Details

analyze117.0ms (9.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
50%	43.7%	6.3%	7
59.3%	34.3%	6.3%	8
67.1%	23.4%	9.5%	9
72.6%	18%	9.5%	10
76.9%	12.1%	11%	11
79.8%	9.2%	11%	12
82%	6.1%	11.8%	13
83.6%	4.6%	11.8%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample726.0ms (57.8%)

Results

703.0ms	8256×	body	128	valid
8.0ms	96×	body	128	invalid

preprocess17.0ms (1.3%)

Algorithm

2×	egg-herbie

Rules

5×	`*-commutative_binary64`
4×	`associate-l_binary64`
2×	`associate-r_binary64`
1×	`swap-x-y`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	14	14
2	20	14
3	20	14
0	2	2
1	2	2

Stop Event

1×	unsound
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1
0

Call 2

Inputs
(.f64 (.f64 x 27) y)
(.f64 (.f64 y 27) x)

Outputs
(.f64 (.f64 x 27) y)
(.f64 x (.f64 27 y))
(.f64 (.f64 y 27) x)
(.f64 x (.f64 27 y))

Symmetry

(sort x y)

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify6.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	10	7
2	17	7
3	19	7

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(.f64 (.f64 x 27) y)

Outputs
(.f64 (.f64 x 27) y)
(.f64 x (.f64 27 y))

prune3.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(.f64 x (.f64 27 y))
	0.2b	(.f64 (.f64 x 27) y)

Compiler

Compiled 40 to 28 computations (30% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 x (.f64 27 y))

series6.0ms (0.5%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	y	@	0	(.f64 x (.f64 27 y))
1.0ms	x	@	0	(.f64 x (.f64 27 y))
1.0ms	x	@	inf	(.f64 x (.f64 27 y))
1.0ms	y	@	inf	(.f64 x (.f64 27 y))
0.0ms	y	@	-inf	(.f64 x (.f64 27 y))

rewrite33.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

555×	`pow1_binary64`
512×	`add-log-exp_binary64`
512×	`log1p-expm1-u_binary64`
512×	`expm1-log1p-u_binary64`
502×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	121	7
2	1394	7

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

Inputs
(.f64 x (.f64 27 y))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (.f64 27 (.f64 y x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 27 (.f64 y x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 27 (.f64 y x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 27 (.f64 y x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 27 (.f64 y x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 27 (.f64 y x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 27) y) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 27 (.f64 y x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 x 3) (pow.f64 (.f64 27 y) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 27 y) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 27 (.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 27 (.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 27 (.f64 y x))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 27 (*.f64 y x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 27 (*.f64 y x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 27 (*.f64 y x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 27 (*.f64 y x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 27 (*.f64 y x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 27 (*.f64 y x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 27) y) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 27 (*.f64 y x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 x 3) (pow.f64 (*.f64 27 y) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 27 y) 3) (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 27 (*.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 27 (*.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 27 (*.f64 y x))))))))

simplify9.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	10	168
2	17	168
3	19	168

Stop Event

1×

saturated

Counts

37 → 15

Calls

Call 1

Inputs
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))

Outputs
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))

prune13.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	12	5	17

Error

0.0b

Counts

17 → 5

Alt Table

Status	Error	Program
	25.6b	(pow.f64 (sqrt.f64 (.f64 27 (.f64 y x))) 2)
✓	0.2b	(.f64 x (.f64 27 y))
	0.3b	(.f64 27 (.f64 y x))
▶	0.2b	(.f64 (.f64 x 27) y)
	47.1b	(cbrt.f64 (.f64 (pow.f64 x 3) (pow.f64 (.f64 27 y) 3)))

Compiler

Compiled 196 to 138 computations (29.6% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 x 27) y)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(.f64 (.f64 x 27) y)
0.0ms	x	@	-inf	(.f64 (.f64 x 27) y)
0.0ms	y	@	-inf	(.f64 (.f64 x 27) y)
0.0ms	x	@	inf	(.f64 (.f64 x 27) y)
0.0ms	y	@	inf	(.f64 (.f64 x 27) y)

rewrite35.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

554×	`pow1_binary64`
511×	`add-log-exp_binary64`
511×	`log1p-expm1-u_binary64`
511×	`expm1-log1p-u_binary64`
501×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	121	7
2	1392	7

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

Inputs
(.f64 (.f64 x 27) y)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (.f64 27 (.f64 x y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 27 (.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 27 (.f64 x y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 27 (.f64 x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 27 (.f64 x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 27 (.f64 x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) (.f64 x 27)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 27 (.f64 x y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 x 27) 3) (pow.f64 y 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 y 3) (pow.f64 (.f64 x 27) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 27 (.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 27 (.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 27 (*.f64 x y))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 27 (*.f64 x y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 27 (*.f64 x y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 27 (*.f64 x y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 27 (*.f64 x y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 27 (*.f64 x y))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 27 (*.f64 x y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 y) (*.f64 x 27)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 27 (*.f64 x y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (*.f64 x 27) 3) (pow.f64 y 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 y 3) (pow.f64 (*.f64 x 27) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 27 (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 27 (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 27 (*.f64 x y))))))))

simplify9.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	168
1	10	168
2	17	168
3	19	168

Stop Event

1×

saturated

Counts

37 → 15

Calls

Call 1

Inputs
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))
(.f64 27 (.f64 y x))

Outputs
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))
(.f64 27 (.f64 y x))
(.f64 x (.f64 27 y))

prune21.0ms (1.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	14	1	15
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	14	6	20

Error

0.0b

Counts

20 → 6

Alt Table

Status	Error	Program
	25.6b	(pow.f64 (sqrt.f64 (.f64 27 (.f64 y x))) 2)
✓	0.2b	(.f64 x (.f64 27 y))
▶	0.3b	(.f64 27 (.f64 y x))
✓	0.2b	(.f64 (.f64 x 27) y)
	47.1b	(cbrt.f64 (.f64 (pow.f64 (.f64 x 27) 3) (pow.f64 y 3)))
	47.1b	(cbrt.f64 (.f64 (pow.f64 x 3) (pow.f64 (.f64 27 y) 3)))

Compiler

Compiled 213 to 154 computations (27.7% saved)

localize3.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 27 (.f64 y x))

series2.0ms (0.1%)

Counts

1 → 0

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	y	@	0	(.f64 27 (.f64 y x))
0.0ms	y	@	inf	(.f64 27 (.f64 y x))
0.0ms	x	@	inf	(.f64 27 (.f64 y x))
0.0ms	y	@	-inf	(.f64 27 (.f64 y x))
0.0ms	x	@	-inf	(.f64 27 (.f64 y x))

rewrite35.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

555×	`pow1_binary64`
512×	`add-log-exp_binary64`
512×	`log1p-expm1-u_binary64`
512×	`expm1-log1p-u_binary64`
502×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	121	7
2	1394	7

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(.f64 27 (.f64 y x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 27 (*.f64 y x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 27 (*.f64 y x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 27 (*.f64 y x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 27 (*.f64 y x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 27 (*.f64 y x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (*.f64 y x) 2) 729))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (pow.f64 (exp.f64 y) x) 27))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 27 (*.f64 y x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 27 (*.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 27 (*.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 27 (*.f64 y x))))))))

simplify6.0ms (0.5%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

11 → 11

Calls

Call 1

Inputs

Outputs

prune10.0ms (0.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	11	0	11
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	11	6	17

Error

0.0b

Counts

17 → 6

Alt Table

Status	Error	Program
▶	25.6b	(pow.f64 (sqrt.f64 (.f64 27 (.f64 y x))) 2)
✓	0.2b	(.f64 x (.f64 27 y))
✓	0.3b	(.f64 27 (.f64 y x))
✓	0.2b	(.f64 (.f64 x 27) y)
	47.1b	(cbrt.f64 (.f64 (pow.f64 (.f64 x 27) 3) (pow.f64 y 3)))
	47.1b	(cbrt.f64 (.f64 (pow.f64 x 3) (pow.f64 (.f64 27 y) 3)))

Compiler

Compiled 176 to 127 computations (27.8% saved)

localize5.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (sqrt.f64 (.f64 27 (.f64 y x))) 2)
	0.3b	(.f64 27 (.f64 y x))
✓	8.4b	(sqrt.f64 (.f64 27 (.f64 y x)))

series14.0ms (1.1%)

Counts

2 → 0

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	y	@	0	(sqrt.f64 (.f64 27 (.f64 y x)))
1.0ms	x	@	0	(pow.f64 (sqrt.f64 (.f64 27 (.f64 y x))) 2)
1.0ms	x	@	inf	(pow.f64 (sqrt.f64 (.f64 27 (.f64 y x))) 2)
1.0ms	y	@	inf	(sqrt.f64 (.f64 27 (.f64 y x)))
1.0ms	y	@	0	(pow.f64 (sqrt.f64 (.f64 27 (.f64 y x))) 2)

rewrite41.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

709×	`pow1_binary64`
658×	`add-log-exp_binary64`
658×	`log1p-expm1-u_binary64`
658×	`expm1-log1p-u_binary64`
79×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	187	16
2	1845	16

Stop Event

1×	node limit

Counts

2 → 58

Calls

Call 1

Inputs
(sqrt.f64 (.f64 27 (.f64 y x)))
(pow.f64 (sqrt.f64 (.f64 27 (.f64 y x))) 2)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (sqrt.f64 (*.f64 x (*.f64 27 y))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (*.f64 27 y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 (*.f64 x (*.f64 27 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (*.f64 27 y))) (cbrt.f64 (sqrt.f64 (*.f64 x (*.f64 27 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (*.f64 27 y)))) (cbrt.f64 (*.f64 x (*.f64 27 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 y x)) (sqrt.f64 27))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 27) (sqrt.f64 (*.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (*.f64 27 y)) 1/4) (pow.f64 (*.f64 x (*.f64 27 y)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 27 y)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 27 y))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 x (*.f64 27 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (sqrt.f64 (*.f64 x (*.f64 27 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 27 y))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 x (*.f64 27 y))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 27 y) 1/2) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (*.f64 27 y)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 x (*.f64 27 y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 27 y)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (*.f64 27 y)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 x (*.f64 27 y)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (sqrt.f64 (*.f64 x (*.f64 27 y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 (*.f64 x (*.f64 27 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (*.f64 x (*.f64 27 y))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (*.f64 27 y)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 (*.f64 x (*.f64 27 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 (*.f64 x (*.f64 27 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 (*.f64 x (*.f64 27 y)))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 x (*.f64 27 y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 27 (*.f64 y x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 y (*.f64 x 27))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 27 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 y x) 27)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (*.f64 27 y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x (*.f64 27 y))) (sqrt.f64 (*.f64 x (*.f64 27 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 x (*.f64 27 y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 y x)) 2) (*.f64 (cbrt.f64 (*.f64 y x)) 27))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (*.f64 27 y))) (pow.f64 (cbrt.f64 (*.f64 x (*.f64 27 y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x (*.f64 27 y))) (*.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (*.f64 27 y)))) (sqrt.f64 (*.f64 x (*.f64 27 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x (*.f64 27 y))) 2) (cbrt.f64 (*.f64 x (*.f64 27 y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 y x)) (*.f64 (sqrt.f64 (*.f64 y x)) 27))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 27) (*.f64 (sqrt.f64 (*.f64 y x)) (sqrt.f64 (*.f64 x (*.f64 27 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 x (*.f64 27 y)) 1/4) (*.f64 (pow.f64 (*.f64 x (*.f64 27 y)) 1/4) (sqrt.f64 (*.f64 x (*.f64 27 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 27 y) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 27 y))) (pow.f64 (*.f64 x (*.f64 27 y)) 1/4)) (pow.f64 (*.f64 x (*.f64 27 y)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 27) 2) (*.f64 y x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 27 x) y)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 27 (pow.f64 (cbrt.f64 (*.f64 y x)) 2)) (cbrt.f64 (*.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 27 (sqrt.f64 (*.f64 y x))) (sqrt.f64 (*.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 27 y))) (cbrt.f64 (*.f64 x (*.f64 27 y)))) (cbrt.f64 (sqrt.f64 (*.f64 x (*.f64 27 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (*.f64 x (*.f64 27 y))) (sqrt.f64 27)) (sqrt.f64 (*.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 27 y) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 27 y) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 27 y) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 x (*.f64 27 y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 27) (*.f64 y x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 x (*.f64 27 y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 x (*.f64 27 y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 x (*.f64 27 y))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 x (*.f64 27 y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 x (*.f64 27 y))))))))

simplify7.0ms (0.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

58 → 58

Calls

Call 1

Inputs

Outputs

prune39.0ms (3.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	2	2
Picked	1	0	1
Done	0	3	3
Total	69	6	75

Error

0.0b

Counts

75 → 6

Alt Table

Status	Error	Program
✓	0.3b	(.f64 27 (.f64 y x))
✓	0.2b	(.f64 (.f64 x 27) y)
✓	0.2b	(.f64 x (.f64 27 y))
	25.5b	(.f64 (sqrt.f64 (.f64 y x)) (.f64 (sqrt.f64 (.f64 y x)) 27))
	47.1b	(cbrt.f64 (.f64 (pow.f64 (.f64 x 27) 3) (pow.f64 y 3)))
	47.1b	(cbrt.f64 (.f64 (pow.f64 x 3) (pow.f64 (.f64 27 y) 3)))

Compiler

Compiled 817 to 578 computations (29.3% saved)

regimes31.0ms (2.5%)

Accuracy

Total -52.0b remaining (-20515.4%)

Threshold costs -52.0b (-20515.4%)

Counts

8 → 1

Compiler

Compiled 94 to 64 computations (31.9% saved)

simplify2.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	8	7

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 x (.f64 27 y))

Outputs
(.f64 x (.f64 27 y))

end58.0ms (4.6%)

Stop Event

1×

fuel

Remove

(sort x y)

Compiler

Compiled 74 to 49 computations (33.8% saved)

Details

analyze117.0ms (9.3%)

sample726.0ms (57.8%)

preprocess17.0ms (1.3%)

simplify6.0ms (0.5%)

prune3.0ms (0.2%)

localize3.0ms (0.2%)

series6.0ms (0.5%)

rewrite33.0ms (2.6%)

simplify9.0ms (0.7%)

prune13.0ms (1%)

localize3.0ms (0.2%)

series2.0ms (0.1%)

rewrite35.0ms (2.8%)

simplify9.0ms (0.7%)

prune21.0ms (1.6%)

localize3.0ms (0.3%)

series2.0ms (0.1%)

rewrite35.0ms (2.8%)

simplify6.0ms (0.5%)

prune10.0ms (0.8%)

localize5.0ms (0.4%)

series14.0ms (1.1%)

rewrite41.0ms (3.3%)

simplify7.0ms (0.6%)

prune39.0ms (3.1%)

regimes31.0ms (2.5%)

simplify2.0ms (0.2%)

end58.0ms (4.6%)

Profiling