Details

analyze90.0ms (5.5%)

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
25%	50%	25.1%	6
25%	31.2%	43.8%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

Compiler

Compiled 18 to 8 computations (55.6% saved)

sample753.0ms (45.5%)

Results

741.0ms	8256×	body	128	valid
1.0ms	10×	body	128	invalid

Compiler

Compiled 36 to 16 computations (55.6% saved)

preprocess22.0ms (1.4%)

Algorithm

2×	egg-herbie

Rules

54×	`fma-def_binary64`
8×	`*-commutative_binary64`
8×	`associate-+l+_binary64`
8×	`associate-r_binary64`
6×	`associate-+r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	40
1	25	30
2	52	22
3	91	22
4	125	22
5	137	22
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
(+.f64 (+.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 x x)) (.f64 x x))

Outputs
(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
(+.f64 (.f64 y y) (+.f64 (.f64 y y) (fma.f64 x x (*.f64 y y))))
(fma.f64 y y (fma.f64 x x (*.f64 y (+.f64 y y))))
(fma.f64 x x (.f64 3 (.f64 y y)))
(fma.f64 x x (.f64 y (.f64 3 y)))
(fma.f64 x x (.f64 y (.f64 y 3)))
(+.f64 (+.f64 (+.f64 (.f64 y y) (.f64 x x)) (.f64 x x)) (.f64 x x))
(+.f64 (.f64 x x) (+.f64 (.f64 x x) (fma.f64 x x (*.f64 y y))))
(fma.f64 x x (fma.f64 y y (*.f64 x (+.f64 x x))))
(fma.f64 y y (.f64 3 (.f64 x x)))
(fma.f64 x (.f64 3 x) (.f64 y y))
(fma.f64 x (.f64 x 3) (.f64 y y))

Compiler

Compiled 17 to 7 computations (58.8% saved)

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

28×	`fma-def_binary64`
4×	`*-commutative_binary64`
4×	`associate-+l+_binary64`
4×	`associate-r_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	15	15
2	30	11
3	51	11
4	69	11
5	75	11

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

Outputs
(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
(+.f64 (.f64 y y) (+.f64 (.f64 y y) (fma.f64 x x (*.f64 y y))))
(fma.f64 y y (fma.f64 x x (*.f64 y (+.f64 y y))))
(fma.f64 x x (.f64 3 (.f64 y y)))
(fma.f64 x x (.f64 y (.f64 3 y)))
(fma.f64 y (.f64 y 3) (.f64 x x))

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))
▶	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 79 to 36 computations (54.4% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

series6.0ms (0.4%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	y	@	inf	(fma.f64 y (.f64 y 3) (.f64 x x))
1.0ms	y	@	-inf	(fma.f64 y (.f64 y 3) (.f64 x x))
1.0ms	y	@	0	(fma.f64 y (.f64 y 3) (.f64 x x))
1.0ms	x	@	0	(fma.f64 y (.f64 y 3) (.f64 x x))
0.0ms	x	@	inf	(fma.f64 y (.f64 y 3) (.f64 x x))

rewrite36.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

621×	`pow1_binary64`
571×	`add-log-exp_binary64`
571×	`log1p-expm1-u_binary64`
571×	`expm1-log1p-u_binary64`
70×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	140	11
2	1594	11

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

Inputs
(fma.f64 y (.f64 y 3) (.f64 x x))

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

Outputs

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

simplify64.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

632×	`sqr-pow_binary64`
591×	`associate-l_binary64`
372×	`cube-prod_binary64`
330×	`associate-r_binary64`
284×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	231
1	20	231
2	36	231
3	67	231
4	152	231
5	441	231
6	1734	231
7	2049	231
8	2327	231
9	2578	231
10	2919	231
11	3416	231
12	4073	231
13	4861	231

Stop Event

1×	node limit

Counts

46 → 28

Calls

Call 1

Inputs
(pow.f64 x 2)
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(*.f64 3 (pow.f64 y 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(*.f64 3 (pow.f64 y 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(*.f64 3 (pow.f64 y 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))

Outputs
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(*.f64 3 (pow.f64 y 2))
(.f64 3 (.f64 y y))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(*.f64 3 (pow.f64 y 2))
(.f64 3 (.f64 y y))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(*.f64 3 (pow.f64 y 2))
(.f64 3 (.f64 y y))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))

prune19.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	25	3	28
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	26	4	30

Error

0.0b

Counts

30 → 4

Alt Table

Status	Error	Program
	0.3b	(pow.f64 (sqrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) 2)
	1.2b	(.f64 (cbrt.f64 (fma.f64 y (.f64 y 3) (.f64 x x))) (pow.f64 (cbrt.f64 (fma.f64 y (.f64 y 3) (*.f64 x x))) 2))
▶	0.1b	(fma.f64 x x (.f64 3 (.f64 y y)))
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))

Compiler

Compiled 441 to 250 computations (43.3% saved)

localize12.0ms (0.7%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (.f64 3 (.f64 y y)))
✓	0.2b	(.f64 3 (.f64 y y))

series5.0ms (0.3%)

Counts

2 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(fma.f64 x x (.f64 3 (.f64 y y)))
1.0ms	y	@	0	(.f64 3 (.f64 y y))
1.0ms	x	@	-inf	(fma.f64 x x (.f64 3 (.f64 y y)))
0.0ms	y	@	inf	(.f64 3 (.f64 y y))
0.0ms	x	@	inf	(fma.f64 x x (.f64 3 (.f64 y y)))

rewrite38.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

621×	`pow1_binary64`
571×	`add-log-exp_binary64`
571×	`log1p-expm1-u_binary64`
571×	`expm1-log1p-u_binary64`
70×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	141	18
2	1599	18

Stop Event

1×	node limit

Counts

2 → 34

Calls

Call 1

Inputs
(.f64 3 (.f64 y y))
(fma.f64 x x (.f64 3 (.f64 y y)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 3 (.f64 y y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 3 (.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 3 (.f64 y y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 3 (.f64 y y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 y (sqrt.f64 3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 9 (pow.f64 y 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 3) (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 3 (.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 3 (.f64 y y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 3 (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 3 (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 3 (*.f64 y y))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 3 (.f64 y y)) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x x) (.f64 3 (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 x x) 1) (.f64 3 (.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x x (.f64 3 (.f64 y y))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x x (.f64 3 (.f64 y y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x x (.f64 3 (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x x (.f64 3 (.f64 y y)))) (pow.f64 (cbrt.f64 (fma.f64 x x (.f64 3 (.f64 y y)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x x (.f64 3 (.f64 y y)))) 2) (cbrt.f64 (fma.f64 x x (.f64 3 (.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 x (.f64 y (sqrt.f64 3))) (hypot.f64 x (.f64 y (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (.f64 x x) 3) (pow.f64 (.f64 3 (.f64 y y)) 3)) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (.f64 9 (pow.f64 y 4)) (.f64 (.f64 x x) (.f64 3 (.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 9 (pow.f64 y 4))) (-.f64 (.f64 x x) (.f64 3 (.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x (.f64 3 (.f64 y y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x (.f64 3 (.f64 y y))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x (.f64 3 (.f64 y y)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (.f64 y (sqrt.f64 3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x (.f64 3 (.f64 y y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x (.f64 3 (.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x x (.f64 3 (.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x (.f64 3 (.f64 y y))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x (.f64 3 (.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x (.f64 3 (.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x (.f64 3 (.f64 y y)))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 3 (*.f64 y y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 3 (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 3 (*.f64 y y)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 3 (*.f64 y y))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 y (sqrt.f64 3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 9 (pow.f64 y 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 3) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 3 (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 3 (*.f64 y y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 3 (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 3 (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 3 (*.f64 y y))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 3 (*.f64 y y)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 3 (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) 1) (*.f64 3 (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x x (*.f64 3 (*.f64 y y))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x x (*.f64 3 (*.f64 y y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x x (*.f64 3 (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x (*.f64 3 (*.f64 y y)))) (pow.f64 (cbrt.f64 (fma.f64 x x (*.f64 3 (*.f64 y y)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x x (*.f64 3 (*.f64 y y)))) 2) (cbrt.f64 (fma.f64 x x (*.f64 3 (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x (*.f64 y (sqrt.f64 3))) (hypot.f64 x (*.f64 y (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x x) 3) (pow.f64 (*.f64 3 (*.f64 y y)) 3)) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 (*.f64 9 (pow.f64 y 4)) (*.f64 (*.f64 x x) (*.f64 3 (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 9 (pow.f64 y 4))) (-.f64 (*.f64 x x) (*.f64 3 (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x (*.f64 3 (*.f64 y y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x (*.f64 3 (*.f64 y y))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x (*.f64 3 (*.f64 y y)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (*.f64 y (sqrt.f64 3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x (*.f64 3 (*.f64 y y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x (*.f64 3 (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x x (*.f64 3 (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x (*.f64 3 (*.f64 y y))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x (*.f64 3 (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x (*.f64 3 (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x (*.f64 3 (*.f64 y y)))))))))

simplify74.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

632×	`sqr-pow_binary64`
607×	`associate-l_binary64`
372×	`cube-prod_binary64`
347×	`associate-r_binary64`
284×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	315
1	20	315
2	36	315
3	67	315
4	154	315
5	463	315
6	1791	315
7	2102	315
8	2380	315
9	2631	315
10	2972	315
11	3470	315
12	4125	315
13	4915	315

Stop Event

1×	node limit

Counts

70 → 40

Calls

Call 1

Inputs
(*.f64 3 (pow.f64 y 2))
(*.f64 3 (pow.f64 y 2))
(*.f64 3 (pow.f64 y 2))
(*.f64 3 (pow.f64 y 2))
(*.f64 3 (pow.f64 y 2))
(*.f64 3 (pow.f64 y 2))
(*.f64 3 (pow.f64 y 2))
(*.f64 3 (pow.f64 y 2))
(*.f64 3 (pow.f64 y 2))
(*.f64 3 (pow.f64 y 2))
(*.f64 3 (pow.f64 y 2))
(*.f64 3 (pow.f64 y 2))
(*.f64 3 (pow.f64 y 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(*.f64 3 (pow.f64 y 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(*.f64 3 (pow.f64 y 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))

Outputs
(*.f64 3 (pow.f64 y 2))
(.f64 3 (.f64 y y))
(*.f64 3 (pow.f64 y 2))
(.f64 3 (.f64 y y))
(*.f64 3 (pow.f64 y 2))
(.f64 3 (.f64 y y))
(*.f64 3 (pow.f64 y 2))
(.f64 3 (.f64 y y))
(*.f64 3 (pow.f64 y 2))
(.f64 3 (.f64 y y))
(*.f64 3 (pow.f64 y 2))
(.f64 3 (.f64 y y))
(*.f64 3 (pow.f64 y 2))
(.f64 3 (.f64 y y))
(*.f64 3 (pow.f64 y 2))
(.f64 3 (.f64 y y))
(*.f64 3 (pow.f64 y 2))
(.f64 3 (.f64 y y))
(*.f64 3 (pow.f64 y 2))
(.f64 3 (.f64 y y))
(*.f64 3 (pow.f64 y 2))
(.f64 3 (.f64 y y))
(*.f64 3 (pow.f64 y 2))
(.f64 3 (.f64 y y))
(*.f64 3 (pow.f64 y 2))
(.f64 3 (.f64 y y))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(*.f64 3 (pow.f64 y 2))
(.f64 3 (.f64 y y))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(*.f64 3 (pow.f64 y 2))
(.f64 3 (.f64 y y))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))

prune25.0ms (1.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	39	5	44

Error

Counts

44 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
▶	0.3b	(fma.f64 x x (pow.f64 (*.f64 y (sqrt.f64 3)) 2))
✓	0.1b	(fma.f64 x x (.f64 3 (.f64 y y)))
	14.8b	(fma.f64 x x (sqrt.f64 (*.f64 9 (pow.f64 y 4))))
	0.6b	(fma.f64 x x (pow.f64 (cbrt.f64 (.f64 3 (.f64 y y))) 3))

Compiler

Compiled 548 to 305 computations (44.3% saved)

localize6.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (pow.f64 (*.f64 y (sqrt.f64 3)) 2))
✓	0.4b	(pow.f64 (*.f64 y (sqrt.f64 3)) 2)
✓	0.4b	(*.f64 y (sqrt.f64 3))

series5.0ms (0.3%)

Counts

3 → 36

Calls

12 calls:

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

rewrite44.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

739×	`pow1_binary64`
681×	`log1p-expm1-u_binary64`
681×	`expm1-log1p-u_binary64`
88×	`add-sqr-sqrt_binary64`
83×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	28
1	186	24
2	1991	24

Stop Event

1×	node limit

Counts

3 → 64

Calls

Call 1

Inputs
(*.f64 y (sqrt.f64 3))
(pow.f64 (*.f64 y (sqrt.f64 3)) 2)
(fma.f64 x x (pow.f64 (*.f64 y (sqrt.f64 3)) 2))

Outputs

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

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

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

simplify79.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

677×	`associate-l_binary64`
570×	`sqr-pow_binary64`
469×	`associate-r_binary64`
455×	`*-commutative_binary64`
255×	`cube-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	480
1	25	315
2	52	315
3	127	315
4	444	315
5	2260	315
6	2461	315
7	2717	315
8	2963	315
9	3281	315
10	3703	315
11	4502	315

Stop Event

1×	node limit

Counts

100 → 69

Calls

Call 1

Inputs
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))

Outputs
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2))
(.f64 y (.f64 y 3))
(.f64 (.f64 y y) 3)
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2))
(.f64 y (.f64 y 3))
(.f64 (.f64 y y) 3)
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2))
(.f64 y (.f64 y 3))
(.f64 (.f64 y y) 3)
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2))
(.f64 y (.f64 y 3))
(.f64 (.f64 y y) 3)
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2))
(.f64 y (.f64 y 3))
(.f64 (.f64 y y) 3)
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2))
(.f64 y (.f64 y 3))
(.f64 (.f64 y y) 3)
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2))
(.f64 y (.f64 y 3))
(.f64 (.f64 y y) 3)
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2))
(.f64 y (.f64 y 3))
(.f64 (.f64 y y) 3)
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2))
(.f64 y (.f64 y 3))
(.f64 (.f64 y y) 3)
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2))
(.f64 y (.f64 y 3))
(.f64 (.f64 y y) 3)
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2))
(.f64 y (.f64 y 3))
(.f64 (.f64 y y) 3)
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2))
(.f64 y (.f64 y 3))
(.f64 (.f64 y y) 3)
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2))
(.f64 y (.f64 y 3))
(.f64 (.f64 y y) 3)
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(fma.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2) (.f64 x x))
(fma.f64 (.f64 y y) 3 (.f64 x x))
(fma.f64 y (.f64 y 3) (.f64 x x))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(fma.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2) (.f64 x x))
(fma.f64 (.f64 y y) 3 (.f64 x x))
(fma.f64 y (.f64 y 3) (.f64 x x))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(fma.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2) (.f64 x x))
(fma.f64 (.f64 y y) 3 (.f64 x x))
(fma.f64 y (.f64 y 3) (.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(fma.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2) (.f64 x x))
(fma.f64 (.f64 y y) 3 (.f64 x x))
(fma.f64 y (.f64 y 3) (.f64 x x))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(fma.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2) (.f64 x x))
(fma.f64 (.f64 y y) 3 (.f64 x x))
(fma.f64 y (.f64 y 3) (.f64 x x))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(fma.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2) (.f64 x x))
(fma.f64 (.f64 y y) 3 (.f64 x x))
(fma.f64 y (.f64 y 3) (.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(fma.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2) (.f64 x x))
(fma.f64 (.f64 y y) 3 (.f64 x x))
(fma.f64 y (.f64 y 3) (.f64 x x))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(fma.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2) (.f64 x x))
(fma.f64 (.f64 y y) 3 (.f64 x x))
(fma.f64 y (.f64 y 3) (.f64 x x))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(fma.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2) (.f64 x x))
(fma.f64 (.f64 y y) 3 (.f64 x x))
(fma.f64 y (.f64 y 3) (.f64 x x))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(fma.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2) (.f64 x x))
(fma.f64 (.f64 y y) 3 (.f64 x x))
(fma.f64 y (.f64 y 3) (.f64 x x))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(fma.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2) (.f64 x x))
(fma.f64 (.f64 y y) 3 (.f64 x x))
(fma.f64 y (.f64 y 3) (.f64 x x))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(fma.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2) (.f64 x x))
(fma.f64 (.f64 y y) 3 (.f64 x x))
(fma.f64 y (.f64 y 3) (.f64 x x))
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2))
(.f64 y (.f64 y 3))
(.f64 (.f64 y y) 3)
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(fma.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2) (.f64 x x))
(fma.f64 (.f64 y y) 3 (.f64 x x))
(fma.f64 y (.f64 y 3) (.f64 x x))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(fma.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2) (.f64 x x))
(fma.f64 (.f64 y y) 3 (.f64 x x))
(fma.f64 y (.f64 y 3) (.f64 x x))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(fma.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2) (.f64 x x))
(fma.f64 (.f64 y y) 3 (.f64 x x))
(fma.f64 y (.f64 y 3) (.f64 x x))
(*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2))
(.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2))
(.f64 y (.f64 y 3))
(.f64 (.f64 y y) 3)
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(fma.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2) (.f64 x x))
(fma.f64 (.f64 y y) 3 (.f64 x x))
(fma.f64 y (.f64 y 3) (.f64 x x))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(fma.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2) (.f64 x x))
(fma.f64 (.f64 y y) 3 (.f64 x x))
(fma.f64 y (.f64 y 3) (.f64 x x))
(+.f64 (*.f64 (pow.f64 y 2) (pow.f64 (sqrt.f64 3) 2)) (pow.f64 x 2))
(fma.f64 (.f64 y y) (pow.f64 (sqrt.f64 3) 2) (.f64 x x))
(fma.f64 (.f64 y y) 3 (.f64 x x))
(fma.f64 y (.f64 y 3) (.f64 x x))

prune43.0ms (2.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	69	5	74

Error

Counts

74 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
✓	0.3b	(fma.f64 x x (pow.f64 (*.f64 y (sqrt.f64 3)) 2))
✓	0.1b	(fma.f64 x x (.f64 3 (.f64 y y)))
	14.8b	(fma.f64 x x (sqrt.f64 (*.f64 9 (pow.f64 y 4))))
▶	0.6b	(fma.f64 x x (pow.f64 (cbrt.f64 (.f64 3 (.f64 y y))) 3))

Compiler

Compiled 932 to 574 computations (38.4% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (pow.f64 (cbrt.f64 (.f64 3 (.f64 y y))) 3))
	0.2b	(.f64 3 (.f64 y y))
✓	0.5b	(pow.f64 (cbrt.f64 (.f64 3 (.f64 y y))) 3)
✓	20.3b	(cbrt.f64 (.f64 3 (.f64 y y)))

series14.0ms (0.8%)

Counts

3 → 15

Calls

12 calls:

Time	Variable		Point	Expression
5.0ms	y	@	0	(pow.f64 (cbrt.f64 (.f64 3 (.f64 y y))) 3)
2.0ms	x	@	0	(fma.f64 x x (pow.f64 (cbrt.f64 (.f64 3 (.f64 y y))) 3))
1.0ms	y	@	0	(cbrt.f64 (.f64 3 (.f64 y y)))
1.0ms	y	@	inf	(pow.f64 (cbrt.f64 (.f64 3 (.f64 y y))) 3)
1.0ms	y	@	inf	(cbrt.f64 (.f64 3 (.f64 y y)))

rewrite48.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

721×	`pow1_binary64`
672×	`add-log-exp_binary64`
672×	`log1p-expm1-u_binary64`
672×	`expm1-log1p-u_binary64`
81×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	190	27
2	1932	27

Stop Event

1×	node limit

Counts

3 → 78

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (cbrt.f64 (*.f64 3 (*.f64 y y))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 3 (*.f64 y y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cbrt.f64 (*.f64 3 (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 3) (pow.f64 (cbrt.f64 y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 3 (*.f64 y y)))) (cbrt.f64 (cbrt.f64 (*.f64 9 (pow.f64 y 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 3 (*.f64 y y)))) (pow.f64 (cbrt.f64 (*.f64 9 (pow.f64 y 4))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 9 (pow.f64 y 4)))) (cbrt.f64 (cbrt.f64 (*.f64 3 (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 y) 2) (cbrt.f64 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 y (sqrt.f64 3))) (cbrt.f64 (*.f64 y (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 3 y)) (cbrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 9 (pow.f64 y 4))) 1/3) (cbrt.f64 (cbrt.f64 (*.f64 3 (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/3) (cbrt.f64 (*.f64 3 (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 y (sqrt.f64 3)) 1/3) (pow.f64 (*.f64 y (sqrt.f64 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 3 y) 1/3) (cbrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 3 (*.f64 y y)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 3 (*.f64 y y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 3 (*.f64 y y)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (cbrt.f64 (*.f64 9 (pow.f64 y 4))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (cbrt.f64 (*.f64 3 (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (cbrt.f64 (*.f64 3 (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (cbrt.f64 (*.f64 3 (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (cbrt.f64 (*.f64 3 (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (cbrt.f64 (*.f64 3 (*.f64 y y)))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 3 (*.f64 y y)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 3 (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 y (*.f64 3 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 y y) 3)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 3 (*.f64 y y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 3 (*.f64 y y))) (cbrt.f64 (*.f64 9 (pow.f64 y 4))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 3 (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 9 (pow.f64 y 4))) (cbrt.f64 (*.f64 3 (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 3) (*.f64 (pow.f64 (cbrt.f64 y) 2) (cbrt.f64 (*.f64 9 (pow.f64 y 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (cbrt.f64 (*.f64 9 (pow.f64 y 4)))) (*.f64 (cbrt.f64 (cbrt.f64 (*.f64 3 (*.f64 y y)))) (cbrt.f64 (*.f64 9 (pow.f64 y 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 y 4)) (*.f64 (pow.f64 (cbrt.f64 y) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 y (sqrt.f64 3)) (*.f64 y (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 y (sqrt.f64 3))) (*.f64 (cbrt.f64 (*.f64 y (sqrt.f64 3))) (cbrt.f64 (*.f64 9 (pow.f64 y 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 3 y) y)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 3) 3) (*.f64 y y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 9 (pow.f64 y 4)))) 3) (cbrt.f64 (*.f64 3 (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 3))) 3) (pow.f64 (cbrt.f64 (*.f64 y (sqrt.f64 3))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 3 (cbrt.f64 (pow.f64 y 4))) (pow.f64 (cbrt.f64 y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 9 (pow.f64 y 4))) 1) (cbrt.f64 (*.f64 3 (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 9 (pow.f64 y 4))) (cbrt.f64 3)) (pow.f64 (cbrt.f64 y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 9 (pow.f64 y 4))) (cbrt.f64 (cbrt.f64 (*.f64 9 (pow.f64 y 4))))) (cbrt.f64 (cbrt.f64 (*.f64 3 (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (*.f64 9 (pow.f64 y 4))) (cbrt.f64 (*.f64 y (sqrt.f64 3)))) (cbrt.f64 (*.f64 y (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 3 y) 1) y)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 3 y) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 3 y) (sqrt.f64 y)) (sqrt.f64 y))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 9 (pow.f64 y 4)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 3) (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 3 (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 3 (*.f64 y y)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 3 (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 3 (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 3 (*.f64 y y))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 3 (*.f64 y y)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x x) (*.f64 3 (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) 1) (*.f64 3 (*.f64 y y)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x x (*.f64 3 (*.f64 y y))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x x (*.f64 3 (*.f64 y y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 x x (*.f64 3 (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 x x (*.f64 3 (*.f64 y y)))) (pow.f64 (cbrt.f64 (fma.f64 x x (*.f64 3 (*.f64 y y)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x x (*.f64 3 (*.f64 y y)))) 2) (cbrt.f64 (fma.f64 x x (*.f64 3 (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x (*.f64 y (sqrt.f64 3))) (hypot.f64 x (*.f64 y (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (*.f64 x x) 3) (pow.f64 (*.f64 3 (*.f64 y y)) 3)) (+.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (-.f64 (*.f64 9 (pow.f64 y 4)) (*.f64 (*.f64 x x) (*.f64 3 (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (*.f64 x x) (*.f64 x x)) (*.f64 9 (pow.f64 y 4))) (-.f64 (*.f64 x x) (*.f64 3 (*.f64 y y))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x (*.f64 3 (*.f64 y y))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x (*.f64 3 (*.f64 y y))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x (*.f64 3 (*.f64 y y)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 x (*.f64 y (sqrt.f64 3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x (*.f64 3 (*.f64 y y))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x (*.f64 3 (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x x (*.f64 3 (*.f64 y y))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x (*.f64 3 (*.f64 y y))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x (*.f64 3 (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x (*.f64 3 (*.f64 y y)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x (*.f64 3 (*.f64 y y)))))))))

simplify64.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

632×	`sqr-pow_binary64`
607×	`associate-l_binary64`
372×	`cube-prod_binary64`
347×	`associate-r_binary64`
284×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	126
1	20	126
2	36	126
3	67	126
4	154	126
5	463	126
6	1791	126
7	2102	126
8	2380	126
9	2631	126
10	2972	126
11	3470	126
12	4125	126
13	4915	126

Stop Event

1×	node limit

Counts

93 → 83

Calls

Call 1

Inputs
(*.f64 3 (pow.f64 y 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(pow.f64 x 2)
(pow.f64 x 2)
(pow.f64 x 2)

Outputs
(*.f64 3 (pow.f64 y 2))
(.f64 3 (.f64 y y))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(+.f64 (*.f64 3 (pow.f64 y 2)) (pow.f64 x 2))
(fma.f64 3 (.f64 y y) (.f64 x x))
(fma.f64 x x (.f64 3 (.f64 y y)))
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)
(pow.f64 x 2)
(*.f64 x x)

prune67.0ms (4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	97	5	102

Error

Counts

102 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 y (.f64 y 3) (.f64 x x))
✓	0.3b	(fma.f64 x x (pow.f64 (*.f64 y (sqrt.f64 3)) 2))
✓	0.1b	(fma.f64 x x (.f64 3 (.f64 y y)))
	14.8b	(fma.f64 x x (sqrt.f64 (*.f64 9 (pow.f64 y 4))))
✓	0.6b	(fma.f64 x x (pow.f64 (cbrt.f64 (.f64 3 (.f64 y y))) 3))

Compiler

Compiled 1344 to 833 computations (38% saved)

regimes52.0ms (3.1%)

Accuracy

Total 0.1b remaining (88.4%)

Threshold costs 0.1b (88.4%)

Counts

16 → 1

Compiler

Compiled 195 to 104 computations (46.7% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	8	11

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 y (.f64 y 3) (.f64 x x))

Outputs
(fma.f64 y (.f64 y 3) (.f64 x x))

end64.0ms (3.9%)

Stop Event

1×

fuel

Compiler

Compiled 75 to 49 computations (34.7% saved)

Details

analyze90.0ms (5.5%)

sample753.0ms (45.5%)

preprocess22.0ms (1.4%)

simplify7.0ms (0.4%)

prune3.0ms (0.2%)

localize4.0ms (0.3%)

series6.0ms (0.4%)

rewrite36.0ms (2.2%)

simplify64.0ms (3.9%)

prune19.0ms (1.1%)

localize12.0ms (0.7%)

series5.0ms (0.3%)

rewrite38.0ms (2.3%)

simplify74.0ms (4.5%)

prune25.0ms (1.5%)

localize6.0ms (0.4%)

series5.0ms (0.3%)

rewrite44.0ms (2.7%)

simplify79.0ms (4.8%)

prune43.0ms (2.6%)

localize7.0ms (0.4%)

series14.0ms (0.8%)

rewrite48.0ms (2.9%)

simplify64.0ms (3.8%)

prune67.0ms (4%)

regimes52.0ms (3.1%)

simplify3.0ms (0.2%)

end64.0ms (3.9%)

Profiling