Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
50%	50%	50%	0%	0%	0%	0%	3
75%	75%	25%	0%	0%	0%	0%	4
87.5%	87.5%	12.5%	0%	0%	0%	0%	5
93.8%	93.7%	6.2%	0%	0%	0%	0%	6
96.9%	96.8%	3.1%	0%	0%	0%	0%	7
98.4%	98.4%	1.6%	0%	0%	0%	0%	8
99.2%	99.2%	0.8%	0%	0%	0%	0%	9
99.6%	99.6%	0.4%	0%	0%	0%	0%	10
99.8%	99.8%	0.2%	0%	0%	0%	0%	11
99.9%	99.9%	0.1%	0%	0%	0%	0%	12

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample1.1s (22.4%)

Results

1.1s

8256×

body

256

valid

Bogosity

preprocess33.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	10	4
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(+.f64 x (/.f64 1 3))

Outputs
(+.f64 x (/.f64 1 3))
(+.f64 x 1/3)

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	10	4

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(+.f64 x (/.f64 1 3))

Outputs
(+.f64 x (/.f64 1 3))
(+.f64 x 1/3)

eval1.0ms (0%)

Compiler: Compiled 9 to 7 computations (22.2% saved)

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(+.f64 x 1/3)

Compiler

Compiled 4 to 3 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x 1/3)

Compiler

Compiled 6 to 4 computations (33.3% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(+.f64 x 1/3)
1.0ms	x	@	0	(+.f64 x 1/3)
0.0ms	x	@	-inf	(+.f64 x 1/3)

rewrite110.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

473×	`pow1_binary64`
468×	`add-sqr-sqrt_binary64`
456×	`*-un-lft-identity_binary64`
446×	`add-log-exp_binary64`
446×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	91	4
2	1150	4

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

Inputs
(+.f64 x 1/3)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 x 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 x x) (+.f64 x -1/3)) (/.f64 1/9 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 x 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 x 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 x 1/3)) (pow.f64 (cbrt.f64 (+.f64 x 1/3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 x 1/3)) 2) (cbrt.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 x 1/3)) (sqrt.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1/27 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x (-.f64 1/9 (.f64 x 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (-.f64 1/9 (.f64 x 1/3))) (+.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 x -1/3) (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x x (-.f64 1/9 (.f64 x 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 x x -1/9) (+.f64 x -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/27 (pow.f64 x 3))) (neg.f64 (fma.f64 x x (-.f64 1/9 (.f64 x 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 x x -1/9)) (neg.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x 1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x 1/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) 1/3)))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 x 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (+.f64 x -1/3)) (/.f64 1/9 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x 1/3)) (pow.f64 (cbrt.f64 (+.f64 x 1/3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x 1/3)) 2) (cbrt.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x 1/3)) (sqrt.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1/27 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x (-.f64 1/9 (*.f64 x 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (-.f64 1/9 (*.f64 x 1/3))) (+.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 x -1/3) (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x x (-.f64 1/9 (*.f64 x 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (-.f64 (*.f64 x x) (*.f64 x 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 x x -1/9) (+.f64 x -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/27 (pow.f64 x 3))) (neg.f64 (fma.f64 x x (-.f64 1/9 (*.f64 x 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 x x -1/9)) (neg.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x 1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x 1/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) 1/3)))))

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	39
1	5	39

Stop Event

1×

saturated

Counts

42 → 33

Calls

Call 1

Inputs
1/3
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)

Outputs
1/3
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)

eval33.0ms (0.7%)

Compiler: Compiled 265 to 196 computations (26% saved)

prune11.0ms (0.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	28	5	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	6	34

Error

Counts

34 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 x 1/3)
▶	17.0b	(/.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))
	29.8b	x
	33.0b	1/3
▶	23.0b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3))))
▶	17.1b	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))

Compiler

Compiled 45 to 33 computations (26.7% saved)

localize28.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x -1/3))
✓	0.0b	(+.f64 x -1/3)
✓	15.9b	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))

Compiler

Compiled 27 to 19 computations (29.6% saved)

series8.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))
1.0ms	x	@	0	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))
1.0ms	x	@	inf	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))
1.0ms	x	@	inf	(/.f64 1 (+.f64 x -1/3))
1.0ms	x	@	0	(/.f64 1 (+.f64 x -1/3))

rewrite97.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

906×	`pow1_binary64`
848×	`add-log-exp_binary64`
848×	`log1p-expm1-u_binary64`
848×	`expm1-log1p-u_binary64`
834×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	194	15
2	2374	15

Stop Event

1×	node limit

Counts

3 → 89

Calls

Call 1

Inputs
(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))
(+.f64 x -1/3)
(/.f64 1 (+.f64 x -1/3))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 x 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 x x) (/.f64 1 (+.f64 x -1/3))) (.f64 -1/9 (/.f64 1 (+.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 1 (+.f64 x -1/3)) (.f64 x x)) (.f64 (/.f64 1 (+.f64 x -1/3)) -1/9))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 x -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 x 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 x x -1/9) (+.f64 x -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 x -1/3) (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1/9)) 2) (/.f64 (+.f64 x -1/3) (cbrt.f64 (fma.f64 x x -1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (fma.f64 x x -1/9)) (/.f64 (+.f64 x -1/3) (sqrt.f64 (fma.f64 x x -1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 x x -1/9)) (neg.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (fma.f64 x x -1/9) (sqrt.f64 (+.f64 x -1/3))) (sqrt.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (fma.f64 x x -1/9) 1) (+.f64 x -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (fma.f64 x x -1/9) (pow.f64 (cbrt.f64 (+.f64 x -1/3)) 2)) (cbrt.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 3) -1/27) (+.f64 (.f64 x x) (+.f64 1/9 (.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1 (fma.f64 x x -1/9)) (neg.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (fma.f64 x x -1/9) -1) (neg.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x 1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x 1/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (fma.f64 x x -1/9) 3) (pow.f64 (+.f64 x -1/3) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (fma.f64 x x -1/9) 3) (pow.f64 (/.f64 1 (+.f64 x -1/3)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (/.f64 1 (+.f64 x -1/3)) 3) (pow.f64 (fma.f64 x x -1/9) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) 1/3)))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 x -1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (.f64 x x) (+.f64 x 1/3)) (/.f64 1/9 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 x -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 x -1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 x -1/3)) (pow.f64 (cbrt.f64 (+.f64 x -1/3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 x -1/3)) 2) (cbrt.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 x -1/3)) (sqrt.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 -1/27 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x (-.f64 1/9 (.f64 x -1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 x x -1/9) (+.f64 x 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (-.f64 1/9 (.f64 x -1/3))) (+.f64 -1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 x 1/3) (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 x -1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (+.f64 x -1/3)) 2) (cbrt.f64 (/.f64 1 (+.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 x -1/3)) (pow.f64 (+.f64 x -1/3) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 x -1/3)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1/27 (pow.f64 x 3)) (fma.f64 x x (-.f64 1/9 (.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1/27 (pow.f64 x 3)) (+.f64 1/9 (-.f64 (.f64 x x) (.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 x x -1/9)) (neg.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 -1/27 (pow.f64 x 3))) (neg.f64 (fma.f64 x x (-.f64 1/9 (.f64 x -1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 -1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x -1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x -1/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x -1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x -1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x -1/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x -1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) -1/3)))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1 (+.f64 x -1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (+.f64 x -1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 1 (+.f64 x -1/3))) (cbrt.f64 (pow.f64 (+.f64 x -1/3) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (+.f64 x -1/3) -2)) (cbrt.f64 (/.f64 1 (+.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (+.f64 x -1/3) -1/2) (pow.f64 (+.f64 x -1/3) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (/.f64 1 (neg.f64 (+.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x -1/3)) 2) -1) (pow.f64 (cbrt.f64 (+.f64 x -1/3)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (+.f64 x -1/3)) -1) (pow.f64 (sqrt.f64 (+.f64 x -1/3)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (+.f64 -1/27 (pow.f64 x 3))) (fma.f64 x x (-.f64 1/9 (.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 x x -1/9)) (+.f64 x 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x -1/3) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 x -1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (+.f64 x -1/3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1 (+.f64 x -1/3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x -1/3) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x -1/3) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (+.f64 x -1/3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (+.f64 x -1/3))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 x 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) (/.f64 1 (+.f64 x -1/3))) (*.f64 -1/9 (/.f64 1 (+.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (+.f64 x -1/3)) (*.f64 x x)) (*.f64 (/.f64 1 (+.f64 x -1/3)) -1/9))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 x -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 x 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 x x -1/9) (+.f64 x -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 x -1/3) (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1/9)) 2) (/.f64 (+.f64 x -1/3) (cbrt.f64 (fma.f64 x x -1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (fma.f64 x x -1/9)) (/.f64 (+.f64 x -1/3) (sqrt.f64 (fma.f64 x x -1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 x x -1/9)) (neg.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (fma.f64 x x -1/9) (sqrt.f64 (+.f64 x -1/3))) (sqrt.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (fma.f64 x x -1/9) 1) (+.f64 x -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (fma.f64 x x -1/9) (pow.f64 (cbrt.f64 (+.f64 x -1/3)) 2)) (cbrt.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 3) -1/27) (+.f64 (*.f64 x x) (+.f64 1/9 (*.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (fma.f64 x x -1/9)) (neg.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (fma.f64 x x -1/9) -1) (neg.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x 1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x 1/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (fma.f64 x x -1/9) 3) (pow.f64 (+.f64 x -1/3) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (fma.f64 x x -1/9) 3) (pow.f64 (/.f64 1 (+.f64 x -1/3)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (pow.f64 (/.f64 1 (+.f64 x -1/3)) 3) (pow.f64 (fma.f64 x x -1/9) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) 1/3)))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (+.f64 x -1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (+.f64 x 1/3)) (/.f64 1/9 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x -1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x -1/3)) (pow.f64 (cbrt.f64 (+.f64 x -1/3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x -1/3)) 2) (cbrt.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x -1/3)) (sqrt.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1/27 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x (-.f64 1/9 (*.f64 x -1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 x x -1/9) (+.f64 x 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (-.f64 1/9 (*.f64 x -1/3))) (+.f64 -1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 x 1/3) (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 x -1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 (+.f64 x -1/3)) 2) (cbrt.f64 (/.f64 1 (+.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 x -1/3)) (pow.f64 (+.f64 x -1/3) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 x -1/3)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1/27 (pow.f64 x 3)) (fma.f64 x x (-.f64 1/9 (*.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1/27 (pow.f64 x 3)) (+.f64 1/9 (-.f64 (*.f64 x x) (*.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 x x -1/9)) (neg.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 -1/27 (pow.f64 x 3))) (neg.f64 (fma.f64 x x (-.f64 1/9 (*.f64 x -1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 -1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x -1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x -1/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x -1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x -1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x -1/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x -1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) -1/3)))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1 (+.f64 x -1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 x -1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 1 (+.f64 x -1/3))) (cbrt.f64 (pow.f64 (+.f64 x -1/3) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (+.f64 x -1/3) -2)) (cbrt.f64 (/.f64 1 (+.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x -1/3) -1/2) (pow.f64 (+.f64 x -1/3) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (+.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 x -1/3)) 2) -1) (pow.f64 (cbrt.f64 (+.f64 x -1/3)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (sqrt.f64 (+.f64 x -1/3)) -1) (pow.f64 (sqrt.f64 (+.f64 x -1/3)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 -1/27 (pow.f64 x 3))) (fma.f64 x x (-.f64 1/9 (*.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 x x -1/9)) (+.f64 x 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x -1/3) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (+.f64 x -1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1 (+.f64 x -1/3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1 (+.f64 x -1/3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x -1/3) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x -1/3) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (+.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1 (+.f64 x -1/3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (+.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (+.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (+.f64 x -1/3))))))))

simplify83.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

724×	`associate-l_binary64`
685×	`fma-neg_binary64`
619×	`associate-/r*_binary64`
585×	`distribute-rgt-neg-in_binary64`
563×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	259
1	103	257
2	222	255
3	539	249
4	1445	246
5	6129	246

Stop Event

1×	node limit

Counts

125 → 109

Calls

Call 1

Inputs
1/3
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
-1/3
(-.f64 x 1/3)
(-.f64 x 1/3)
(-.f64 x 1/3)
x
(-.f64 x 1/3)
(-.f64 x 1/3)
(-.f64 x 1/3)
x
(-.f64 x 1/3)
(-.f64 x 1/3)
(-.f64 x 1/3)
-3
(-.f64 (*.f64 -9 x) 3)
(-.f64 (+.f64 (.f64 -9 x) (.f64 -27 (pow.f64 x 2))) 3)
(-.f64 (+.f64 (.f64 -9 x) (+.f64 (.f64 -81 (pow.f64 x 3)) (*.f64 -27 (pow.f64 x 2)))) 3)
(/.f64 1 x)
(+.f64 (*.f64 1/3 (/.f64 1 (pow.f64 x 2))) (/.f64 1 x))
(+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))
(+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 1/9 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x))))
(/.f64 1 x)
(+.f64 (*.f64 1/3 (/.f64 1 (pow.f64 x 2))) (/.f64 1 x))
(+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))
(+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 1/9 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x))))

Outputs
1/3
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
-1/3
(-.f64 x 1/3)
(+.f64 x -1/3)
(-.f64 x 1/3)
(+.f64 x -1/3)
(-.f64 x 1/3)
(+.f64 x -1/3)
x
(-.f64 x 1/3)
(+.f64 x -1/3)
(-.f64 x 1/3)
(+.f64 x -1/3)
(-.f64 x 1/3)
(+.f64 x -1/3)
x
(-.f64 x 1/3)
(+.f64 x -1/3)
(-.f64 x 1/3)
(+.f64 x -1/3)
(-.f64 x 1/3)
(+.f64 x -1/3)
-3
(-.f64 (*.f64 -9 x) 3)
(fma.f64 -9 x -3)
(fma.f64 x -9 -3)
(-.f64 (+.f64 (.f64 -9 x) (.f64 -27 (pow.f64 x 2))) 3)
(+.f64 (fma.f64 -9 x (.f64 -27 (.f64 x x))) -3)
(fma.f64 x -9 (fma.f64 -27 (*.f64 x x) -3))
(fma.f64 x (*.f64 x -27) (fma.f64 x -9 -3))
(fma.f64 x (fma.f64 x -27 -9) -3)
(-.f64 (+.f64 (.f64 -9 x) (+.f64 (.f64 -81 (pow.f64 x 3)) (*.f64 -27 (pow.f64 x 2)))) 3)
(+.f64 (fma.f64 -9 x (fma.f64 -81 (pow.f64 x 3) (.f64 -27 (.f64 x x)))) -3)
(+.f64 (fma.f64 -27 (.f64 x x) (.f64 -81 (pow.f64 x 3))) (fma.f64 x -9 -3))
(fma.f64 x -9 (fma.f64 x (*.f64 x -27) (fma.f64 -81 (pow.f64 x 3) -3)))
(fma.f64 x (*.f64 x (fma.f64 x -81 -27)) (fma.f64 x -9 -3))
(fma.f64 x (fma.f64 x (fma.f64 x -81 -27) -9) -3)
(/.f64 1 x)
(+.f64 (*.f64 1/3 (/.f64 1 (pow.f64 x 2))) (/.f64 1 x))
(+.f64 (/.f64 1 x) (/.f64 1/3 (*.f64 x x)))
(+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))
(+.f64 (/.f64 1/3 (*.f64 x x)) (+.f64 (/.f64 1 x) (/.f64 1/9 (pow.f64 x 3))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1/3 (*.f64 x x)) (/.f64 1/9 (pow.f64 x 3))))
(+.f64 (/.f64 1 x) (*.f64 (/.f64 (/.f64 1 x) x) (+.f64 1/3 (/.f64 1/9 x))))
(+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 1/9 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x))))
(+.f64 (/.f64 1/3 (*.f64 x x)) (+.f64 (+.f64 (/.f64 1 x) (/.f64 1/9 (pow.f64 x 3))) (/.f64 1/27 (pow.f64 x 4))))
(+.f64 (/.f64 1/3 (*.f64 x x)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1/9 (pow.f64 x 3)) (/.f64 1/27 (pow.f64 x 4)))))
(+.f64 (/.f64 1/9 (pow.f64 x 3)) (+.f64 (+.f64 (/.f64 1 x) (/.f64 1/27 (pow.f64 x 4))) (/.f64 1/3 (*.f64 x x))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1/3 (*.f64 x x)) (+.f64 (/.f64 1/9 (pow.f64 x 3)) (/.f64 1/27 (pow.f64 x 4)))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1/27 (pow.f64 x 4)) (*.f64 (/.f64 (/.f64 1 x) x) (+.f64 1/3 (/.f64 1/9 x)))))
(/.f64 1 x)
(+.f64 (*.f64 1/3 (/.f64 1 (pow.f64 x 2))) (/.f64 1 x))
(+.f64 (/.f64 1 x) (/.f64 1/3 (*.f64 x x)))
(+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))
(+.f64 (/.f64 1/3 (*.f64 x x)) (+.f64 (/.f64 1 x) (/.f64 1/9 (pow.f64 x 3))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1/3 (*.f64 x x)) (/.f64 1/9 (pow.f64 x 3))))
(+.f64 (/.f64 1 x) (*.f64 (/.f64 (/.f64 1 x) x) (+.f64 1/3 (/.f64 1/9 x))))
(+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 1/9 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x))))
(+.f64 (/.f64 1/3 (*.f64 x x)) (+.f64 (+.f64 (/.f64 1 x) (/.f64 1/9 (pow.f64 x 3))) (/.f64 1/27 (pow.f64 x 4))))
(+.f64 (/.f64 1/3 (*.f64 x x)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1/9 (pow.f64 x 3)) (/.f64 1/27 (pow.f64 x 4)))))
(+.f64 (/.f64 1/9 (pow.f64 x 3)) (+.f64 (+.f64 (/.f64 1 x) (/.f64 1/27 (pow.f64 x 4))) (/.f64 1/3 (*.f64 x x))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1/3 (*.f64 x x)) (+.f64 (/.f64 1/9 (pow.f64 x 3)) (/.f64 1/27 (pow.f64 x 4)))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1/27 (pow.f64 x 4)) (*.f64 (/.f64 (/.f64 1 x) x) (+.f64 1/3 (/.f64 1/9 x)))))

localize52.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3)))
✓	0.0b	(-.f64 (.f64 x x) (.f64 x 1/3))
✓	0.3b	(*.f64 x 1/3)
✓	22.1b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3))))

Compiler

Compiled 51 to 32 computations (37.3% saved)

series10.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3))))
1.0ms	x	@	inf	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3))))
1.0ms	x	@	0	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3))))
1.0ms	x	@	-inf	(*.f64 x 1/3)
1.0ms	x	@	inf	(*.f64 x 1/3)

rewrite181.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

987×	`prod-diff_binary64`
639×	`fma-def_binary64`
275×	`fma-neg_binary64`
251×	`expm1-udef_binary64`
251×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	316	36
2	4212	36

Stop Event

1×	node limit

Counts

4 → 342

Calls

Call 1

Inputs
(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3))))
(*.f64 x 1/3)
(-.f64 (.f64 x x) (.f64 x 1/3))
(+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3)))

Outputs
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x 1/3 -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (+.f64 x -1/3) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (+.f64 x -1/3) (+.f64 (fma.f64 x -1/3 (.f64 x 1/3)) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x x) 1 (fma.f64 x -1/3 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x x) 1 (neg.f64 (fma.f64 x 1/3 -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (+.f64 x -1/3)) 1 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (+.f64 x -1/3)) 1 (+.f64 (fma.f64 x -1/3 (.f64 x 1/3)) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (fma.f64 x (+.f64 x -1/3) 1/9) 1 (fma.f64 x -1/3 (.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x x) (fma.f64 x -1/3 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x x) (neg.f64 (fma.f64 x 1/3 -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x (+.f64 x -1/3)) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x (+.f64 x -1/3)) (+.f64 (fma.f64 x -1/3 (.f64 x 1/3)) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x (+.f64 x -1/3) 1/9) (fma.f64 x -1/3 (.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (fma.f64 x x 1/9) (.f64 x -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 x (+.f64 x -1/3))) (pow.f64 (cbrt.f64 (.f64 x (+.f64 x -1/3))) 2) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 x (+.f64 x -1/3))) (pow.f64 (cbrt.f64 (.f64 x (+.f64 x -1/3))) 2) (+.f64 (fma.f64 x -1/3 (.f64 x 1/3)) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 x (+.f64 x -1/3))) 2) (cbrt.f64 (.f64 x (+.f64 x -1/3))) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 x (+.f64 x -1/3))) 2) (cbrt.f64 (.f64 x (+.f64 x -1/3))) (+.f64 (fma.f64 x -1/3 (.f64 x 1/3)) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 x 4)) (fma.f64 x -1/3 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 x 4)) (neg.f64 (fma.f64 x 1/3 -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) x) (fma.f64 x -1/3 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) x) (neg.f64 (fma.f64 x 1/3 -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (+.f64 x -1/3)) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (+.f64 x -1/3)) (+.f64 (fma.f64 x -1/3 (.f64 x 1/3)) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (fma.f64 x -1/3 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (neg.f64 (fma.f64 x 1/3 -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 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((x fma.f64 (-.f64 (pow.f64 x 4) (.f64 1/9 (.f64 x x))) (/.f64 1 (.f64 x (+.f64 x 1/3))) (+.f64 (fma.f64 x -1/3 (.f64 x 1/3)) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 1/81 (pow.f64 (.f64 x (+.f64 x -1/3)) 2)) (/.f64 1 (-.f64 1/9 (.f64 x (+.f64 x -1/3)))) (fma.f64 x -1/3 (.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (fma.f64 x -1/3 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) (neg.f64 (fma.f64 x 1/3 -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x -1/3) x 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x -1/3) x (+.f64 (fma.f64 x -1/3 (.f64 x 1/3)) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (cbrt.f64 (fma.f64 x x 1/9)) (cbrt.f64 (fma.f64 x x 1/9))) (cbrt.f64 (fma.f64 x x 1/9)) (.f64 x -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (fma.f64 x x 1/9)) (sqrt.f64 (fma.f64 x x 1/9)) (.f64 x -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x (sqrt.f64 (.f64 x 1/3))) (-.f64 x (sqrt.f64 (.f64 x 1/3))) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x (sqrt.f64 (.f64 x 1/3))) (-.f64 x (sqrt.f64 (.f64 x 1/3))) (+.f64 (fma.f64 x -1/3 (.f64 x 1/3)) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (fma.f64 x -1/3 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (neg.f64 (fma.f64 x 1/3 -1/9)))))))

simplify220.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
652×	`fma-def_binary64`
560×	`cube-prod_binary64`
557×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	269
1	26	250
2	48	238
3	84	238
4	168	238
5	423	238
6	1301	238
7	2536	238
8	2930	238
9	3122	238
10	3332	238
11	3646	238
12	4054	238
13	4535	238
14	5107	238
15	5801	238
16	6643	238
17	7041	238
18	7331	238
19	7609	238
20	7683	238
21	7719	238

Stop Event

1×	node limit

Counts

390 → 355

Calls

Call 1

Inputs
1/3
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 -1/3 x)
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(pow.f64 x 2)
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
1/9
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 1/9 (+.f64 (*.f64 -1/3 x) (pow.f64 x 2)))
(+.f64 1/9 (+.f64 (*.f64 -1/3 x) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(+.f64 1/9 (+.f64 (*.f64 -1/3 x) (pow.f64 x 2)))
(+.f64 1/9 (+.f64 (*.f64 -1/3 x) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(+.f64 1/9 (+.f64 (*.f64 -1/3 x) (pow.f64 x 2)))
(+.f64 1/9 (+.f64 (*.f64 -1/3 x) (pow.f64 x 2)))

Outputs
1/3
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 1/3 x)
(*.f64 -1/3 x)
(*.f64 x -1/3)
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(fma.f64 -1/3 x (*.f64 x x))
(*.f64 x (+.f64 -1/3 x))
(*.f64 x (+.f64 x -1/3))
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(fma.f64 -1/3 x (*.f64 x x))
(*.f64 x (+.f64 -1/3 x))
(*.f64 x (+.f64 x -1/3))
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(fma.f64 -1/3 x (*.f64 x x))
(*.f64 x (+.f64 -1/3 x))
(*.f64 x (+.f64 x -1/3))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(fma.f64 -1/3 x (*.f64 x x))
(*.f64 x (+.f64 -1/3 x))
(*.f64 x (+.f64 x -1/3))
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(fma.f64 -1/3 x (*.f64 x x))
(*.f64 x (+.f64 -1/3 x))
(*.f64 x (+.f64 x -1/3))
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(fma.f64 -1/3 x (*.f64 x x))
(*.f64 x (+.f64 -1/3 x))
(*.f64 x (+.f64 x -1/3))
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(fma.f64 -1/3 x (*.f64 x x))
(*.f64 x (+.f64 -1/3 x))
(*.f64 x (+.f64 x -1/3))
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(fma.f64 -1/3 x (*.f64 x x))
(*.f64 x (+.f64 -1/3 x))
(*.f64 x (+.f64 x -1/3))
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(fma.f64 -1/3 x (*.f64 x x))
(*.f64 x (+.f64 -1/3 x))
(*.f64 x (+.f64 x -1/3))
1/9
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 (*.f64 x -1/3) 1/9)
(fma.f64 x -1/3 1/9)
(+.f64 1/9 (+.f64 (*.f64 -1/3 x) (pow.f64 x 2)))
(+.f64 (fma.f64 -1/3 x (*.f64 x x)) 1/9)
(+.f64 (*.f64 x (+.f64 -1/3 x)) 1/9)
(fma.f64 x (+.f64 x -1/3) 1/9)
(+.f64 1/9 (+.f64 (*.f64 -1/3 x) (pow.f64 x 2)))
(+.f64 (fma.f64 -1/3 x (*.f64 x x)) 1/9)
(+.f64 (*.f64 x (+.f64 -1/3 x)) 1/9)
(fma.f64 x (+.f64 x -1/3) 1/9)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(fma.f64 -1/3 x (*.f64 x x))
(*.f64 x (+.f64 -1/3 x))
(*.f64 x (+.f64 x -1/3))
(+.f64 1/9 (+.f64 (*.f64 -1/3 x) (pow.f64 x 2)))
(+.f64 (fma.f64 -1/3 x (*.f64 x x)) 1/9)
(+.f64 (*.f64 x (+.f64 -1/3 x)) 1/9)
(fma.f64 x (+.f64 x -1/3) 1/9)
(+.f64 1/9 (+.f64 (*.f64 -1/3 x) (pow.f64 x 2)))
(+.f64 (fma.f64 -1/3 x (*.f64 x x)) 1/9)
(+.f64 (*.f64 x (+.f64 -1/3 x)) 1/9)
(fma.f64 x (+.f64 x -1/3) 1/9)
(pow.f64 x 2)
(*.f64 x x)
(+.f64 (*.f64 -1/3 x) (pow.f64 x 2))
(fma.f64 -1/3 x (*.f64 x x))
(*.f64 x (+.f64 -1/3 x))
(*.f64 x (+.f64 x -1/3))
(+.f64 1/9 (+.f64 (*.f64 -1/3 x) (pow.f64 x 2)))
(+.f64 (fma.f64 -1/3 x (*.f64 x x)) 1/9)
(+.f64 (*.f64 x (+.f64 -1/3 x)) 1/9)
(fma.f64 x (+.f64 x -1/3) 1/9)
(+.f64 1/9 (+.f64 (*.f64 -1/3 x) (pow.f64 x 2)))
(+.f64 (fma.f64 -1/3 x (*.f64 x x)) 1/9)
(+.f64 (*.f64 x (+.f64 -1/3 x)) 1/9)
(fma.f64 x (+.f64 x -1/3) 1/9)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1/9 (*.f64 x x))
✓	0.0b	(-.f64 1/3 x)
✓	15.9b	(/.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))

Compiler

Compiled 24 to 13 computations (45.8% saved)

series3.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))
0.0ms	x	@	inf	(/.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))
0.0ms	x	@	-inf	(/.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))
0.0ms	x	@	inf	(-.f64 1/9 (*.f64 x x))
0.0ms	x	@	0	(-.f64 1/9 (*.f64 x x))

rewrite255.0ms (5.2%)

Algorithm

1×	batch-egg-rewrite

Rules

614×	`unpow-prod-down_binary64`
430×	`log-prod_binary64`
251×	`prod-diff_binary64`
244×	`pow2_binary64`
241×	`pow-prod-down_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	192	15
2	2734	15

Stop Event

1×	node limit

Counts

3 → 278

Calls

Call 1

Inputs
(/.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))
(-.f64 1/3 x)
(-.f64 1/9 (*.f64 x x))

Outputs

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egg-rr> (2) ((x /.f64 (-.f64 1/81 (pow.f64 x 4)) (fma.f64 x x 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/729 (pow.f64 x 6))) (neg.f64 (fma.f64 (*.f64 x x) (fma.f64 x x 1/9) 1/81)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/81 (pow.f64 x 4))) (neg.f64 (fma.f64 x x 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/729 (*.f64 -1 (pow.f64 x 6))) (+.f64 1/81 (-.f64 (pow.f64 (*.f64 x (neg.f64 x)) 2) (*.f64 1/9 (*.f64 x (neg.f64 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/81 (pow.f64 (*.f64 x (neg.f64 x)) 2)) (-.f64 1/9 (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1/9 (*.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1/9 (*.f64 x x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1/9 (*.f64 x x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1/9 (*.f64 x x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1/9 (*.f64 x x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (*.f64 x x) (fma.f64 x x 1/9) 1/81) (-.f64 1/729 (pow.f64 x 6))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 x x 1/9) (-.f64 1/81 (pow.f64 x 4))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1/9 (*.f64 x x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (-.f64 1/9 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (-.f64 1/9 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1/9 (*.f64 x x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (-.f64 1/9 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (-.f64 1/9 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (-.f64 1/9 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 1/9 (*.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 1/9 (*.f64 x x)) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (-.f64 1/9 (*.f64 x x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (-.f64 1/9 (*.f64 x x)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (neg.f64 x) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x (neg.f64 x)) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 x) x) (neg.f64 (pow.f64 (cbrt.f64 x) 2)) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 x) x 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (*.f64 x (neg.f64 x))) 2) (cbrt.f64 (*.f64 x (neg.f64 x))) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 x (neg.f64 x))) (sqrt.f64 (*.f64 x (neg.f64 x))) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1 (*.f64 x x) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (*.f64 (cbrt.f64 x) x)) (pow.f64 (cbrt.f64 x) 2) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 x) 1) x 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (neg.f64 x) (sqrt.f64 x)) (sqrt.f64 x) 1/9)))))

simplify100.0ms (2%)

Algorithm

1×	egg-herbie

Rules

667×	`distribute-lft-neg-in_binary64`
648×	`distribute-rgt-neg-in_binary64`
458×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
365×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	194
1	24	158
2	41	158
3	76	158
4	183	158
5	522	158
6	1688	158
7	3517	158
8	4849	158
9	6171	158
10	7020	158

Stop Event

1×	node limit

Counts

314 → 289

Calls

Call 1

Inputs
1/3
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
1/3
(+.f64 1/3 (*.f64 -1 x))
(+.f64 1/3 (*.f64 -1 x))
(+.f64 1/3 (*.f64 -1 x))
(*.f64 -1 x)
(+.f64 1/3 (*.f64 -1 x))
(+.f64 1/3 (*.f64 -1 x))
(+.f64 1/3 (*.f64 -1 x))
(*.f64 -1 x)
(+.f64 1/3 (*.f64 -1 x))
(+.f64 1/3 (*.f64 -1 x))
(+.f64 1/3 (*.f64 -1 x))
1/9
(+.f64 1/9 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1/9 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1/9 (*.f64 -1 (pow.f64 x 2)))
(*.f64 -1 (pow.f64 x 2))
(+.f64 1/9 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1/9 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1/9 (*.f64 -1 (pow.f64 x 2)))
(*.f64 -1 (pow.f64 x 2))
(+.f64 1/9 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1/9 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1/9 (*.f64 -1 (pow.f64 x 2)))

Outputs
1/3
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
1/3
(+.f64 1/3 (*.f64 -1 x))
(+.f64 1/3 (neg.f64 x))
(-.f64 1/3 x)
(+.f64 1/3 (*.f64 -1 x))
(+.f64 1/3 (neg.f64 x))
(-.f64 1/3 x)
(+.f64 1/3 (*.f64 -1 x))
(+.f64 1/3 (neg.f64 x))
(-.f64 1/3 x)
(*.f64 -1 x)
(neg.f64 x)
(+.f64 1/3 (*.f64 -1 x))
(+.f64 1/3 (neg.f64 x))
(-.f64 1/3 x)
(+.f64 1/3 (*.f64 -1 x))
(+.f64 1/3 (neg.f64 x))
(-.f64 1/3 x)
(+.f64 1/3 (*.f64 -1 x))
(+.f64 1/3 (neg.f64 x))
(-.f64 1/3 x)
(*.f64 -1 x)
(neg.f64 x)
(+.f64 1/3 (*.f64 -1 x))
(+.f64 1/3 (neg.f64 x))
(-.f64 1/3 x)
(+.f64 1/3 (*.f64 -1 x))
(+.f64 1/3 (neg.f64 x))
(-.f64 1/3 x)
(+.f64 1/3 (*.f64 -1 x))
(+.f64 1/3 (neg.f64 x))
(-.f64 1/3 x)
1/9
(+.f64 1/9 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1/9 (neg.f64 (*.f64 x x)))
(-.f64 1/9 (*.f64 x x))
(neg.f64 (fma.f64 x x -1/9))
(+.f64 1/9 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1/9 (neg.f64 (*.f64 x x)))
(-.f64 1/9 (*.f64 x x))
(neg.f64 (fma.f64 x x -1/9))
(+.f64 1/9 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1/9 (neg.f64 (*.f64 x x)))
(-.f64 1/9 (*.f64 x x))
(neg.f64 (fma.f64 x x -1/9))
(*.f64 -1 (pow.f64 x 2))
(neg.f64 (*.f64 x x))
(*.f64 x (neg.f64 x))
(+.f64 1/9 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1/9 (neg.f64 (*.f64 x x)))
(-.f64 1/9 (*.f64 x x))
(neg.f64 (fma.f64 x x -1/9))
(+.f64 1/9 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1/9 (neg.f64 (*.f64 x x)))
(-.f64 1/9 (*.f64 x x))
(neg.f64 (fma.f64 x x -1/9))
(+.f64 1/9 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1/9 (neg.f64 (*.f64 x x)))
(-.f64 1/9 (*.f64 x x))
(neg.f64 (fma.f64 x x -1/9))
(*.f64 -1 (pow.f64 x 2))
(neg.f64 (*.f64 x x))
(*.f64 x (neg.f64 x))
(+.f64 1/9 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1/9 (neg.f64 (*.f64 x x)))
(-.f64 1/9 (*.f64 x x))
(neg.f64 (fma.f64 x x -1/9))
(+.f64 1/9 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1/9 (neg.f64 (*.f64 x x)))
(-.f64 1/9 (*.f64 x x))
(neg.f64 (fma.f64 x x -1/9))
(+.f64 1/9 (*.f64 -1 (pow.f64 x 2)))
(+.f64 1/9 (neg.f64 (*.f64 x x)))
(-.f64 1/9 (*.f64 x x))
(neg.f64 (fma.f64 x x -1/9))

eval1.0s (20.4%)

Compiler: Compiled 17339 to 12195 computations (29.7% saved)

prune279.0ms (5.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	749	4	753
Fresh	2	0	2
Picked	0	1	1
Done	2	1	3
Total	753	6	759

Error

Counts

759 → 6

Alt Table

Click to see full alt table

Status	Error	Program
	29.8b	x
▶	17.1b	(.f64 (/.f64 1 (-.f64 1/3 x)) (-.f64 1/9 (.f64 x x)))
✓	17.0b	(/.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))
▶	33.3b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (*.f64 x -1/3)))
✓	0.0b	(+.f64 x 1/3)
	33.0b	1/3

Compiler

Compiled 42 to 32 computations (23.8% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 1/3 x))
	0.0b	(-.f64 1/9 (*.f64 x x))
	0.0b	(-.f64 1/3 x)
✓	15.9b	(.f64 (/.f64 1 (-.f64 1/3 x)) (-.f64 1/9 (.f64 x x)))

Compiler

Compiled 32 to 20 computations (37.5% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(/.f64 1 (-.f64 1/3 x))
0.0ms	x	@	0	(.f64 (/.f64 1 (-.f64 1/3 x)) (-.f64 1/9 (.f64 x x)))
0.0ms	x	@	inf	(.f64 (/.f64 1 (-.f64 1/3 x)) (-.f64 1/9 (.f64 x x)))
0.0ms	x	@	0	(/.f64 1 (-.f64 1/3 x))
0.0ms	x	@	-inf	(/.f64 1 (-.f64 1/3 x))

rewrite71.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

450×	`log-prod_binary64`
349×	`exp-prod_binary64`
280×	`pow-prod-down_binary64`
262×	`pow2_binary64`
181×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	223	11
2	2897	11

Stop Event

1×	node limit

Counts

2 → 109

Calls

Call 1

Inputs
(.f64 (/.f64 1 (-.f64 1/3 x)) (-.f64 1/9 (.f64 x x)))
(/.f64 1 (-.f64 1/3 x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1/3 x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/9 (/.f64 1 (-.f64 1/3 x))) (*.f64 (*.f64 x (neg.f64 x)) (/.f64 1 (-.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (-.f64 1/3 x)) 1/9) (*.f64 (/.f64 1 (-.f64 1/3 x)) (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (+.f64 1/3 x))) 2)) (log.f64 (cbrt.f64 (exp.f64 (+.f64 1/3 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (+.f64 1/3 x)))) (log.f64 (sqrt.f64 (exp.f64 (+.f64 1/3 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1/3 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/9 (-.f64 1/3 x)) (/.f64 (*.f64 x x) (-.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1/3 x) (-.f64 1/9 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (cbrt.f64 (pow.f64 (-.f64 1/9 (*.f64 x x)) 2)) (/.f64 (-.f64 1/3 x) (cbrt.f64 (-.f64 1/9 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (-.f64 1/9 (*.f64 x x))) (/.f64 (-.f64 1/3 x) (sqrt.f64 (-.f64 1/9 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/729 (pow.f64 x 6)) (*.f64 (-.f64 1/3 x) (fma.f64 (*.f64 x x) (fma.f64 x x 1/9) 1/81)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/81 (pow.f64 x 4)) (*.f64 (-.f64 1/3 x) (fma.f64 x x 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/9 (*.f64 x x))) (neg.f64 (-.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (-.f64 1/729 (pow.f64 x 6))) (*.f64 (neg.f64 (-.f64 1/3 x)) (fma.f64 (*.f64 x x) (fma.f64 x x 1/9) 1/81)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (-.f64 1/81 (pow.f64 x 4))) (*.f64 (neg.f64 (-.f64 1/3 x)) (fma.f64 x x 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/729 (pow.f64 x 6)) 1) (*.f64 (fma.f64 (*.f64 x x) (fma.f64 x x 1/9) 1/81) (-.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/81 (pow.f64 x 4)) 1) (*.f64 (fma.f64 x x 1/9) (-.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/729 (pow.f64 x 6)) -1) (*.f64 (fma.f64 (*.f64 x x) (fma.f64 x x 1/9) 1/81) (neg.f64 (-.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/81 (pow.f64 x 4)) -1) (*.f64 (fma.f64 x x 1/9) (neg.f64 (-.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (-.f64 1/9 (*.f64 x x)) (sqrt.f64 (-.f64 1/3 x))) (sqrt.f64 (-.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (-.f64 (*.f64 x x) (*.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (-.f64 1/9 (*.f64 x x)) 1) (-.f64 1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (-.f64 1/9 (*.f64 x x)) (pow.f64 (cbrt.f64 (-.f64 1/3 x)) 2)) (cbrt.f64 (-.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 (-.f64 1/9 (*.f64 x x))) (neg.f64 (-.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/729 (pow.f64 x 6)) (/.f64 1 (-.f64 1/3 x))) (fma.f64 (*.f64 x x) (fma.f64 x x 1/9) 1/81))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/81 (pow.f64 x 4)) (/.f64 1 (-.f64 1/3 x))) (fma.f64 x x 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (-.f64 1/3 x)) (-.f64 1/729 (pow.f64 x 6))) (fma.f64 (*.f64 x x) (fma.f64 x x 1/9) 1/81))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (-.f64 1/3 x)) (-.f64 1/81 (pow.f64 x 4))) (fma.f64 x x 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 1/9 (*.f64 x x)) -1) (neg.f64 (-.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/3 x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (+.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/3 x) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/3 x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1/3 x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/3 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (-.f64 1/9 (*.f64 x x)) 3) (pow.f64 (-.f64 1/3 x) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1/3 x) (-.f64 1/9 (*.f64 x x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (+.f64 1/3 x))) 2)) (cbrt.f64 (log.f64 (+.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (+.f64 1/3 x)))) (sqrt.f64 (log.f64 (+.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1/3 x) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1/3 x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (-.f64 1/9 (*.f64 x x)) 3) (pow.f64 (-.f64 1/3 x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (+.f64 1/3 x)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (+.f64 1/3 x))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (+.f64 1/3 x))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 1/3 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (+.f64 1/3 x)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (-.f64 1/9 (*.f64 x x))) 1) (log.f64 (-.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (log.f64 (-.f64 1/9 (*.f64 x x))) (*.f64 (log.f64 (-.f64 1/3 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (-.f64 (*.f64 (log.f64 (-.f64 1/9 (*.f64 x x))) 1) (*.f64 (log.f64 (-.f64 1/3 x)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x 1 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 (-.f64 1/3 x)) 1/9 (*.f64 (/.f64 1 (-.f64 1/3 x)) (*.f64 x (neg.f64 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1/9 (/.f64 1 (-.f64 1/3 x)) (*.f64 (*.f64 x (neg.f64 x)) (/.f64 1 (-.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 x) (pow.f64 (cbrt.f64 x) 2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (*.f64 (cbrt.f64 x) x)) (sqrt.f64 (pow.f64 (cbrt.f64 x) 2)) 1/3)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (-.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (-.f64 1/3 x)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (-.f64 1/3 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (-.f64 1/3 x))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (-.f64 1/3 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 1 (-.f64 1/3 x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (-.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 1/3 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 (-.f64 1/3 x))) (cbrt.f64 (pow.f64 (-.f64 1/3 x) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (-.f64 1/3 x) -2)) (/.f64 1 (cbrt.f64 (-.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 1/3 x) -1/2) (pow.f64 (-.f64 1/3 x) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (-.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (-.f64 1/3 x)) -2) (/.f64 1 (cbrt.f64 (-.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 1/9 (*.f64 x x))) (+.f64 1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (-.f64 1/27 (pow.f64 x 3))) (fma.f64 x (+.f64 1/3 x) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 1/3 x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (-.f64 1/3 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (neg.f64 (log.f64 (-.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1/3 x) 2) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1/3 x) 3) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1/3 x) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1/3 x) -3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (-.f64 1/3 x)) -3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (cbrt.f64 (-.f64 1/3 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (-.f64 1/3 x)) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (-.f64 1/3 x) -1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 -1) (log.f64 (-.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (neg.f64 (-.f64 1/3 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (neg.f64 (log.f64 (-.f64 1/3 x)))) 2)) (cbrt.f64 (neg.f64 (log.f64 (-.f64 1/3 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (neg.f64 (log.f64 (-.f64 1/3 x))))) (sqrt.f64 (neg.f64 (log.f64 (-.f64 1/3 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (-.f64 1/3 x) -2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (-.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (-.f64 1/3 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (-.f64 1/3 x) -3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (-.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (-.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (log.f64 (-.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (-.f64 1/3 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (-.f64 1/3 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 1/3 x) -3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (cbrt.f64 (-.f64 1/3 x)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 1/3 x) -1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (-.f64 1/3 x)) 1) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (-.f64 1/3 x)) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (neg.f64 (log.f64 (-.f64 1/3 x))) 1) 1))))))

simplify45.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-def_binary64`
672×	`associate-r_binary64`
573×	`fma-neg_binary64`
495×	`times-frac_binary64`
329×	`associate-*l/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	41	234
1	111	220
2	293	216
3	897	210
4	2669	207

Stop Event

1×	node limit

Counts

133 → 125

Calls

Call 1

Inputs
1/3
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
3
(+.f64 3 (*.f64 9 x))
(+.f64 3 (+.f64 (.f64 27 (pow.f64 x 2)) (.f64 9 x)))
(+.f64 3 (+.f64 (.f64 81 (pow.f64 x 3)) (+.f64 (.f64 27 (pow.f64 x 2)) (*.f64 9 x))))
(/.f64 -1 x)
(neg.f64 (+.f64 (*.f64 1/3 (/.f64 1 (pow.f64 x 2))) (/.f64 1 x)))
(neg.f64 (+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x))))
(neg.f64 (+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 1/9 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))))
(/.f64 -1 x)
(neg.f64 (+.f64 (*.f64 1/3 (/.f64 1 (pow.f64 x 2))) (/.f64 1 x)))
(neg.f64 (+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x))))
(neg.f64 (+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 1/9 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))))

Outputs
1/3
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
3
(+.f64 3 (*.f64 9 x))
(+.f64 3 (*.f64 x 9))
(fma.f64 x 9 3)
(+.f64 3 (+.f64 (.f64 27 (pow.f64 x 2)) (.f64 9 x)))
(+.f64 3 (fma.f64 27 (.f64 x x) (.f64 x 9)))
(+.f64 3 (fma.f64 x 9 (.f64 27 (.f64 x x))))
(fma.f64 x (*.f64 x 27) (fma.f64 x 9 3))
(fma.f64 x (fma.f64 x 27 9) 3)
(+.f64 3 (+.f64 (.f64 81 (pow.f64 x 3)) (+.f64 (.f64 27 (pow.f64 x 2)) (*.f64 9 x))))
(+.f64 3 (fma.f64 81 (pow.f64 x 3) (fma.f64 27 (.f64 x x) (.f64 x 9))))
(+.f64 3 (fma.f64 81 (pow.f64 x 3) (fma.f64 x 9 (.f64 27 (.f64 x x)))))
(fma.f64 81 (pow.f64 x 3) (fma.f64 x (*.f64 x 27) (fma.f64 x 9 3)))
(fma.f64 x (fma.f64 x 27 9) (fma.f64 81 (pow.f64 x 3) 3))
(fma.f64 x (fma.f64 x (fma.f64 x 81 27) 9) 3)
(/.f64 -1 x)
(neg.f64 (+.f64 (*.f64 1/3 (/.f64 1 (pow.f64 x 2))) (/.f64 1 x)))
(neg.f64 (+.f64 (/.f64 1/3 (*.f64 x x)) (/.f64 1 x)))
(-.f64 (/.f64 -1 x) (/.f64 1/3 (*.f64 x x)))
(+.f64 (/.f64 -1/3 (*.f64 x x)) (/.f64 -1 x))
(neg.f64 (+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/3 (*.f64 x x)) (+.f64 (/.f64 1 x) (/.f64 1/9 (pow.f64 x 3)))))
(-.f64 (/.f64 -1/3 (*.f64 x x)) (+.f64 (/.f64 1 x) (/.f64 1/9 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 -1/3 (*.f64 x x)) (/.f64 -1 x)) (/.f64 -1/9 (pow.f64 x 3)))
(+.f64 (/.f64 -1/3 (*.f64 x x)) (+.f64 (/.f64 -1 x) (/.f64 -1/9 (pow.f64 x 3))))
(neg.f64 (+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 1/9 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))))
(neg.f64 (+.f64 (/.f64 1/3 (*.f64 x x)) (+.f64 (+.f64 (/.f64 1 x) (/.f64 1/9 (pow.f64 x 3))) (/.f64 1/27 (pow.f64 x 4)))))
(-.f64 (/.f64 -1/3 (*.f64 x x)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1/9 (pow.f64 x 3)) (/.f64 1/27 (pow.f64 x 4)))))
(+.f64 (+.f64 (+.f64 (/.f64 -1/3 (*.f64 x x)) (/.f64 -1 x)) (/.f64 -1/9 (pow.f64 x 3))) (/.f64 -1/27 (pow.f64 x 4)))
(+.f64 (+.f64 (/.f64 -1/3 (*.f64 x x)) (+.f64 (/.f64 -1 x) (/.f64 -1/9 (pow.f64 x 3)))) (/.f64 -1/27 (pow.f64 x 4)))
(+.f64 (+.f64 (/.f64 -1/3 (*.f64 x x)) (/.f64 -1 x)) (+.f64 (/.f64 -1/9 (pow.f64 x 3)) (/.f64 -1/27 (pow.f64 x 4))))
(/.f64 -1 x)
(neg.f64 (+.f64 (*.f64 1/3 (/.f64 1 (pow.f64 x 2))) (/.f64 1 x)))
(neg.f64 (+.f64 (/.f64 1/3 (*.f64 x x)) (/.f64 1 x)))
(-.f64 (/.f64 -1 x) (/.f64 1/3 (*.f64 x x)))
(+.f64 (/.f64 -1/3 (*.f64 x x)) (/.f64 -1 x))
(neg.f64 (+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/3 (*.f64 x x)) (+.f64 (/.f64 1 x) (/.f64 1/9 (pow.f64 x 3)))))
(-.f64 (/.f64 -1/3 (*.f64 x x)) (+.f64 (/.f64 1 x) (/.f64 1/9 (pow.f64 x 3))))
(+.f64 (+.f64 (/.f64 -1/3 (*.f64 x x)) (/.f64 -1 x)) (/.f64 -1/9 (pow.f64 x 3)))
(+.f64 (/.f64 -1/3 (*.f64 x x)) (+.f64 (/.f64 -1 x) (/.f64 -1/9 (pow.f64 x 3))))
(neg.f64 (+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 4))) (+.f64 (*.f64 1/9 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))))
(neg.f64 (+.f64 (/.f64 1/3 (*.f64 x x)) (+.f64 (+.f64 (/.f64 1 x) (/.f64 1/9 (pow.f64 x 3))) (/.f64 1/27 (pow.f64 x 4)))))
(-.f64 (/.f64 -1/3 (*.f64 x x)) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1/9 (pow.f64 x 3)) (/.f64 1/27 (pow.f64 x 4)))))
(+.f64 (+.f64 (+.f64 (/.f64 -1/3 (*.f64 x x)) (/.f64 -1 x)) (/.f64 -1/9 (pow.f64 x 3))) (/.f64 -1/27 (pow.f64 x 4)))
(+.f64 (+.f64 (/.f64 -1/3 (*.f64 x x)) (+.f64 (/.f64 -1 x) (/.f64 -1/9 (pow.f64 x 3)))) (/.f64 -1/27 (pow.f64 x 4)))
(+.f64 (+.f64 (/.f64 -1/3 (*.f64 x x)) (/.f64 -1 x)) (+.f64 (/.f64 -1/9 (pow.f64 x 3)) (/.f64 -1/27 (pow.f64 x 4))))

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/27 (pow.f64 x 3))
✓	0.0b	(+.f64 1/9 (*.f64 x -1/3))
✓	0.3b	(*.f64 x -1/3)
✓	5.4b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (*.f64 x -1/3)))

Compiler

Compiled 33 to 26 computations (21.2% saved)

series23.0ms (0.5%)

Counts

4 → 39

Calls

12 calls:

Time	Variable		Point	Expression
19.0ms	x	@	0	(+.f64 1/9 (*.f64 x -1/3))
0.0ms	x	@	0	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (*.f64 x -1/3)))
0.0ms	x	@	inf	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (*.f64 x -1/3)))
0.0ms	x	@	inf	(+.f64 1/27 (pow.f64 x 3))
0.0ms	x	@	0	(*.f64 x -1/3)

rewrite86.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

505×	`log-prod_binary64`
298×	`pow2_binary64`
291×	`pow-prod-down_binary64`
221×	`prod-diff_binary64`
206×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	256	30
2	3178	30

Stop Event

1×	node limit

Counts

4 → 156

Calls

Call 1

Inputs
(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (*.f64 x -1/3)))
(*.f64 x -1/3)
(+.f64 1/9 (*.f64 x -1/3))
(+.f64 1/27 (pow.f64 x 3))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1/27 (pow.f64 x 3)) (/.f64 1 (fma.f64 x -1/3 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9))) (pow.f64 (cbrt.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9))) 2) (cbrt.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 1/27 (pow.f64 x 3))) 2) (.f64 (cbrt.f64 (+.f64 1/27 (pow.f64 x 3))) (/.f64 1 (fma.f64 x -1/3 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9))) (sqrt.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 1/27 (pow.f64 x 3))) (.f64 (sqrt.f64 (+.f64 1/27 (pow.f64 x 3))) (/.f64 1 (fma.f64 x -1/3 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 -1/27 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3)) (fma.f64 x -1/3 1/9)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 x -1/3 1/9) (+.f64 1/27 (pow.f64 x 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (pow.f64 (+.f64 1/27 (pow.f64 x 3)) 3) (pow.f64 (fma.f64 x -1/3 1/9) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 (fma.f64 x -1/3 1/9) (+.f64 1/27 (pow.f64 x 3))) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (neg.f64 (fma.f64 x -1/3 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (+.f64 1/27 (pow.f64 x 3)) 3) (pow.f64 (fma.f64 x -1/3 1/9) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x -1/3 1/9)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (fma.f64 x -1/3 1/9) (+.f64 1/27 (pow.f64 x 3)))) -1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 x -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/3) x)) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -1/3) x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/3) x))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -1/3) x))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 x -1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 x -1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 1/9 (.f64 x x)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 x -1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 x -1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 x 3) -1/27) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 1/9 (.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 -1/3) x))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 x 3) -1/27))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 x -1/3)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 x -1/3))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (.f64 x -1/3))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (.f64 x -1/3))) 1/3))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (fma.f64 x -1/3 1/9))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/81 (-.f64 1/9 (.f64 x -1/3))) (/.f64 (.f64 1/9 (.f64 x x)) (-.f64 1/9 (.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x -1/3 1/9) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x -1/3 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x -1/3 1/9)) (pow.f64 (cbrt.f64 (fma.f64 x -1/3 1/9)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x -1/3 1/9)) 2) (cbrt.f64 (fma.f64 x -1/3 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 x -1/3 1/9)) (sqrt.f64 (fma.f64 x -1/3 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (pow.f64 x 3) -1/27 1/729) (/.f64 1 (fma.f64 (.f64 x -1/3) (fma.f64 x -1/3 -1/9) 1/81)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1/81 (.f64 1/9 (.f64 x x))) (/.f64 1 (-.f64 1/9 (.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (.f64 x -1/3) (fma.f64 x -1/3 -1/9) 1/81) (fma.f64 (pow.f64 x 3) -1/27 1/729)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1/9 (.f64 x -1/3)) (-.f64 1/81 (.f64 1/9 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 3) -1/27 1/729) (fma.f64 (.f64 x -1/3) (fma.f64 x -1/3 -1/9) 1/81))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 x 3) -1/27 1/729) (fma.f64 1/9 (.f64 x x) (-.f64 1/81 (.f64 -1/27 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/81 (.f64 1/9 (.f64 x x))) (-.f64 1/9 (.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (pow.f64 x 3) -1/27 1/729)) (neg.f64 (fma.f64 (.f64 x -1/3) (fma.f64 x -1/3 -1/9) 1/81)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/81 (.f64 1/9 (.f64 x x)))) (neg.f64 (-.f64 1/9 (.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 1/9 (.f64 x x) -1/81) (fma.f64 x -1/3 -1/9))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x -1/3 1/9) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x -1/3 1/9) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x -1/3 1/9) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x -1/3 1/9)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x -1/3 1/9)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (.f64 x -1/3) (fma.f64 x -1/3 -1/9) 1/81) (fma.f64 (pow.f64 x 3) -1/27 1/729)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1/9 (.f64 x -1/3)) (-.f64 1/81 (.f64 1/9 (.f64 x x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x -1/3 1/9) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x -1/3 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (fma.f64 x -1/3 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x -1/3 1/9) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x -1/3 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x -1/3 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x -1/3 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (fma.f64 x -1/3 1/9)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (fma.f64 x -1/3 1/9))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (fma.f64 x -1/3 1/9))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (fma.f64 x -1/3 1/9))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x -1/3 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/3 x 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x -1/3) 1 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (.f64 x -1/3) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 x -1/3)) (pow.f64 (cbrt.f64 (.f64 x -1/3)) 2) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (.f64 x -1/3)) 2) (cbrt.f64 (.f64 x -1/3)) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) -1/3) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (.f64 x -1/3)) (sqrt.f64 (.f64 x -1/3)) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) -1/3) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 -1/3 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 -1/3 (sqrt.f64 x)) (sqrt.f64 x) 1/9)))))
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1/27 (pow.f64 x 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/729 (-.f64 1/27 (pow.f64 x 3))) (/.f64 (pow.f64 x 6) (-.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1/27 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 1/27 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 1/27 (pow.f64 x 3))) (pow.f64 (cbrt.f64 (+.f64 1/27 (pow.f64 x 3))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 1/27 (pow.f64 x 3))) 2) (cbrt.f64 (+.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 1/27 (pow.f64 x 3))) (sqrt.f64 (+.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1/19683 (pow.f64 x 9)) (/.f64 1 (fma.f64 (pow.f64 x 3) (-.f64 (pow.f64 x 3) 1/27) 1/729)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1/729 (pow.f64 x 6)) (/.f64 1 (-.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (pow.f64 x 3) (-.f64 (pow.f64 x 3) 1/27) 1/729) (+.f64 1/19683 (pow.f64 x 9))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1/27 (pow.f64 x 3)) (-.f64 1/729 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/19683 (pow.f64 x 9)) (fma.f64 (pow.f64 x 3) (-.f64 (pow.f64 x 3) 1/27) 1/729))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/19683 (pow.f64 x 9)) (+.f64 (pow.f64 x 6) (-.f64 1/729 (.f64 1/27 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/729 (pow.f64 x 6)) (-.f64 1/27 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/19683 (pow.f64 x 9))) (neg.f64 (fma.f64 (pow.f64 x 3) (-.f64 (pow.f64 x 3) 1/27) 1/729)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/729 (pow.f64 x 6))) (neg.f64 (-.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 6) 1/729) (-.f64 (pow.f64 x 3) 1/27))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/27 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/27 (pow.f64 x 3)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/27 (pow.f64 x 3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1/27 (pow.f64 x 3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/27 (pow.f64 x 3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (fma.f64 (pow.f64 x 3) (-.f64 (pow.f64 x 3) 1/27) 1/729) (+.f64 1/19683 (pow.f64 x 9))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 1/27 (pow.f64 x 3)) (-.f64 1/729 (pow.f64 x 6))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1/27 (pow.f64 x 3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1/27 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1/27 (pow.f64 x 3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (+.f64 1/27 (pow.f64 x 3))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (+.f64 1/27 (pow.f64 x 3)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (+.f64 1/27 (pow.f64 x 3)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 1/27 (pow.f64 x 3)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (.f64 x x) 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3) 1 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 x 3) 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x x) x 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (.f64 x x)) 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (pow.f64 x 5/2) 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (pow.f64 x 3/2) 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 5/2) (sqrt.f64 x) 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (.f64 x x) 1) x 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (.f64 x (cbrt.f64 x)) 2) (cbrt.f64 x) 1/27)))))

simplify54.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

608×	`fma-def_binary64`
581×	`associate-l_binary64`
536×	`unswap-sqr_binary64`
380×	`associate-r_binary64`
309×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	32	261
1	80	239
2	193	235
3	515	219
4	1459	218
5	4519	218

Stop Event

1×	node limit

Counts

195 → 176

Calls

Call 1

Inputs
1/3
(+.f64 1/3 x)
(+.f64 (*.f64 3 (pow.f64 x 2)) (+.f64 1/3 x))
(+.f64 (.f64 3 (pow.f64 x 2)) (+.f64 1/3 (+.f64 (.f64 18 (pow.f64 x 3)) x)))
(*.f64 -3 (pow.f64 x 2))
(+.f64 (.f64 -3 (pow.f64 x 2)) (.f64 -1 x))
(-.f64 (+.f64 (.f64 -3 (pow.f64 x 2)) (.f64 -1 x)) 1/3)
(-.f64 (+.f64 (.f64 -3 (pow.f64 x 2)) (.f64 -1 x)) (+.f64 1/3 (*.f64 2/9 (/.f64 1 x))))
(*.f64 -3 (pow.f64 x 2))
(+.f64 (.f64 -3 (pow.f64 x 2)) (.f64 -1 x))
(-.f64 (+.f64 (.f64 -3 (pow.f64 x 2)) (.f64 -1 x)) 1/3)
(-.f64 (+.f64 (.f64 -3 (pow.f64 x 2)) (.f64 -1 x)) (+.f64 1/3 (*.f64 2/9 (/.f64 1 x))))
(*.f64 -1/3 x)
(*.f64 -1/3 x)
(*.f64 -1/3 x)
(*.f64 -1/3 x)
(*.f64 -1/3 x)
(*.f64 -1/3 x)
(*.f64 -1/3 x)
(*.f64 -1/3 x)
(*.f64 -1/3 x)
(*.f64 -1/3 x)
(*.f64 -1/3 x)
(*.f64 -1/3 x)
1/9
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 1/9 (*.f64 -1/3 x))
(*.f64 -1/3 x)
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 1/9 (*.f64 -1/3 x))
(*.f64 -1/3 x)
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 1/9 (*.f64 -1/3 x))
1/27
(pow.f64 x 3)
(pow.f64 x 3)

Outputs
1/3
(+.f64 1/3 x)
(+.f64 (*.f64 3 (pow.f64 x 2)) (+.f64 1/3 x))
(fma.f64 3 (*.f64 x x) (+.f64 1/3 x))
(+.f64 x (fma.f64 3 (*.f64 x x) 1/3))
(+.f64 1/3 (fma.f64 x (*.f64 x 3) x))
(fma.f64 (fma.f64 x 3 1) x 1/3)
(fma.f64 x (fma.f64 x 3 1) 1/3)
(+.f64 (.f64 3 (pow.f64 x 2)) (+.f64 1/3 (+.f64 (.f64 18 (pow.f64 x 3)) x)))
(fma.f64 3 (*.f64 x x) (+.f64 1/3 (fma.f64 18 (pow.f64 x 3) x)))
(+.f64 (fma.f64 18 (pow.f64 x 3) x) (fma.f64 3 (*.f64 x x) 1/3))
(+.f64 1/3 (fma.f64 x (*.f64 x 3) (fma.f64 18 (pow.f64 x 3) x)))
(fma.f64 18 (pow.f64 x 3) (fma.f64 (fma.f64 x 3 1) x 1/3))
(+.f64 1/3 (fma.f64 (*.f64 x x) (fma.f64 x 18 3) x))
(+.f64 x (fma.f64 (*.f64 x x) (fma.f64 x 18 3) 1/3))
(*.f64 -3 (pow.f64 x 2))
(.f64 (.f64 x x) -3)
(.f64 x (.f64 x -3))
(+.f64 (.f64 -3 (pow.f64 x 2)) (.f64 -1 x))
(fma.f64 -3 (*.f64 x x) (neg.f64 x))
(fma.f64 (*.f64 x x) -3 (neg.f64 x))
(-.f64 (.f64 x (.f64 x -3)) x)
(*.f64 x (fma.f64 x -3 -1))
(-.f64 (+.f64 (.f64 -3 (pow.f64 x 2)) (.f64 -1 x)) 1/3)
(+.f64 (fma.f64 -3 (*.f64 x x) (neg.f64 x)) -1/3)
(fma.f64 (*.f64 x x) -3 (fma.f64 x -1 -1/3))
(-.f64 (fma.f64 x (*.f64 x -3) -1/3) x)
(fma.f64 x (fma.f64 x -3 -1) -1/3)
(-.f64 (+.f64 (.f64 -3 (pow.f64 x 2)) (.f64 -1 x)) (+.f64 1/3 (*.f64 2/9 (/.f64 1 x))))
(-.f64 (fma.f64 -3 (*.f64 x x) (neg.f64 x)) (+.f64 1/3 (/.f64 2/9 x)))
(-.f64 (fma.f64 (*.f64 x x) -3 (fma.f64 x -1 -1/3)) (/.f64 2/9 x))
(-.f64 (fma.f64 x (*.f64 x -3) (-.f64 -1/3 (/.f64 2/9 x))) x)
(+.f64 -1/3 (fma.f64 x (fma.f64 x -3 -1) (/.f64 -2/9 x)))
(+.f64 (fma.f64 x (fma.f64 x -3 -1) -1/3) (/.f64 -2/9 x))
(-.f64 (/.f64 -2/9 x) (fma.f64 x (fma.f64 x 3 1) 1/3))
(*.f64 -3 (pow.f64 x 2))
(.f64 (.f64 x x) -3)
(.f64 x (.f64 x -3))
(+.f64 (.f64 -3 (pow.f64 x 2)) (.f64 -1 x))
(fma.f64 -3 (*.f64 x x) (neg.f64 x))
(fma.f64 (*.f64 x x) -3 (neg.f64 x))
(-.f64 (.f64 x (.f64 x -3)) x)
(*.f64 x (fma.f64 x -3 -1))
(-.f64 (+.f64 (.f64 -3 (pow.f64 x 2)) (.f64 -1 x)) 1/3)
(+.f64 (fma.f64 -3 (*.f64 x x) (neg.f64 x)) -1/3)
(fma.f64 (*.f64 x x) -3 (fma.f64 x -1 -1/3))
(-.f64 (fma.f64 x (*.f64 x -3) -1/3) x)
(fma.f64 x (fma.f64 x -3 -1) -1/3)
(-.f64 (+.f64 (.f64 -3 (pow.f64 x 2)) (.f64 -1 x)) (+.f64 1/3 (*.f64 2/9 (/.f64 1 x))))
(-.f64 (fma.f64 -3 (*.f64 x x) (neg.f64 x)) (+.f64 1/3 (/.f64 2/9 x)))
(-.f64 (fma.f64 (*.f64 x x) -3 (fma.f64 x -1 -1/3)) (/.f64 2/9 x))
(-.f64 (fma.f64 x (*.f64 x -3) (-.f64 -1/3 (/.f64 2/9 x))) x)
(+.f64 -1/3 (fma.f64 x (fma.f64 x -3 -1) (/.f64 -2/9 x)))
(+.f64 (fma.f64 x (fma.f64 x -3 -1) -1/3) (/.f64 -2/9 x))
(-.f64 (/.f64 -2/9 x) (fma.f64 x (fma.f64 x 3 1) 1/3))
(*.f64 -1/3 x)
(*.f64 x -1/3)
(*.f64 -1/3 x)
(*.f64 x -1/3)
(*.f64 -1/3 x)
(*.f64 x -1/3)
(*.f64 -1/3 x)
(*.f64 x -1/3)
(*.f64 -1/3 x)
(*.f64 x -1/3)
(*.f64 -1/3 x)
(*.f64 x -1/3)
(*.f64 -1/3 x)
(*.f64 x -1/3)
(*.f64 -1/3 x)
(*.f64 x -1/3)
(*.f64 -1/3 x)
(*.f64 x -1/3)
(*.f64 -1/3 x)
(*.f64 x -1/3)
(*.f64 -1/3 x)
(*.f64 x -1/3)
(*.f64 -1/3 x)
(*.f64 x -1/3)
1/9
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 (*.f64 x -1/3) 1/9)
(fma.f64 x -1/3 1/9)
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 (*.f64 x -1/3) 1/9)
(fma.f64 x -1/3 1/9)
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 (*.f64 x -1/3) 1/9)
(fma.f64 x -1/3 1/9)
(*.f64 -1/3 x)
(*.f64 x -1/3)
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 (*.f64 x -1/3) 1/9)
(fma.f64 x -1/3 1/9)
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 (*.f64 x -1/3) 1/9)
(fma.f64 x -1/3 1/9)
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 (*.f64 x -1/3) 1/9)
(fma.f64 x -1/3 1/9)
(*.f64 -1/3 x)
(*.f64 x -1/3)
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 (*.f64 x -1/3) 1/9)
(fma.f64 x -1/3 1/9)
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 (*.f64 x -1/3) 1/9)
(fma.f64 x -1/3 1/9)
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 (*.f64 x -1/3) 1/9)
(fma.f64 x -1/3 1/9)
1/27
(pow.f64 x 3)
(pow.f64 x 3)

eval312.0ms (6.4%)

Compiler: Compiled 6535 to 4891 computations (25.2% saved)

prune58.0ms (1.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	423	3	426
Fresh	1	1	2
Picked	1	0	1
Done	1	2	3
Total	426	6	432

Error

Counts

432 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	33.2b	(/.f64 1/27 (+.f64 1/9 (*.f64 x -1/3)))
	29.8b	x
✓	17.0b	(/.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))
	33.0b	1/3
✓	0.0b	(+.f64 x 1/3)
▶	33.2b	(*.f64 (/.f64 1 (-.f64 1/3 x)) 1/9)

Compiler

Compiled 34 to 27 computations (20.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (-.f64 1/3 x))
	0.0b	(-.f64 1/3 x)
✓	0.2b	(*.f64 (/.f64 1 (-.f64 1/3 x)) 1/9)

Compiler

Compiled 20 to 16 computations (20% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(*.f64 (/.f64 1 (-.f64 1/3 x)) 1/9)
0.0ms	x	@	0	(*.f64 (/.f64 1 (-.f64 1/3 x)) 1/9)
0.0ms	x	@	-inf	(*.f64 (/.f64 1 (-.f64 1/3 x)) 1/9)

rewrite51.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

795×	`pow1_binary64`
745×	`add-log-exp_binary64`
745×	`log1p-expm1-u_binary64`
745×	`expm1-log1p-u_binary64`
733×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	7
1	171	7
2	2016	7

Stop Event

1×	node limit

Counts

1 → 16

Calls

Call 1

Inputs
(*.f64 (/.f64 1 (-.f64 1/3 x)) 1/9)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1/9 (-.f64 1/3 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1/3 x) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1/9 (-.f64 1/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 -1/9 (neg.f64 (-.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1/9 (pow.f64 (cbrt.f64 (-.f64 1/3 x)) 2)) (cbrt.f64 (-.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1/9 (sqrt.f64 (-.f64 1/3 x))) (sqrt.f64 (-.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/9 (-.f64 1/3 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/9 (-.f64 1/3 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 1/9 (-.f64 1/3 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/3 (sqrt.f64 (-.f64 1/3 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (-.f64 1/3 x) -2) 1/81))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/9 (-.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/9 (-.f64 1/3 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/9 (-.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/9 (-.f64 1/3 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/9 (-.f64 1/3 x))))))))

simplify45.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

898×	`fma-neg_binary64`
810×	`times-frac_binary64`
473×	`associate-*l/_binary64`
462×	`cancel-sign-sub-inv_binary64`
410×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	186
1	108	174
2	309	174
3	972	170
4	2962	170

Stop Event

1×	node limit

Counts

28 → 29

Calls

Call 1

Inputs
1/3
(+.f64 1/3 x)
(+.f64 (*.f64 3 (pow.f64 x 2)) (+.f64 1/3 x))
(+.f64 (.f64 3 (pow.f64 x 2)) (+.f64 1/3 (+.f64 (.f64 9 (pow.f64 x 3)) x)))
(/.f64 -1/9 x)
(neg.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/9 (/.f64 1 x))))
(neg.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (*.f64 1/27 (/.f64 1 (pow.f64 x 2))))))
(neg.f64 (+.f64 (.f64 1/243 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))))))
(/.f64 -1/9 x)
(neg.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/9 (/.f64 1 x))))
(neg.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (*.f64 1/27 (/.f64 1 (pow.f64 x 2))))))
(neg.f64 (+.f64 (.f64 1/243 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))))))

Outputs
1/3
(+.f64 1/3 x)
(+.f64 (*.f64 3 (pow.f64 x 2)) (+.f64 1/3 x))
(fma.f64 3 (*.f64 x x) (+.f64 1/3 x))
(+.f64 1/3 (fma.f64 x (*.f64 x 3) x))
(fma.f64 (fma.f64 x 3 1) x 1/3)
(+.f64 (.f64 3 (pow.f64 x 2)) (+.f64 1/3 (+.f64 (.f64 9 (pow.f64 x 3)) x)))
(fma.f64 3 (*.f64 x x) (+.f64 1/3 (fma.f64 9 (pow.f64 x 3) x)))
(+.f64 (fma.f64 9 (pow.f64 x 3) x) (fma.f64 3 (*.f64 x x) 1/3))
(+.f64 1/3 (fma.f64 x (*.f64 x 3) (fma.f64 9 (pow.f64 x 3) x)))
(fma.f64 9 (pow.f64 x 3) (fma.f64 (fma.f64 x 3 1) x 1/3))
(fma.f64 (fma.f64 x 3 1) x (fma.f64 9 (pow.f64 x 3) 1/3))
(/.f64 -1/9 x)
(neg.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/9 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/9 x)))
(+.f64 (/.f64 -1/27 (*.f64 x x)) (/.f64 -1/9 x))
(neg.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (*.f64 1/27 (/.f64 1 (pow.f64 x 2))))))
(neg.f64 (+.f64 (/.f64 1/81 (pow.f64 x 3)) (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/9 x))))
(+.f64 (+.f64 (/.f64 -1/81 (pow.f64 x 3)) (/.f64 -1/27 (*.f64 x x))) (/.f64 -1/9 x))
(+.f64 (/.f64 -1/27 (*.f64 x x)) (+.f64 (/.f64 -1/9 x) (/.f64 -1/81 (pow.f64 x 3))))
(neg.f64 (+.f64 (.f64 1/243 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))))))
(neg.f64 (+.f64 (+.f64 (/.f64 1/81 (pow.f64 x 3)) (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/9 x))) (/.f64 1/243 (pow.f64 x 4))))
(+.f64 (+.f64 (+.f64 (/.f64 -1/81 (pow.f64 x 3)) (/.f64 -1/27 (*.f64 x x))) (/.f64 -1/9 x)) (/.f64 -1/243 (pow.f64 x 4)))
(+.f64 (+.f64 (/.f64 -1/27 (*.f64 x x)) (+.f64 (/.f64 -1/9 x) (/.f64 -1/81 (pow.f64 x 3)))) (/.f64 -1/243 (pow.f64 x 4)))
(+.f64 (/.f64 -1/27 (*.f64 x x)) (+.f64 (/.f64 -1/243 (pow.f64 x 4)) (+.f64 (/.f64 -1/9 x) (/.f64 -1/81 (pow.f64 x 3)))))
(/.f64 -1/9 x)
(neg.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/9 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/9 x)))
(+.f64 (/.f64 -1/27 (*.f64 x x)) (/.f64 -1/9 x))
(neg.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (*.f64 1/27 (/.f64 1 (pow.f64 x 2))))))
(neg.f64 (+.f64 (/.f64 1/81 (pow.f64 x 3)) (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/9 x))))
(+.f64 (+.f64 (/.f64 -1/81 (pow.f64 x 3)) (/.f64 -1/27 (*.f64 x x))) (/.f64 -1/9 x))
(+.f64 (/.f64 -1/27 (*.f64 x x)) (+.f64 (/.f64 -1/9 x) (/.f64 -1/81 (pow.f64 x 3))))
(neg.f64 (+.f64 (.f64 1/243 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))))))
(neg.f64 (+.f64 (+.f64 (/.f64 1/81 (pow.f64 x 3)) (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/9 x))) (/.f64 1/243 (pow.f64 x 4))))
(+.f64 (+.f64 (+.f64 (/.f64 -1/81 (pow.f64 x 3)) (/.f64 -1/27 (*.f64 x x))) (/.f64 -1/9 x)) (/.f64 -1/243 (pow.f64 x 4)))
(+.f64 (+.f64 (/.f64 -1/27 (*.f64 x x)) (+.f64 (/.f64 -1/9 x) (/.f64 -1/81 (pow.f64 x 3)))) (/.f64 -1/243 (pow.f64 x 4)))
(+.f64 (/.f64 -1/27 (*.f64 x x)) (+.f64 (/.f64 -1/243 (pow.f64 x 4)) (+.f64 (/.f64 -1/9 x) (/.f64 -1/81 (pow.f64 x 3)))))

localize19.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1/9 (*.f64 x -1/3))
✓	0.2b	(/.f64 1/27 (+.f64 1/9 (*.f64 x -1/3)))
	0.3b	(*.f64 x -1/3)

Compiler

Compiled 20 to 16 computations (20% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(/.f64 1/27 (+.f64 1/9 (*.f64 x -1/3)))
0.0ms	x	@	0	(/.f64 1/27 (+.f64 1/9 (*.f64 x -1/3)))
0.0ms	x	@	-inf	(/.f64 1/27 (+.f64 1/9 (*.f64 x -1/3)))

rewrite87.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

841×	`pow1_binary64`
790×	`add-log-exp_binary64`
790×	`log1p-expm1-u_binary64`
790×	`expm1-log1p-u_binary64`
778×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	178	8
2	2127	8

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

Inputs
(/.f64 1/27 (+.f64 1/9 (*.f64 x -1/3)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1/27 (fma.f64 x -1/3 1/9))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/27 (/.f64 1 (fma.f64 x -1/3 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/27 (fma.f64 x -1/3 1/9)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1/27 (fma.f64 x -1/3 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/27 (/.f64 1 (neg.f64 (fma.f64 x -1/3 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/3 (cbrt.f64 (fma.f64 x -1/3 1/9))) (pow.f64 (/.f64 1/3 (cbrt.f64 (fma.f64 x -1/3 1/9))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (/.f64 1/3 (cbrt.f64 (fma.f64 x -1/3 1/9))) 2) (/.f64 1/3 (cbrt.f64 (fma.f64 x -1/3 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 1/27 (fma.f64 x -1/3 1/9))) (sqrt.f64 (/.f64 1/27 (fma.f64 x -1/3 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (fma.f64 x -1/3 1/9)) 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/27 (+.f64 1/729 (*.f64 -1/27 (pow.f64 x 3)))) (+.f64 1/81 (-.f64 (*.f64 1/9 (*.f64 x x)) (*.f64 -1/27 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1/27 (-.f64 1/81 (*.f64 1/9 (*.f64 x x)))) (+.f64 1/9 (*.f64 1/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/27 (fma.f64 x -1/3 1/9)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 1/27 (fma.f64 x -1/3 1/9)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1/3 (cbrt.f64 (fma.f64 x -1/3 1/9))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 1/27 (fma.f64 x -1/3 1/9))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (fma.f64 x -1/3 1/9) 27) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 1/729 (pow.f64 (fma.f64 x -1/3 1/9) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1/27 (fma.f64 x -1/3 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 1/27 (fma.f64 x -1/3 1/9)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1/27 (fma.f64 x -1/3 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1/27 (fma.f64 x -1/3 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1/27 (fma.f64 x -1/3 1/9))))))))

simplify45.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

898×	`fma-neg_binary64`
810×	`times-frac_binary64`
473×	`associate-*l/_binary64`
462×	`cancel-sign-sub-inv_binary64`
410×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	186
1	108	174
2	309	174
3	972	170
4	2962	170

Stop Event

1×	node limit

Counts

34 → 35

Calls

Call 1

Inputs
1/3
(+.f64 1/3 x)
(+.f64 (*.f64 3 (pow.f64 x 2)) (+.f64 1/3 x))
(+.f64 (.f64 3 (pow.f64 x 2)) (+.f64 1/3 (+.f64 (.f64 9 (pow.f64 x 3)) x)))
(/.f64 -1/9 x)
(neg.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/9 (/.f64 1 x))))
(neg.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (*.f64 1/27 (/.f64 1 (pow.f64 x 2))))))
(neg.f64 (+.f64 (.f64 1/243 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))))))
(/.f64 -1/9 x)
(neg.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/9 (/.f64 1 x))))
(neg.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (*.f64 1/27 (/.f64 1 (pow.f64 x 2))))))
(neg.f64 (+.f64 (.f64 1/243 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))))))

Outputs
1/3
(+.f64 1/3 x)
(+.f64 (*.f64 3 (pow.f64 x 2)) (+.f64 1/3 x))
(fma.f64 3 (*.f64 x x) (+.f64 1/3 x))
(+.f64 1/3 (fma.f64 x (*.f64 x 3) x))
(fma.f64 (fma.f64 x 3 1) x 1/3)
(+.f64 (.f64 3 (pow.f64 x 2)) (+.f64 1/3 (+.f64 (.f64 9 (pow.f64 x 3)) x)))
(fma.f64 3 (*.f64 x x) (+.f64 1/3 (fma.f64 9 (pow.f64 x 3) x)))
(+.f64 (fma.f64 9 (pow.f64 x 3) x) (fma.f64 3 (*.f64 x x) 1/3))
(+.f64 1/3 (fma.f64 x (*.f64 x 3) (fma.f64 9 (pow.f64 x 3) x)))
(fma.f64 9 (pow.f64 x 3) (fma.f64 (fma.f64 x 3 1) x 1/3))
(fma.f64 (fma.f64 x 3 1) x (fma.f64 9 (pow.f64 x 3) 1/3))
(/.f64 -1/9 x)
(neg.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/9 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/9 x)))
(+.f64 (/.f64 -1/27 (*.f64 x x)) (/.f64 -1/9 x))
(neg.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (*.f64 1/27 (/.f64 1 (pow.f64 x 2))))))
(neg.f64 (+.f64 (/.f64 1/81 (pow.f64 x 3)) (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/9 x))))
(+.f64 (+.f64 (/.f64 -1/81 (pow.f64 x 3)) (/.f64 -1/27 (*.f64 x x))) (/.f64 -1/9 x))
(+.f64 (/.f64 -1/27 (*.f64 x x)) (+.f64 (/.f64 -1/9 x) (/.f64 -1/81 (pow.f64 x 3))))
(neg.f64 (+.f64 (.f64 1/243 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))))))
(neg.f64 (+.f64 (+.f64 (/.f64 1/81 (pow.f64 x 3)) (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/9 x))) (/.f64 1/243 (pow.f64 x 4))))
(+.f64 (+.f64 (+.f64 (/.f64 -1/81 (pow.f64 x 3)) (/.f64 -1/27 (*.f64 x x))) (/.f64 -1/9 x)) (/.f64 -1/243 (pow.f64 x 4)))
(+.f64 (+.f64 (/.f64 -1/27 (*.f64 x x)) (+.f64 (/.f64 -1/9 x) (/.f64 -1/81 (pow.f64 x 3)))) (/.f64 -1/243 (pow.f64 x 4)))
(+.f64 (/.f64 -1/27 (*.f64 x x)) (+.f64 (/.f64 -1/243 (pow.f64 x 4)) (+.f64 (/.f64 -1/9 x) (/.f64 -1/81 (pow.f64 x 3)))))
(/.f64 -1/9 x)
(neg.f64 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/9 (/.f64 1 x))))
(neg.f64 (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/9 x)))
(+.f64 (/.f64 -1/27 (*.f64 x x)) (/.f64 -1/9 x))
(neg.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (*.f64 1/27 (/.f64 1 (pow.f64 x 2))))))
(neg.f64 (+.f64 (/.f64 1/81 (pow.f64 x 3)) (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/9 x))))
(+.f64 (+.f64 (/.f64 -1/81 (pow.f64 x 3)) (/.f64 -1/27 (*.f64 x x))) (/.f64 -1/9 x))
(+.f64 (/.f64 -1/27 (*.f64 x x)) (+.f64 (/.f64 -1/9 x) (/.f64 -1/81 (pow.f64 x 3))))
(neg.f64 (+.f64 (.f64 1/243 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))))))
(neg.f64 (+.f64 (+.f64 (/.f64 1/81 (pow.f64 x 3)) (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/9 x))) (/.f64 1/243 (pow.f64 x 4))))
(+.f64 (+.f64 (+.f64 (/.f64 -1/81 (pow.f64 x 3)) (/.f64 -1/27 (*.f64 x x))) (/.f64 -1/9 x)) (/.f64 -1/243 (pow.f64 x 4)))
(+.f64 (+.f64 (/.f64 -1/27 (*.f64 x x)) (+.f64 (/.f64 -1/9 x) (/.f64 -1/81 (pow.f64 x 3)))) (/.f64 -1/243 (pow.f64 x 4)))
(+.f64 (/.f64 -1/27 (*.f64 x x)) (+.f64 (/.f64 -1/243 (pow.f64 x 4)) (+.f64 (/.f64 -1/9 x) (/.f64 -1/81 (pow.f64 x 3)))))

eval109.0ms (2.2%)

Compiler: Compiled 2982 to 2487 computations (16.6% saved)

prune31.0ms (0.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	251	2	253
Fresh	1	1	2
Picked	0	1	1
Done	1	2	3
Total	253	6	259

Error

Counts

259 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	33.2b	(/.f64 1/27 (+.f64 1/9 (*.f64 x -1/3)))
	29.8b	x
	0.2b	(.f64 (+.f64 3 (.f64 9 x)) 1/9)
	33.0b	1/3
✓	0.0b	(+.f64 x 1/3)
✓	33.2b	(*.f64 (/.f64 1 (-.f64 1/3 x)) 1/9)

Compiler

Compiled 32 to 27 computations (15.6% saved)

regimes26.0ms (0.5%)

Counts

16 → 1

Calls

Call 1

Inputs
1/3
1/3
x
1/3
x
1/3
(+.f64 x 1/3)
(+.f64 x (/.f64 1 3))
(.f64 (+.f64 3 (.f64 9 x)) 1/9)
(/.f64 1/27 (+.f64 1/9 (*.f64 x -1/3)))
(*.f64 (/.f64 1 (-.f64 1/3 x)) 1/9)
(/.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))
(.f64 (/.f64 1 (-.f64 1/3 x)) (-.f64 1/9 (.f64 x x)))
(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))
(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (*.f64 x -1/3)))
(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3))))

Outputs
(+.f64 x 1/3)

Calls

3 calls:

10.0ms	x
6.0ms	(+.f64 x (/.f64 1 3))
6.0ms	(+.f64 x (/.f64 1 3))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(+.f64 x (/.f64 1 3))`
0.0b	1	`(+.f64 x (/.f64 1 3))`

Compiler

Compiled 106 to 79 computations (25.5% saved)

regimes15.0ms (0.3%)

Counts

6 → 3

Calls

Call 1

Inputs
1/3
1/3
x
1/3
x
1/3

Outputs
x
1/3
x

Calls

1 calls:

13.0ms

Results

Error	Segments	Branch
1.1b	3	`x`

Compiler

Compiled 9 to 6 computations (33.3% saved)

bsearch63.0ms (1.3%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
13.0ms	1.9528963858121105e-8	1.521228129001963
50.0ms	-4279664386679.3286	-4.217355735732614e-10

Compiler

Compiled 10 to 8 computations (20% saved)

regimes4.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs
1/3
1/3

Outputs
1/3

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
33.0b	1	`x`

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	12	20

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 x 1/3)
(if (<=.f64 x -8764752663919265/2048) x (if (<=.f64 x 2951133579800441/151115727451828646838272) 1/3 x))
1/3

Outputs
(+.f64 x 1/3)
(if (<=.f64 x -8764752663919265/2048) x (if (<=.f64 x 2951133579800441/151115727451828646838272) 1/3 x))
1/3

Compiler

Compiled 18 to 13 computations (27.8% saved)

soundness7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	10	4

Stop Event

1×

saturated

Compiler

Compiled 10 to 8 computations (20% saved)

end59.0ms (1.2%)

Compiler: Compiled 16 to 11 computations (31.3% saved)

Details

analyze3.0ms (0.1%)

sample1.1s (22.4%)

preprocess33.0ms (0.7%)

simplify12.0ms (0.2%)

eval1.0ms (0%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series2.0ms (0%)

rewrite110.0ms (2.3%)

simplify13.0ms (0.3%)

eval33.0ms (0.7%)

prune11.0ms (0.2%)

localize28.0ms (0.6%)

series8.0ms (0.2%)

rewrite97.0ms (2%)

simplify83.0ms (1.7%)

localize52.0ms (1.1%)

series10.0ms (0.2%)

rewrite181.0ms (3.7%)

simplify220.0ms (4.5%)

localize9.0ms (0.2%)

series3.0ms (0.1%)

rewrite255.0ms (5.2%)

simplify100.0ms (2%)

eval1.0s (20.4%)

prune279.0ms (5.7%)

localize13.0ms (0.3%)

series2.0ms (0%)

rewrite71.0ms (1.5%)

simplify45.0ms (0.9%)

localize14.0ms (0.3%)

series23.0ms (0.5%)

rewrite86.0ms (1.7%)

simplify54.0ms (1.1%)

eval312.0ms (6.4%)

prune58.0ms (1.2%)

localize8.0ms (0.2%)

series1.0ms (0%)

rewrite51.0ms (1%)

simplify45.0ms (0.9%)

localize19.0ms (0.4%)

series1.0ms (0%)

rewrite87.0ms (1.8%)

simplify45.0ms (0.9%)

eval109.0ms (2.2%)

prune31.0ms (0.6%)

regimes26.0ms (0.5%)

regimes15.0ms (0.3%)

bsearch63.0ms (1.3%)

regimes4.0ms (0.1%)

simplify5.0ms (0.1%)

soundness7.0ms (0.2%)

end59.0ms (1.2%)

Profiling