Details

analyze112.0ms (8.7%)

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)

sample795.0ms (61.2%)

Results

771.0ms	8256×	body	128	valid
10.0ms	90×	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)

simplify7.0ms (0.6%)

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 (.f64 x 27) y)
	0.2b	(.f64 x (.f64 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 (.f64 x 27) y)

series4.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

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

rewrite33.0ms (2.5%)

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 exp.f64 (log.f64 (.f64 27 (.f64 x y))))))) (#(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))))))))

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 exp.f64 (log.f64 (*.f64 27 (*.f64 x y))))))) (#(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))))))))

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))

prune10.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	13	2	15
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	13	4	17

Error

0.0b

Counts

17 → 4

Alt Table

Status	Error	Program
▶	0.2b	(.f64 27 (.f64 y x))
	0.2b	(.f64 x (.f64 27 y))
✓	0.2b	(.f64 (.f64 x 27) y)
	1.2b	(pow.f64 (cbrt.f64 (.f64 27 (.f64 x y))) 3)

Compiler

Compiled 172 to 119 computations (30.8% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.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	y	@	-inf	(.f64 27 (.f64 y x))
0.0ms	x	@	inf	(.f64 27 (.f64 y x))
0.0ms	x	@	-inf	(.f64 27 (.f64 y x))

rewrite32.0ms (2.4%)

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 exp.f64 (log.f64 (.f64 27 (.f64 y x))))))) (#(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))))))))

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 exp.f64 (log.f64 (*.f64 27 (*.f64 y x))))))) (#(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))))))))

simplify8.0ms (0.6%)

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

prune7.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	11	0	11
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	11	4	15

Error

0.0b

Counts

15 → 4

Alt Table

Status	Error	Program
✓	0.2b	(.f64 27 (.f64 y x))
▶	0.2b	(.f64 x (.f64 27 y))
✓	0.2b	(.f64 (.f64 x 27) y)
	1.2b	(pow.f64 (cbrt.f64 (.f64 27 (.f64 x y))) 3)

Compiler

Compiled 135 to 92 computations (31.9% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

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

rewrite34.0ms (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 exp.f64 (log.f64 (*.f64 27 (*.f64 y x))))))) (#(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))))))))

simplify10.0ms (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))

prune9.0ms (0.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	15	0	15
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	15	4	19

Error

0.0b

Counts

19 → 4

Alt Table

Status	Error	Program
✓	0.2b	(.f64 27 (.f64 y x))
✓	0.2b	(.f64 x (.f64 27 y))
✓	0.2b	(.f64 (.f64 x 27) y)
▶	1.2b	(pow.f64 (cbrt.f64 (.f64 27 (.f64 x y))) 3)

Compiler

Compiled 158 to 108 computations (31.6% saved)

localize5.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 27 (.f64 x y))
✓	0.6b	(pow.f64 (cbrt.f64 (.f64 27 (.f64 x y))) 3)
✓	9.6b	(cbrt.f64 (.f64 27 (.f64 x y)))

series15.0ms (1.1%)

Counts

3 → 24

Calls

18 calls:

Time	Variable		Point	Expression
3.0ms	y	@	-inf	(pow.f64 (cbrt.f64 (.f64 27 (.f64 x y))) 3)
2.0ms	x	@	-inf	(pow.f64 (cbrt.f64 (.f64 27 (.f64 x y))) 3)
2.0ms	x	@	-inf	(cbrt.f64 (.f64 27 (.f64 x y)))
1.0ms	x	@	0	(pow.f64 (cbrt.f64 (.f64 27 (.f64 x y))) 3)
1.0ms	x	@	0	(cbrt.f64 (.f64 27 (.f64 x y)))

rewrite44.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

711×	`pow1_binary64`
666×	`add-log-exp_binary64`
666×	`log1p-expm1-u_binary64`
666×	`expm1-log1p-u_binary64`
78×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	186	23
2	1863	23

Stop Event

1×	node limit

Counts

3 → 74

Calls

Call 1

Inputs
(cbrt.f64 (.f64 27 (.f64 x y)))
(pow.f64 (cbrt.f64 (.f64 27 (.f64 x y))) 3)
(.f64 27 (.f64 x y))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 3 (cbrt.f64 (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (*.f64 y (*.f64 27 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 x y)) (pow.f64 27 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 y (*.f64 27 x)))) (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 y (*.f64 27 x)))) (pow.f64 (pow.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) 2) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) 2)) (cbrt.f64 (cbrt.f64 (*.f64 y (*.f64 27 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 y (*.f64 27 x)) 1/6) (pow.f64 (*.f64 y (*.f64 27 x)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 27 x)) (cbrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 27 1/3) (cbrt.f64 (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) 2) 1/3) (cbrt.f64 (cbrt.f64 (*.f64 y (*.f64 27 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (*.f64 y (*.f64 27 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (*.f64 y (*.f64 27 x))) 1/3) (pow.f64 (sqrt.f64 (*.f64 y (*.f64 27 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 27 x) 1/3) (cbrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y (*.f64 27 x)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 y (*.f64 27 x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 y (*.f64 27 x)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 3) (cbrt.f64 (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (*.f64 y (*.f64 27 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (*.f64 y (*.f64 27 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (*.f64 y (*.f64 27 x)))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 y (*.f64 27 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 27 (*.f64 x y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 y 27))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 y (*.f64 27 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x y) 27)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 y (*.f64 27 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) (pow.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 3 (*.f64 (cbrt.f64 (*.f64 x y)) (pow.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 y (*.f64 27 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) 2) (cbrt.f64 (*.f64 y (*.f64 27 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 x y)) 2) (*.f64 (cbrt.f64 (*.f64 x y)) 27))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) 2)) (*.f64 (cbrt.f64 (cbrt.f64 (*.f64 y (*.f64 27 x)))) (pow.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 x y)) (*.f64 (sqrt.f64 (*.f64 x y)) 27))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 y (*.f64 27 x))) (sqrt.f64 (*.f64 y (*.f64 27 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 y (*.f64 27 x)) 1/6) (*.f64 (pow.f64 (*.f64 y (*.f64 27 x)) 1/6) (pow.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 27 x) y)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) 2)) 3) (cbrt.f64 (*.f64 y (*.f64 27 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (*.f64 y (*.f64 27 x)) 1/6) 3) (pow.f64 (pow.f64 (*.f64 y (*.f64 27 x)) 1/6) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 27 y) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 27 (pow.f64 (cbrt.f64 (*.f64 x y)) 2)) (cbrt.f64 (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 27 (sqrt.f64 (*.f64 x y))) (sqrt.f64 (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) 2) 3) (cbrt.f64 (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) 2) 1) (cbrt.f64 (*.f64 y (*.f64 27 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) 2))) (cbrt.f64 (cbrt.f64 (*.f64 y (*.f64 27 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (cbrt.f64 (*.f64 y (*.f64 27 x))) 2) (pow.f64 (*.f64 y (*.f64 27 x)) 1/6)) (pow.f64 (*.f64 y (*.f64 27 x)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 27 x) 1) y)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 27 x) (cbrt.f64 (*.f64 y y))) (cbrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 27 x) (sqrt.f64 y)) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (*.f64 x y) 2) 729))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 27) (*.f64 x y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 y (*.f64 27 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 y (*.f64 27 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 y (*.f64 27 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 y (*.f64 27 x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 y (*.f64 27 x))))))))

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

simplify11.0ms (0.9%)

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

98 → 68

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))

prune38.0ms (2.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	66	6	72

Error

0.0b

Counts

72 → 6

Alt Table

Status	Error	Program
✓	0.2b	(.f64 27 (.f64 y x))
✓	0.2b	(.f64 x (.f64 27 y))
	14.9b	(.f64 (.f64 (*.f64 27 x) (sqrt.f64 y)) (sqrt.f64 y))
	1.2b	(.f64 (pow.f64 (cbrt.f64 (.f64 x y)) 2) (.f64 (cbrt.f64 (.f64 x y)) 27))
✓	0.2b	(.f64 (.f64 x 27) y)
✓	1.2b	(pow.f64 (cbrt.f64 (.f64 27 (.f64 x y))) 3)

Compiler

Compiled 857 to 614 computations (28.4% saved)

regimes23.0ms (1.8%)

Accuracy

Total -31.8b remaining (-12040.2%)

Threshold costs -31.8b (-12040.2%)

Counts

6 → 1

Compiler

Compiled 65 to 41 computations (36.9% 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 27 (.f64 y x))

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

end56.0ms (4.3%)

Stop Event

1×

fuel

Remove

(sort x y)

Compiler

Compiled 73 to 45 computations (38.4% saved)

Details

analyze112.0ms (8.7%)

sample795.0ms (61.2%)

preprocess17.0ms (1.3%)

simplify7.0ms (0.6%)

prune3.0ms (0.2%)

localize3.0ms (0.2%)

series4.0ms (0.3%)

rewrite33.0ms (2.5%)

simplify9.0ms (0.7%)

prune10.0ms (0.8%)

localize3.0ms (0.2%)

series2.0ms (0.1%)

rewrite32.0ms (2.4%)

simplify8.0ms (0.6%)

prune7.0ms (0.6%)

localize3.0ms (0.2%)

series2.0ms (0.1%)

rewrite34.0ms (2.6%)

simplify10.0ms (0.7%)

prune9.0ms (0.7%)

localize5.0ms (0.4%)

series15.0ms (1.1%)

rewrite44.0ms (3.4%)

simplify11.0ms (0.9%)

prune38.0ms (2.9%)

regimes23.0ms (1.8%)

simplify2.0ms (0.2%)

end56.0ms (4.3%)

Profiling