64 (sqrt.f64 2) x)
✓	41.4b	(cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 2) x) 3))

series6.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

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

rewrite44.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	170	15
2	1635	15

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

Outputs

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

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

simplify151.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	244
1	36	244
2	103	244
3	269	244
4	773	244
5	1353	244
6	2800	244
7	2922	244
8	3214	244
9	3486	244
10	3705	244
11	3936	244
12	4228	244
13	4571	244
14	5403	244
15	5928	244
16	6610	244
17	6918	244
18	7278	244
19	7610	244
20	7982	244

Stop Event

1×	node limit

Counts

78 → 58

Calls

Call 1

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

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

localize5.0ms (0.1%)

Local error

Found 6 expressions with local error:

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

series6.0ms (0.2%)

Counts

2 → 0

Calls

6 calls:

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

rewrite39.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	144	14
2	1321	14

Stop Event

1×	node limit

Counts

2 → 50

Calls

Call 1

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

Outputs

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

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

50 → 50

Calls

Call 1

Inputs

Outputs

eval50.0ms (1.6%)

Compiler: Compiled 1715 to 1394 computations (18.7% saved)

prune28.0ms (0.9%)

Pruning

10 alts after pruning (5 fresh and 5 done)

	Pruned	Kept	Total
New	179	4	183
Fresh	0	1	1
Picked	0	1	1
Done	1	4	5
Total	180	10	190

Error

0.1b

Counts

190 → 10

Alt Table

Click to see full alt table

Status	Error	Program
▶	32.1b	(pow.f64 (*.f64 (pow.f64 2 1/4) (sqrt.f64 x)) 2)
✓	32.1b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
✓	31.6b	(sqrt.f64 (.f64 (.f64 2 x) x))
▶	52.4b	(cbrt.f64 (.f64 (.f64 2 (.f64 x x)) (.f64 (sqrt.f64 2) x)))
✓	31.7b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	31.2b	(*.f64 (sqrt.f64 2) x)
▶	31.2b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
▶	31.9b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 x x)))))
✓	31.9b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	42.8b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 x x))) 3))

Compiler

Compiled 152 to 121 computations (20.4% saved)

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))

series38.0ms (1.2%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
35.0ms	x	@	0	(*.f64 (pow.f64 2 1/4) x)
1.0ms	x	@	inf	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
0.0ms	x	@	-inf	(*.f64 (pow.f64 2 1/4) x)
0.0ms	x	@	inf	(*.f64 (pow.f64 2 1/4) x)
0.0ms	x	@	0	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

rewrite45.0ms (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 log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.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 log1p.f64 (expm1.f64 (*.f64 (pow.f64 2 1/4) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (pow.f64 2 1/4) x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.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)

localize7.0ms (0.2%)

Local error

Found 8 expressions with local error:

New	Error	Program
	41.4b	(cbrt.f64 (.f64 (.f64 2 (.f64 x x)) (.f64 (sqrt.f64 2) x)))
	0.4b	(*.f64 (sqrt.f64 2) x)
	0.1b	(.f64 (.f64 2 (.f64 x x)) (.f64 (sqrt.f64 2) x))
	0.0b	(.f64 2 (.f64 x x))
✓	0.0b	(.f64 2 (.f64 x x))
✓	0.1b	(.f64 (.f64 2 (.f64 x x)) (.f64 (sqrt.f64 2) x))
	0.4b	(*.f64 (sqrt.f64 2) x)
✓	41.4b	(cbrt.f64 (.f64 (.f64 2 (.f64 x x)) (.f64 (sqrt.f64 2) x)))

series10.0ms (0.3%)

Counts

3 → 36

Calls

9 calls:

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

rewrite51.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

692×	`pow1_binary64`
643×	`add-log-exp_binary64`
643×	`log1p-expm1-u_binary64`
643×	`expm1-log1p-u_binary64`
626×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	39
1	184	22
2	2184	22

Stop Event

1×	node limit

Counts

3 → 58

Calls

Call 1

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

Outputs

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

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

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

simplify62.0ms (2%)

Algorithm

1×	egg-herbie

Rules

984×	`fma-def_binary64`
576×	`distribute-rgt-neg-in_binary64`
570×	`distribute-lft-neg-in_binary64`
507×	`associate-l_binary64`
427×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	392
1	61	392
2	164	392
3	524	392
4	1774	392
5	2502	392
6	3922	392
7	5588	392

Stop Event

1×	node limit

Counts

94 → 64

Calls

Call 1

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

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

localize5.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series5.0ms (0.2%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(pow.f64 (*.f64 (pow.f64 2 1/4) (sqrt.f64 x)) 2)
1.0ms	x	@	0	(pow.f64 (*.f64 (pow.f64 2 1/4) (sqrt.f64 x)) 2)
1.0ms	x	@	inf	(pow.f64 (*.f64 (pow.f64 2 1/4) (sqrt.f64 x)) 2)
1.0ms	x	@	-inf	(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))
0.0ms	x	@	0	(*.f64 (pow.f64 2 1/4) (sqrt.f64 x))

rewrite79.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

645×	`pow1_binary64`
599×	`add-log-exp_binary64`
599×	`log1p-expm1-u_binary64`
599×	`expm1-log1p-u_binary64`
581×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	172	14
2	1820	14

Stop Event

1×	node limit

Counts

2 → 35

Calls

Call 1

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

35 → 35

Calls

Call 1

Inputs

Outputs

localize6.0ms (0.2%)

Local error

Found 8 expressions with local error:

New	Error	Program
	41.4b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 x x))) 3))
	30.5b	(sqrt.f64 (.f64 2 (.f64 x x)))
	0.2b	(pow.f64 (sqrt.f64 (.f64 2 (.f64 x x))) 3)
	0.0b	(.f64 2 (.f64 x x))
	0.0b	(.f64 2 (.f64 x x))
✓	0.2b	(pow.f64 (sqrt.f64 (.f64 2 (.f64 x x))) 3)
✓	30.5b	(sqrt.f64 (.f64 2 (.f64 x x)))
✓	41.4b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 2 (.f64 x x))) 3))

series2.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite56.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

657×	`pow1_binary64`
619×	`add-log-exp_binary64`
618×	`log1p-expm1-u_binary64`
618×	`expm1-log1p-u_binary64`
602×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	28
1	190	21
2	1876	21

Stop Event

1×	node limit

Counts

3 → 85

Calls

Call 1

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

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

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

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

simplify59.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

778×	`distribute-rgt-neg-in_binary64`
755×	`distribute-lft-neg-in_binary64`
538×	`fma-def_binary64`
416×	`associate-l_binary64`
408×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	312
1	34	304
2	108	304
3	430	304
4	1685	304
5	2982	304
6	5047	304
7	6651	304

Stop Event

1×	node limit

Counts

121 → 65

Calls

Call 1

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

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

localize8.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.4b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 x x)))))
	0.3b	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)
	0.1b	(sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x))))
	0.0b	(.f64 2 (.f64 x x))
✓	0.3b	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)
✓	0.4b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 x x)))))
✓	17.2b	(sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2))
✓	31.5b	(cbrt.f64 (.f64 2 (.f64 x x)))

series151.0ms (4.8%)

Counts

4 → 12

Calls

12 calls:

Time	Variable		Point	Expression
144.0ms	x	@	0	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 x x)))))
1.0ms	x	@	0	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)
1.0ms	x	@	0	(cbrt.f64 (.f64 2 (.f64 x x)))
1.0ms	x	@	inf	(pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)
1.0ms	x	@	inf	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 x x)))))

rewrite96.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	39
1	206	33
2	1913	33

Stop Event

1×	node limit

Counts

4 → 91

Calls

Call 1

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

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

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

Stop Event

1×

saturated

Counts

103 → 66

Calls

Call 1

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

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

eval96.0ms (3.1%)

Compiler: Compiled 3983 to 3011 computations (24.4% saved)

prune58.0ms (1.9%)

Pruning

10 alts after pruning (2 fresh and 8 done)

	Pruned	Kept	Total
New	309	2	311
Fresh	0	0	0
Picked	1	0	1
Done	1	8	9
Total	311	10	321

Error

0.1b

Counts

321 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	32.1b	(pow.f64 (*.f64 (pow.f64 2 1/4) (sqrt.f64 x)) 2)
✓	32.1b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
✓	31.6b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	52.4b	(cbrt.f64 (.f64 (.f64 2 (.f64 x x)) (.f64 (sqrt.f64 2) x)))
✓	31.7b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	31.2b	(*.f64 (sqrt.f64 2) x)
▶	31.6b	(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 x (*.f64 x (sqrt.f64 2)))))
✓	31.2b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
▶	42.8b	(cbrt.f64 (.f64 (.f64 2 (.f64 x x)) (sqrt.f64 (.f64 2 (*.f64 x x)))))
✓	31.9b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Compiler

Compiled 91 to 72 computations (20.9% saved)

localize6.0ms (0.2%)

Local error

Found 8 expressions with local error:

New	Error	Program
	41.4b	(cbrt.f64 (.f64 (.f64 2 (.f64 x x)) (sqrt.f64 (.f64 2 (*.f64 x x)))))
	30.5b	(sqrt.f64 (.f64 2 (.f64 x x)))
	0.1b	(.f64 (.f64 2 (.f64 x x)) (sqrt.f64 (.f64 2 (*.f64 x x))))
	0.0b	(.f64 2 (.f64 x x))
	0.0b	(.f64 2 (.f64 x x))
✓	0.1b	(.f64 (.f64 2 (.f64 x x)) (sqrt.f64 (.f64 2 (*.f64 x x))))
	30.5b	(sqrt.f64 (.f64 2 (.f64 x x)))
✓	41.4b	(cbrt.f64 (.f64 (.f64 2 (.f64 x x)) (sqrt.f64 (.f64 2 (*.f64 x x)))))

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite46.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

592×	`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	8	27
1	164	15
2	1640	15

Stop Event

1×	node limit

Counts

2 → 40

Calls

Call 1

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

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

simplify142.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

773×	`fma-neg_binary64`
608×	`distribute-rgt-neg-in_binary64`
597×	`distribute-lft-neg-in_binary64`
460×	`unswap-sqr_binary64`
411×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	308
1	51	308
2	149	308
3	472	308
4	1226	308
5	1696	308
6	2161	308
7	2863	308
8	4082	308
9	5186	308
10	6092	308
11	6761	308
12	7819	308

Stop Event

1×	node limit

Counts

64 → 48

Calls

Call 1

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

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

localize8.0ms (0.2%)

Local error

Found 8 expressions with local error:

New	Error	Program
	30.4b	(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)))))
	0.1b	(.f64 x (.f64 x (sqrt.f64 2)))
✓	0.1b	(.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))
✓	30.4b	(sqrt.f64 (.f64 x (.f64 x (sqrt.f64 2))))

series6.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(sqrt.f64 (.f64 x (.f64 x (sqrt.f64 2))))
1.0ms	x	@	inf	(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)))))
0.0ms	x	@	inf	(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 x (*.f64 x (sqrt.f64 2)))))
0.0ms	x	@	inf	(.f64 x (.f64 x (sqrt.f64 2)))

rewrite54.0ms (1.7%)

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	32
1	207	28
2	2281	28

Stop Event

1×	node limit

Counts

4 → 68

Calls

Call 1

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

simplify86.0ms (2.8%)

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	16	460
1	39	460
2	95	460
3	270	460
4	1123	460
5	2148	460
6	3816	460
7	5268	460
8	6601	460
9	7439	460

Stop Event

1×	node limit

Counts

116 → 63

Calls

Call 1

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

eval45.0ms (1.5%)

Compiler: Compiled 1708 to 1360 computations (20.4% saved)

prune27.0ms (0.9%)

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	0	0	0
Picked	1	0	1
Done	2	7	9
Total	141	9	150

Error

0.0b

Counts

150 → 9

Alt Table

Click to see full alt table

Status	Error	Program
✓	32.1b	(pow.f64 (*.f64 (pow.f64 2 1/4) (sqrt.f64 x)) 2)
✓	32.1b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
	42.8b	(cbrt.f64 (pow.f64 (.f64 2 (.f64 x x)) 3/2))
✓	31.7b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	31.2b	(*.f64 (sqrt.f64 2) x)
✓	31.6b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	31.2b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
	31.7b	(.f64 (pow.f64 2 1/4) (.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 x)))
✓	31.9b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Compiler

Compiled 73 to 61 computations (16.4% saved)

regimes58.0ms (1.9%)

Counts

15 → 2

Calls

Call 1

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

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

Calls

3 calls:

25.0ms	x
15.0ms	(.f64 (.f64 2 x) x)
13.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))

Results

Error	Segments	Branch
0.4b	2	`x`
14.9b	3	`(sqrt.f64 (.f64 (.f64 2 x) x))`
14.9b	3	`(.f64 (.f64 2 x) x)`

Compiler

Compiled 148 to 107 computations (27.7% saved)

bsearch128.0ms (4.1%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
128.0ms	-5.601383677758517e-304	1.3550938659765927e-303

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes23.0ms (0.7%)

Accuracy

Total -62.1b remaining (-14586.7%)

Threshold costs -62.1b (-14586.7%)

Counts

3 → 2

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Error	Segments	Branch
0.4b	2	`x`
14.9b	3	`(sqrt.f64 (.f64 (.f64 2 x) x))`
14.9b	3	`(.f64 (.f64 2 x) x)`

Compiler

Compiled 31 to 22 computations (29% saved)

bsearch17.0ms (0.5%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
17.0ms	-5.601383677758517e-304	1.3550938659765927e-303

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	51
1	25	51
2	32	51
3	37	51
4	40	51
5	41	51

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 x -864969389356319/1544206644495472857303583883048380333324864576447617480139933456630175320190394187102969236003396030389305708803686614314192266367994640173851115417028339461681498903477221384921775113999124270181577817371160469578262386195561925496048762173836971712805252506350393444460551564142078418977251644200485277277433072975872) (*.f64 (sqrt.f64 2) (neg.f64 x)) (*.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x)))

(if (<=.f64 x -864969389356319/1544206644495472857303583883048380333324864576447617480139933456630175320190394187102969236003396030389305708803686614314192266367994640173851115417028339461681498903477221384921775113999124270181577817371160469578262386195561925496048762173836971712805252506350393444460551564142078418977251644200485277277433072975872) (*.f64 (sqrt.f64 2) (neg.f64 x)) (*.f64 (sqrt.f64 2) x))

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

Outputs
(if (<=.f64 x -864969389356319/1544206644495472857303583883048380333324864576447617480139933456630175320190394187102969236003396030389305708803686614314192266367994640173851115417028339461681498903477221384921775113999124270181577817371160469578262386195561925496048762173836971712805252506350393444460551564142078418977251644200485277277433072975872) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x)))
(if (<=.f64 x -864969389356319/1544206644495472857303583883048380333324864576447617480139933456630175320190394187102969236003396030389305708803686614314192266367994640173851115417028339461681498903477221384921775113999124270181577817371160469578262386195561925496048762173836971712805252506350393444460551564142078418977251644200485277277433072975872) (neg.f64 (.f64 x (sqrt.f64 2))) (.f64 (sqrt.f64 (*.f64 x 2)) (sqrt.f64 x)))
(if (<=.f64 x -864969389356319/1544206644495472857303583883048380333324864576447617480139933456630175320190394187102969236003396030389305708803686614314192266367994640173851115417028339461681498903477221384921775113999124270181577817371160469578262386195561925496048762173836971712805252506350393444460551564142078418977251644200485277277433072975872) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 2) x))
(if (<=.f64 x -864969389356319/1544206644495472857303583883048380333324864576447617480139933456630175320190394187102969236003396030389305708803686614314192266367994640173851115417028339461681498903477221384921775113999124270181577817371160469578262386195561925496048762173836971712805252506350393444460551564142078418977251644200485277277433072975872) (neg.f64 (.f64 x (sqrt.f64 2))) (.f64 x (sqrt.f64 2)))
(*.f64 (sqrt.f64 2) x)
(*.f64 x (sqrt.f64 2))

end145.0ms (4.7%)

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%)

sample851.0ms (27.3%)

preprocess16.0ms (0.5%)

simplify6.0ms (0.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series2.0ms (0.1%)

rewrite36.0ms (1.2%)

simplify12.0ms (0.4%)

eval6.0ms (0.2%)

prune9.0ms (0.3%)

localize3.0ms (0.1%)

series1.0ms (0%)

rewrite30.0ms (1%)

simplify11.0ms (0.3%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite36.0ms (1.1%)

simplify11.0ms (0.4%)

localize5.0ms (0.1%)

series2.0ms (0.1%)

rewrite39.0ms (1.3%)

simplify15.0ms (0.5%)

localize6.0ms (0.2%)

series6.0ms (0.2%)

rewrite44.0ms (1.4%)

simplify151.0ms (4.9%)

localize5.0ms (0.1%)

series6.0ms (0.2%)

rewrite39.0ms (1.3%)

simplify6.0ms (0.2%)

eval50.0ms (1.6%)

prune28.0ms (0.9%)

localize5.0ms (0.1%)

series38.0ms (1.2%)

rewrite45.0ms (1.5%)

simplify7.0ms (0.2%)

localize7.0ms (0.2%)

series10.0ms (0.3%)

rewrite51.0ms (1.6%)

simplify62.0ms (2%)

localize5.0ms (0.2%)

series5.0ms (0.2%)

rewrite79.0ms (2.5%)

simplify6.0ms (0.2%)

localize6.0ms (0.2%)

series2.0ms (0.1%)

rewrite56.0ms (1.8%)

simplify59.0ms (1.9%)

localize8.0ms (0.3%)

series151.0ms (4.8%)

rewrite96.0ms (3.1%)

simplify13.0ms (0.4%)

eval96.0ms (3.1%)

prune58.0ms (1.9%)

localize6.0ms (0.2%)

series2.0ms (0.1%)

rewrite46.0ms (1.5%)

simplify142.0ms (4.6%)

localize8.0ms (0.2%)

series6.0ms (0.2%)

rewrite54.0ms (1.7%)

simplify86.0ms (2.8%)

eval45.0ms (1.5%)

prune27.0ms (0.9%)

regimes58.0ms (1.9%)

bsearch128.0ms (4.1%)

regimes23.0ms (0.7%)

bsearch17.0ms (0.5%)

simplify7.0ms (0.2%)

end145.0ms (4.7%)

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