Details

analyze143.0ms (9.5%)

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)

sample842.0ms (55.9%)

Results

823.0ms	8256×	body	128	valid
7.0ms	79×	body	128	invalid

preprocess19.0ms (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 (0.4%)

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))

eval1.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

prune2.0ms (0.1%)

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

Click to see full alt table

Status	Error	Program
▶	0.2b	(.f64 x (.f64 27 y))
	0.5b	(.f64 (.f64 x 27) y)

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize6.0ms (0.4%)

Local error

Found 1 expressions with local error:

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

series4.0ms (0.3%)

Counts

1 → 24

Calls

6 calls:

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

rewrite31.0ms (2.1%)

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 exp.f64 (log.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 (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 exp.f64 (log.f64 (*.f64 27 (*.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 27 (*.f64 y x))))))))

simplify10.0ms (0.6%)

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	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))

eval18.0ms (1.2%)

Compiler: Compiled 117 to 77 computations (34.2% saved)

prune9.0ms (0.6%)

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

Click to see full alt table

Status	Error	Program
▶	0.3b	(.f64 27 (.f64 y x))
	31.7b	(cbrt.f64 (pow.f64 (.f64 27 (.f64 y x)) 3))
✓	0.2b	(.f64 x (.f64 27 y))
	28.0b	(pow.f64 (sqrt.f64 (.f64 27 (.f64 y x))) 2)
	0.5b	(.f64 (.f64 x 27) y)

Compiler

Compiled 75 to 57 computations (24% saved)

localize3.0ms (0.2%)

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	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))

rewrite33.0ms (2.2%)

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 exp.f64 (log.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 log1p.f64 (expm1.f64 (*.f64 27 (*.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 27 (*.f64 y x))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 27 (*.f64 y x))))))))

simplify6.0ms (0.4%)

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

eval2.0ms (0.2%)

Compiler: Compiled 87 to 56 computations (35.6% saved)

prune9.0ms (0.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	11	0	11
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	11	5	16

Error

0.0b

Counts

16 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.3b	(.f64 27 (.f64 y x))
	31.7b	(cbrt.f64 (pow.f64 (.f64 27 (.f64 y x)) 3))
✓	0.2b	(.f64 x (.f64 27 y))
	28.0b	(pow.f64 (sqrt.f64 (.f64 27 (.f64 y x))) 2)
▶	0.5b	(.f64 (.f64 x 27) y)

Compiler

Compiled 68 to 52 computations (23.5% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.5b	(.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	y	@	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)

rewrite73.0ms (4.8%)

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 exp.f64 (log.f64 (*.f64 27 (*.f64 x y))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 27 (*.f64 x y))))))))

simplify9.0ms (0.6%)

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	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))

eval3.0ms (0.2%)

Compiler: Compiled 117 to 78 computations (33.3% saved)

prune52.0ms (3.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	14	1	15
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	15	5	20

Error

0.0b

Counts

20 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	28.0b	(pow.f64 (sqrt.f64 (.f64 27 (.f64 x y))) 2)
✓	0.3b	(.f64 27 (.f64 y x))
	31.7b	(cbrt.f64 (pow.f64 (.f64 27 (.f64 y x)) 3))
✓	0.2b	(.f64 x (.f64 27 y))
✓	0.5b	(.f64 (.f64 x 27) y)

Compiler

Compiled 61 to 47 computations (23% 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 x y))) 2)
✓	0.3b	(.f64 27 (.f64 x y))
✓	7.8b	(sqrt.f64 (.f64 27 (.f64 x y)))

series16.0ms (1.1%)

Counts

3 → 24

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	y	@	-inf	(.f64 27 (.f64 x y))
2.0ms	x	@	0	(pow.f64 (sqrt.f64 (.f64 27 (.f64 x y))) 2)
2.0ms	x	@	0	(sqrt.f64 (.f64 27 (.f64 x y)))
2.0ms	y	@	0	(pow.f64 (sqrt.f64 (.f64 27 (.f64 x y))) 2)
1.0ms	x	@	inf	(sqrt.f64 (.f64 27 (.f64 x y)))

rewrite47.0ms (3.1%)

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	23
1	187	23
2	1845	23

Stop Event

1×	node limit

Counts

3 → 71

Calls

Call 1

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

Outputs

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

simplify11.0ms (0.7%)

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

95 → 65

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))

eval17.0ms (1.1%)

Compiler: Compiled 737 to 532 computations (27.8% saved)

prune57.0ms (3.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	61	4	65
Fresh	1	0	1
Picked	1	0	1
Done	0	3	3
Total	63	7	70

Error

Counts

70 → 7

Alt Table

Click to see full alt table

Status	Error	Program
	1.5b	(.f64 (.f64 (*.f64 27 x) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))
	28.2b	(pow.f64 (pow.f64 (pow.f64 (.f64 y (.f64 27 x)) 1/4) 2) 2)
	16.4b	(.f64 (.f64 (*.f64 27 x) (sqrt.f64 y)) (sqrt.f64 y))
✓	0.3b	(.f64 27 (.f64 y x))
✓	0.2b	(.f64 x (.f64 27 y))
✓	0.5b	(.f64 (.f64 x 27) y)
	28.0b	(.f64 (sqrt.f64 (.f64 x y)) (.f64 (sqrt.f64 (.f64 x y)) 27))

Compiler

Compiled 71 to 49 computations (31% saved)

regimes35.0ms (2.3%)

Accuracy

Total -50.1b remaining (-22924.3%)

Threshold costs -50.1b (-22924.3%)

Counts

10 → 1

Calls

Call 1

Inputs
(.f64 (.f64 (*.f64 27 x) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))
(pow.f64 (pow.f64 (pow.f64 (.f64 y (.f64 27 x)) 1/4) 2) 2)
(.f64 (.f64 (*.f64 27 x) (sqrt.f64 y)) (sqrt.f64 y))
(.f64 (sqrt.f64 (.f64 x y)) (.f64 (sqrt.f64 (.f64 x y)) 27))
(pow.f64 (sqrt.f64 (.f64 27 (.f64 x y))) 2)
(.f64 27 (.f64 y x))
(cbrt.f64 (pow.f64 (.f64 27 (.f64 y x)) 3))
(pow.f64 (sqrt.f64 (.f64 27 (.f64 y x))) 2)
(.f64 x (.f64 27 y))
(.f64 (.f64 x 27) y)

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

Results

Time	Error	Segments	Branch
11.0ms	0.2b	1	`x`
6.0ms	0.2b	1	`y`
8.0ms	0.2b	1	`(.f64 (.f64 x 27) y)`
7.0ms	0.2b	1	`(*.f64 x 27)`

Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify2.0ms (0.1%)

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))

end28.0ms (1.8%)

Stop Event

1×

fuel

Compiler

Compiled 28 to 20 computations (28.6% saved)

Details

analyze143.0ms (9.5%)

sample842.0ms (55.9%)

preprocess19.0ms (1.3%)

simplify7.0ms (0.4%)

eval1.0ms (0%)

prune2.0ms (0.1%)

localize6.0ms (0.4%)

series4.0ms (0.3%)

rewrite31.0ms (2.1%)

simplify10.0ms (0.6%)

eval18.0ms (1.2%)

prune9.0ms (0.6%)

localize3.0ms (0.2%)

series2.0ms (0.1%)

rewrite33.0ms (2.2%)

simplify6.0ms (0.4%)

eval2.0ms (0.2%)

prune9.0ms (0.6%)

localize3.0ms (0.2%)

series2.0ms (0.1%)

rewrite73.0ms (4.8%)

simplify9.0ms (0.6%)

eval3.0ms (0.2%)

prune52.0ms (3.5%)

localize5.0ms (0.4%)

series16.0ms (1.1%)

rewrite47.0ms (3.1%)

simplify11.0ms (0.7%)

eval17.0ms (1.1%)

prune57.0ms (3.8%)

regimes35.0ms (2.3%)

simplify2.0ms (0.1%)

end28.0ms (1.8%)

Profiling