Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 8 to 6 computations (25% saved)

sample1.1s (26.9%)

Results

1.1s	8256×	body	256	valid
0.0ms	3×	body	256	invalid

preprocess39.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 8 to 6 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

34.1b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	34.1b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 7 to 5 computations (28.6% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	32.7b	(sqrt.f64 (.f64 (.f64 2 x) x))

Compiler

Compiled 17 to 11 computations (35.3% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite91.0ms (2.2%)

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

Outputs

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

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

36 → 26

Calls

Call 1

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

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

eval6.0ms (0.1%)

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

prune8.0ms (0.2%)

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

0.2b

Counts

27 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.4b	(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
▶	32.0b	(*.f64 (sqrt.f64 2) (neg.f64 x))
▶	31.8b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
▶	31.0b	(*.f64 (sqrt.f64 2) x)
✓	34.1b	(sqrt.f64 (.f64 (.f64 2 x) x))
	34.3b	(.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 2 (.f64 x x))) 2)) (sqrt.f64 (cbrt.f64 (.f64 2 (*.f64 x x)))))
▶	31.7b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Compiler

Compiled 113 to 89 computations (21.2% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

series1.0ms (0%)

Counts

1 → 0

Calls

3 calls:

Time	Variable		Point	Expression
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)

rewrite38.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

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

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

Outputs

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

15 → 15

Calls

Call 1

Inputs

Outputs

localize135.0ms (3.3%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 12 to 8 computations (33.3% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite44.0ms (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	1473	6

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

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

Outputs

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

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	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))

localize10.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 12 computations (36.8% saved)

series2.0ms (0.1%)

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))

rewrite191.0ms (4.6%)

Algorithm

1×	batch-egg-rewrite

Rules

597×	`pow1_binary64`
552×	`add-log-exp_binary64`
552×	`log1p-expm1-u_binary64`
552×	`expm1-log1p-u_binary64`
537×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	142	6
2	1593	6

Stop Event

1×	node limit

Counts

1 → 12

Calls

Call 1

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

Outputs

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

simplify19.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

24 → 15

Calls

Call 1

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

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

localize155.0ms (3.7%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 22 to 18 computations (18.2% saved)

series6.0ms (0.2%)

Counts

2 → 0

Calls

6 calls:

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

rewrite52.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 52

Calls

Call 1

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

Outputs

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

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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

52 → 52

Calls

Call 1

Inputs

Outputs

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (*.f64 (sqrt.f64 2) x))
✓	0.2b	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
	0.5b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 21 to 17 computations (19% saved)

series9.0ms (0.2%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	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	@	inf	(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
1.0ms	x	@	0	(sqrt.f64 (*.f64 (sqrt.f64 2) x))

rewrite48.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 50

Calls

Call 1

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

Outputs

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

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

50 → 50

Calls

Call 1

Inputs

Outputs

eval50.0ms (1.2%)

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

prune25.0ms (0.6%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	174	3	177
Fresh	1	0	1
Picked	1	0	1
Done	1	4	5
Total	177	7	184

Error

0.1b

Counts

184 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.9b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
▶	34.4b	(pow.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3)
✓	32.0b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	31.0b	(*.f64 (sqrt.f64 2) x)
✓	34.1b	(sqrt.f64 (.f64 (.f64 2 x) x))
▶	31.9b	(pow.f64 (*.f64 (pow.f64 2 1/4) (sqrt.f64 x)) 2)
✓	31.7b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))

Compiler

Compiled 55 to 45 computations (18.2% saved)

localize12.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 21 to 18 computations (14.3% saved)

series41.0ms (1%)

Counts

2 → 12

Calls

6 calls:

Time	Variable		Point	Expression
39.0ms	x	@	0	(*.f64 (pow.f64 2 1/4) x)
1.0ms	x	@	inf	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
0.0ms	x	@	inf	(*.f64 (pow.f64 2 1/4) x)
0.0ms	x	@	-inf	(*.f64 (pow.f64 2 1/4) x)
0.0ms	x	@	-inf	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))

rewrite51.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 22

Calls

Call 1

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

Outputs

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

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

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	72
1	6	72

Stop Event

1×

saturated

Counts

34 → 23

Calls

Call 1

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

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

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 x x))
✓	0.1b	(sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x))))
✓	0.7b	(pow.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3)
✓	33.8b	(cbrt.f64 (.f64 2 (.f64 x x)))

Compiler

Compiled 34 to 19 computations (44.1% saved)

series81.0ms (2%)

Counts

4 → 12

Calls

12 calls:

Time	Variable		Point	Expression
74.0ms	x	@	0	(pow.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3)
1.0ms	x	@	inf	(pow.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3)
1.0ms	x	@	0	(cbrt.f64 (.f64 2 (.f64 x x)))
1.0ms	x	@	-inf	(pow.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3)
1.0ms	x	@	inf	(cbrt.f64 (.f64 2 (.f64 x x)))

rewrite80.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 90

Calls

Call 1

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

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

simplify170.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

102 → 92

Calls

Call 1

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

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

localize11.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 23 to 17 computations (26.1% saved)

series10.0ms (0.2%)

Counts

2 → 0

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	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	(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))

rewrite53.0ms (1.3%)

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	1824	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 (sqrt.f64 2) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 2 (*.f64 x x))) (cbrt.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (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 (*.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 (*.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 expm1.f64 (log1p.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (sqrt.f64 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (sqrt.f64 2))))))))

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

35 → 35

Calls

Call 1

Inputs

Outputs

eval60.0ms (1.4%)

Compiler: Compiled 1636 to 1311 computations (19.9% saved)

prune23.0ms (0.6%)

Pruning

10 alts after pruning (3 fresh and 7 done)

	Pruned	Kept	Total
New	147	3	150
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	147	10	157

Error

0.1b

Counts

157 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	30.9b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
✓	34.4b	(pow.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3)
✓	32.0b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	31.0b	(*.f64 (sqrt.f64 2) x)
✓	34.1b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	31.9b	(pow.f64 (*.f64 (pow.f64 2 1/4) (sqrt.f64 x)) 2)
▶	1.4b	(pow.f64 (sqrt.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x))) 3)
✓	31.7b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
▶	34.1b	(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 (*.f64 x x) (sqrt.f64 2))))
▶	1.4b	(pow.f64 (fabs.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3)

Compiler

Compiled 87 to 72 computations (17.2% saved)

localize18.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x x) (sqrt.f64 2))
✓	0.3b	(.f64 (pow.f64 2 1/4) (sqrt.f64 (.f64 (*.f64 x x) (sqrt.f64 2))))
✓	32.7b	(sqrt.f64 (.f64 (.f64 x x) (sqrt.f64 2)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite53.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 51

Calls

Call 1

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

Outputs

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

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

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

simplify107.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	388
1	37	388
2	95	388
3	270	388
4	1142	388
5	2167	388
6	3835	388
7	5287	388
8	6626	388
9	7448	388

Stop Event

1×	node limit

Counts

87 → 60

Calls

Call 1

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

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

localize23.0ms (0.6%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 29 to 24 computations (17.2% saved)

series35.0ms (0.9%)

Counts

3 → 24

Calls

9 calls:

Time	Variable		Point	Expression
28.0ms	x	@	0	(pow.f64 (fabs.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3)
3.0ms	x	@	inf	(pow.f64 (fabs.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3)
2.0ms	x	@	-inf	(pow.f64 (fabs.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3)
1.0ms	x	@	-inf	(cbrt.f64 (*.f64 x (sqrt.f64 2)))
1.0ms	x	@	inf	(cbrt.f64 (*.f64 x (sqrt.f64 2)))

rewrite89.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 67

Calls

Call 1

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

Outputs

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

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

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

simplify124.0ms (3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

91 → 64

Calls

Call 1

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

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

localize38.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x))
✓	0.5b	(cbrt.f64 x)
✓	0.5b	(cbrt.f64 (*.f64 2 x))
✓	0.7b	(pow.f64 (sqrt.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x))) 3)

Compiler

Compiled 38 to 25 computations (34.2% saved)

series13.0ms (0.3%)

Counts

4 → 0

Calls

12 calls:

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

rewrite104.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	208	27
2	2216	27

Stop Event

1×	node limit

Counts

4 → 83

Calls

Call 1

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

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

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

83 → 83

Calls

Call 1

Inputs

Outputs

eval122.0ms (3%)

Compiler: Compiled 2549 to 1988 computations (22% saved)

prune57.0ms (1.4%)

Pruning

12 alts after pruning (3 fresh and 9 done)

	Pruned	Kept	Total
New	204	3	207
Fresh	0	0	0
Picked	0	1	1
Done	1	8	9
Total	205	12	217

Error

0.0b

Counts

217 → 12

Alt Table

Click to see full alt table

Status	Error	Program
✓	31.7b	(.f64 (sqrt.f64 (.f64 2 x)) (sqrt.f64 x))
	1.4b	(pow.f64 (fabs.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x))) 3)
	32.0b	(.f64 (pow.f64 2 1/4) (.f64 (sqrt.f64 (sqrt.f64 2)) (neg.f64 x)))
✓	1.4b	(pow.f64 (fabs.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3)
✓	30.9b	(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
✓	34.4b	(pow.f64 (sqrt.f64 (cbrt.f64 (.f64 2 (.f64 x x)))) 3)
	2.5b	(pow.f64 (fabs.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3)) 3)
✓	32.0b	(*.f64 (sqrt.f64 2) (neg.f64 x))
✓	31.0b	(*.f64 (sqrt.f64 2) x)
✓	34.1b	(sqrt.f64 (.f64 (.f64 2 x) x))
✓	31.9b	(pow.f64 (*.f64 (pow.f64 2 1/4) (sqrt.f64 x)) 2)
✓	1.4b	(pow.f64 (sqrt.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x))) 3)

Compiler

Compiled 108 to 92 computations (14.8% saved)

regimes55.0ms (1.3%)

Counts

16 → 1

Calls

Call 1

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

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

Calls

3 calls:

21.0ms	x
12.0ms	(.f64 (.f64 2 x) x)
12.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))

Results

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

Compiler

Compiled 154 to 119 computations (22.7% saved)

regimes46.0ms (1.1%)

Counts

13 → 1

Calls

Call 1

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

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

Calls

3 calls:

17.0ms	x
11.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))
10.0ms	(.f64 (.f64 2 x) x)

Results

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

Compiler

Compiled 117 to 91 computations (22.2% saved)

regimes47.0ms (1.1%)

Counts

12 → 1

Calls

Call 1

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

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

Calls

3 calls:

18.0ms	x
11.0ms	(.f64 (.f64 2 x) x)
10.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))

Results

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

Compiler

Compiled 107 to 83 computations (22.4% saved)

regimes136.0ms (3.3%)

Counts

11 → 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))
(.f64 (pow.f64 2 1/4) (.f64 (pow.f64 2 1/4) x))
(pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x)) 3)
(pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 2) x)) 2)
(pow.f64 (*.f64 (pow.f64 2 1/4) (sqrt.f64 x)) 2)
(pow.f64 (sqrt.f64 (cbrt.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 (*.f64 x x) (sqrt.f64 2))))

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

Calls

3 calls:

74.0ms	(.f64 (.f64 2 x) x)
30.0ms	x
26.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))

Results

Error	Segments	Branch
0.4b	2	`x`
16.5b	3	`(sqrt.f64 (.f64 (.f64 2 x) x))`
16.5b	3	`(.f64 (.f64 2 x) x)`

Compiler

Compiled 99 to 76 computations (23.2% saved)

bsearch31.0ms (0.7%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
30.0ms	-2.713715200157104e-299	5.5881129459418656e-303

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes51.0ms (1.2%)

Accuracy

Total -62.1b remaining (-13358.1%)

Threshold costs -62.1b (-13358.1%)

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:

17.0ms	(.f64 (.f64 2 x) x)
15.0ms	(sqrt.f64 (.f64 (.f64 2 x) x))
7.0ms	x

Results

Error	Segments	Branch
0.5b	2	`x`
16.5b	3	`(sqrt.f64 (.f64 (.f64 2 x) x))`
16.5b	3	`(.f64 (.f64 2 x) x)`

Compiler

Compiled 31 to 22 computations (29% saved)

bsearch16.0ms (0.4%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
15.0ms	-2.713715200157104e-299	5.5881129459418656e-303

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`*-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	30	95
1	44	95
2	52	95
3	57	95
4	60	95
5	61	95

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(pow.f64 (fabs.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x))) 3)
(pow.f64 (sqrt.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x))) 3)
(pow.f64 (fabs.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3)
(if (<=.f64 x -1278850416061695/47125446914534694131579097993419809976955095716785201420286055195012674566357244479460731079205201122720511132925006540350105785156086431086764996857554304860885586653967937772270969055149056096849908977391371752266308172471982589601097478449614615258949356272900190565812730839296826751014759649673012612226351104) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x)))
(if (<=.f64 x -1278850416061695/47125446914534694131579097993419809976955095716785201420286055195012674566357244479460731079205201122720511132925006540350105785156086431086764996857554304860885586653967937772270969055149056096849908977391371752266308172471982589601097478449614615258949356272900190565812730839296826751014759649673012612226351104) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) x)

Outputs
(pow.f64 (fabs.f64 (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 x))) 3)
(pow.f64 (sqrt.f64 (.f64 (cbrt.f64 (.f64 2 x)) (cbrt.f64 x))) 3)
(pow.f64 (sqrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (.f64 2 x)))) 3)
(pow.f64 (fabs.f64 (cbrt.f64 (*.f64 x (sqrt.f64 2)))) 3)
(pow.f64 (fabs.f64 (cbrt.f64 (*.f64 (sqrt.f64 2) x))) 3)
(if (<=.f64 x -1278850416061695/47125446914534694131579097993419809976955095716785201420286055195012674566357244479460731079205201122720511132925006540350105785156086431086764996857554304860885586653967937772270969055149056096849908977391371752266308172471982589601097478449614615258949356272900190565812730839296826751014759649673012612226351104) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 (*.f64 2 x)) (sqrt.f64 x)))
(if (<=.f64 x -1278850416061695/47125446914534694131579097993419809976955095716785201420286055195012674566357244479460731079205201122720511132925006540350105785156086431086764996857554304860885586653967937772270969055149056096849908977391371752266308172471982589601097478449614615258949356272900190565812730839296826751014759649673012612226351104) (.f64 (sqrt.f64 2) (neg.f64 x)) (.f64 (sqrt.f64 2) x))
(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 66 to 54 computations (18.2% saved)

soundness10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Compiler

Compiled 19 to 16 computations (15.8% saved)

end190.0ms (4.6%)

Compiler: Compiled 61 to 47 computations (23% saved)

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

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

Details

analyze6.0ms (0.1%)

sample1.1s (26.9%)

preprocess39.0ms (0.9%)

simplify6.0ms (0.1%)

eval1.0ms (0%)

prune1.0ms (0%)

localize8.0ms (0.2%)

series2.0ms (0%)

rewrite91.0ms (2.2%)

simplify12.0ms (0.3%)

eval6.0ms (0.1%)

prune8.0ms (0.2%)

localize4.0ms (0.1%)

series1.0ms (0%)

rewrite38.0ms (0.9%)

simplify6.0ms (0.1%)

localize135.0ms (3.3%)

series1.0ms (0%)

rewrite44.0ms (1.1%)

simplify13.0ms (0.3%)

localize10.0ms (0.2%)

series2.0ms (0.1%)

rewrite191.0ms (4.6%)

simplify19.0ms (0.5%)

localize155.0ms (3.7%)

series6.0ms (0.2%)

rewrite52.0ms (1.2%)

simplify7.0ms (0.2%)

localize10.0ms (0.2%)

series9.0ms (0.2%)

rewrite48.0ms (1.2%)

simplify6.0ms (0.1%)

eval50.0ms (1.2%)

prune25.0ms (0.6%)

localize12.0ms (0.3%)

series41.0ms (1%)

rewrite51.0ms (1.2%)

simplify7.0ms (0.2%)

localize14.0ms (0.3%)

series81.0ms (2%)

rewrite80.0ms (1.9%)

simplify170.0ms (4.1%)

localize11.0ms (0.3%)

series10.0ms (0.2%)

rewrite53.0ms (1.3%)

simplify6.0ms (0.1%)

eval60.0ms (1.4%)

prune23.0ms (0.6%)

localize18.0ms (0.4%)

series4.0ms (0.1%)

rewrite53.0ms (1.3%)

simplify107.0ms (2.6%)

localize23.0ms (0.6%)

series35.0ms (0.9%)

rewrite89.0ms (2.2%)

simplify124.0ms (3%)

localize38.0ms (0.9%)

series13.0ms (0.3%)

rewrite104.0ms (2.5%)

simplify14.0ms (0.3%)

eval122.0ms (3%)

prune57.0ms (1.4%)

regimes55.0ms (1.3%)

regimes46.0ms (1.1%)

regimes47.0ms (1.1%)

regimes136.0ms (3.3%)

bsearch31.0ms (0.7%)

regimes51.0ms (1.2%)

bsearch16.0ms (0.4%)

simplify8.0ms (0.2%)

soundness10.0ms (0.2%)

end190.0ms (4.6%)

Profiling

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