Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample965.0ms (28.2%)

Results

952.0ms

8256×

body

256

valid

preprocess20.0ms (0.6%)

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)

simplify7.0ms (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)

prune1.0ms (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)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

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

rewrite37.0ms (1.1%)

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	1149	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 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 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 expm1.f64 (log1p.f64 (+.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 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 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 expm1.f64 (log1p.f64 (+.f64 x 1/3)))))))

simplify33.0ms (1%)

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)

eval8.0ms (0.2%)

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

prune14.0ms (0.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	26	7	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	8	34

Error

Counts

34 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 x 1/3)
▶	12.5b	(/.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))
▶	0.5b	(-.f64 (+.f64 1 (+.f64 x 1/3)) 1)
	30.1b	1/3
▶	18.8b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3))))
▶	12.6b	(/.f64 1 (/.f64 (+.f64 x -1/3) (fma.f64 x x -1/9)))
▶	18.8b	(.f64 (+.f64 1/27 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x (-.f64 1/9 (.f64 x 1/3)))))
	33.9b	x

Compiler

Compiled 132 to 100 computations (24.2% saved)

localize9.0ms (0.2%)

Local error

Found 6 expressions with local error:

New	Error	Program
	0.5b	(-.f64 (+.f64 1 (+.f64 x 1/3)) 1)
	0.0b	(+.f64 x 1/3)
	0.0b	(+.f64 1 (+.f64 x 1/3))
✓	0.0b	(+.f64 1 (+.f64 x 1/3))
	0.0b	(+.f64 x 1/3)
✓	0.5b	(-.f64 (+.f64 1 (+.f64 x 1/3)) 1)

Compiler

Compiled 19 to 15 computations (21.1% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite69.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

877×	`pow1_binary64`
831×	`add-log-exp_binary64`
830×	`log1p-expm1-u_binary64`
830×	`expm1-log1p-u_binary64`
820×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	168	8
2	2331	8

Stop Event

1×	node limit

Counts

2 → 89

Calls

Call 1

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

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 x -2/3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (*.f64 (+.f64 x -2/3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 x 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1/3 x)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x 1/3) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x 4/3) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 x 4/3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 x -2/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 x) -2/3)))) (#(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 (pow.f64 (+.f64 x 4/3) 3) -1) (/.f64 1 (+.f64 (pow.f64 (+.f64 x 4/3) 2) (+.f64 1 (+.f64 x 4/3)))))))) (#(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 (+.f64 (pow.f64 (+.f64 x 4/3) 2) -1) (/.f64 1 (+.f64 1 (+.f64 x 4/3))))))) (#(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 (+.f64 (sqrt.f64 (+.f64 x 4/3)) 1) (-.f64 (sqrt.f64 (+.f64 x 4/3)) 1))))) (#(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 1 (/.f64 (+.f64 (pow.f64 (+.f64 x 4/3) 2) (+.f64 1 (+.f64 x 4/3))) (+.f64 (pow.f64 (+.f64 x 4/3) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (+.f64 x 4/3)) (+.f64 (pow.f64 (+.f64 x 4/3) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x 4/3) 3) -1) (+.f64 (pow.f64 (+.f64 x 4/3) 2) (+.f64 1 (+.f64 x 4/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x 4/3) 3) -1) (+.f64 (pow.f64 (+.f64 x 4/3) 2) (-.f64 1 (*.f64 (+.f64 x 4/3) -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 (+.f64 (pow.f64 (+.f64 x 4/3) 2) -1) (+.f64 1 (+.f64 x 4/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x 4/3) 2) -1) (-.f64 (+.f64 x 4/3) -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 (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 (neg.f64 (+.f64 (pow.f64 (+.f64 x 4/3) 3) -1)) (neg.f64 (+.f64 (pow.f64 (+.f64 x 4/3) 2) (+.f64 1 (+.f64 x 4/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 x 4/3) 2) -1)) (neg.f64 (+.f64 1 (+.f64 x 4/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 x -2/3) 3)) (+.f64 1 (-.f64 (*.f64 (+.f64 x -2/3) (+.f64 x -2/3)) (+.f64 x -2/3))))))) (#(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 /.f64 (-.f64 1 (*.f64 (+.f64 x -2/3) (+.f64 x -2/3))) (-.f64 1 (+.f64 x -2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x 1/3) 1)))) (#(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 (pow.f64 (+.f64 x 1/3) 3) 1/3)))) (#(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 fma.f64 1 x 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 x 4/3) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x 4/3)) 2) (cbrt.f64 (+.f64 x 4/3)) -1)))) (#(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 (+.f64 x 4/3)) (sqrt.f64 (+.f64 x 4/3)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.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 expm1.f64 (log.f64 (+.f64 x 4/3)))))))

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

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	78
1	8	78

Stop Event

1×

saturated

Counts

113 → 94

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)
4/3
(+.f64 4/3 x)
(+.f64 4/3 x)
(+.f64 4/3 x)
x
(+.f64 4/3 x)
(+.f64 4/3 x)
(+.f64 4/3 x)
x
(+.f64 4/3 x)
(+.f64 4/3 x)
(+.f64 4/3 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)
4/3
(+.f64 4/3 x)
(+.f64 x 4/3)
(+.f64 4/3 x)
(+.f64 x 4/3)
(+.f64 4/3 x)
(+.f64 x 4/3)
x
(+.f64 4/3 x)
(+.f64 x 4/3)
(+.f64 4/3 x)
(+.f64 x 4/3)
(+.f64 4/3 x)
(+.f64 x 4/3)
x
(+.f64 4/3 x)
(+.f64 x 4/3)
(+.f64 4/3 x)
(+.f64 x 4/3)
(+.f64 4/3 x)
(+.f64 x 4/3)

localize13.0ms (0.4%)

Local error

Found 6 expressions with local error:

New	Error	Program
	11.6b	(/.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))
	0.0b	(-.f64 1/3 x)
	0.0b	(-.f64 1/9 (*.f64 x x))
✓	0.0b	(-.f64 1/9 (*.f64 x x))
✓	0.0b	(-.f64 1/3 x)
✓	11.6b	(/.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))
1.0ms	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))

rewrite234.0ms (6.8%)

Algorithm

1×	batch-egg-rewrite

Rules

617×	`unpow-prod-down_binary64`
431×	`log-prod_binary64`
251×	`prod-diff_binary64`
244×	`pow2_binary64`
239×	`pow-prod-down_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	192	15
2	2717	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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(#(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 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)))) (#(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 (*.f64 3 (log.f64 (-.f64 1/9 (*.f64 x x)))) 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 expm1.f64 (log1p.f64 (-.f64 1/9 (*.f64 x x))))))))

simplify95.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

671×	`distribute-lft-neg-in_binary64`
666×	`distribute-rgt-neg-in_binary64`
465×	`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	182	158
5	504	158
6	1666	158
7	3489	158
8	4815	158
9	6132	158
10	6943	158
11	7989	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))

localize18.0ms (0.5%)

Local error

Found 8 expressions with local error:

New	Error	Program
	11.7b	(/.f64 (+.f64 x -1/3) (fma.f64 x x -1/9))
	0.1b	(/.f64 1 (/.f64 (+.f64 x -1/3) (fma.f64 x x -1/9)))
	0.0b	(+.f64 x -1/3)
	0.0b	(fma.f64 x x -1/9)
✓	0.0b	(fma.f64 x x -1/9)
✓	0.0b	(+.f64 x -1/3)
✓	0.1b	(/.f64 1 (/.f64 (+.f64 x -1/3) (fma.f64 x x -1/9)))
✓	11.7b	(/.f64 (+.f64 x -1/3) (fma.f64 x x -1/9))

Compiler

Compiled 30 to 20 computations (33.3% saved)

series5.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

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

rewrite70.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

409×	`log-prod_binary64`
327×	`exp-prod_binary64`
291×	`prod-exp_binary64`
274×	`cbrt-unprod_binary64`
244×	`pow-prod-down_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	34
1	199	20
2	2555	20

Stop Event

1×	node limit

Counts

4 → 205

Calls

Call 1

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

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

simplify67.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

761×	`distribute-neg-frac_binary64`
740×	`associate-l_binary64`
718×	`fma-def_binary64`
457×	`associate-r_binary64`
415×	`times-frac_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	331
1	102	309
2	244	309
3	651	303
4	1870	300
5	7149	300

Stop Event

1×	node limit

Counts

253 → 230

Calls

Call 1

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

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

localize23.0ms (0.7%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.4b	(*.f64 x 1/3)
	0.0b	(-.f64 (.f64 x x) (.f64 x 1/3))
	0.0b	(+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3)))
	0.0b	(+.f64 1/27 (pow.f64 x 3))
✓	0.0b	(+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3)))
✓	0.0b	(-.f64 (.f64 x x) (.f64 x 1/3))
✓	0.4b	(*.f64 x 1/3)
✓	18.1b	(/.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)

series5.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

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

rewrite129.0ms (3.8%)

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	4200	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
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x (+.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 (+.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 (+.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 (+.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 (+.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 (+.f64 x -1/3) 1/9))) (pow.f64 (cbrt.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x (+.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 (+.f64 x -1/3) 1/9))) 2) (cbrt.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x (+.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 (+.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 (+.f64 x -1/3) 1/9))) (sqrt.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x (+.f64 x -1/3) 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 -1/27 (neg.f64 (pow.f64 x 3))) (/.f64 1 (neg.f64 (fma.f64 x (+.f64 x -1/3) 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (fma.f64 x (+.f64 x -1/3) 1/9)) (+.f64 1/27 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 1/27 (pow.f64 x 3))) 2) 1) (/.f64 (cbrt.f64 (+.f64 1/27 (pow.f64 x 3))) (fma.f64 x (+.f64 x -1/3) 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (+.f64 1/27 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((#(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 (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 1/27 (pow.f64 x 3)) 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 1/27 (pow.f64 x 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 expm1.f64 (log1p.f64 (.f64 x 1/3)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x x) (.f64 x -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x x) (.f64 (.f64 x -1/3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x x) (fma.f64 x -1/3 (fma.f64 x -1/3 (.f64 x 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (+.f64 x -1/3)) (fma.f64 x -1/3 (.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (+.f64 x -1/3)) (fma.f64 (.f64 x -1/3) 1 (.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (+.f64 x -1/3)) (fma.f64 (neg.f64 (cbrt.f64 (.f64 x 1/3))) (cbrt.f64 (.f64 1/9 (.f64 x x))) (.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (+.f64 x -1/3)) (.f64 (fma.f64 x -1/3 (.f64 x 1/3)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x (+.f64 x -1/3)) (+.f64 (fma.f64 x -1/3 (.f64 x 1/3)) (fma.f64 x -1/3 (.f64 x 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 x -1/3 (.f64 x 1/3)) (.f64 x (+.f64 x 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simplify174.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

1105×	`sqr-pow_binary64`
652×	`fma-def_binary64`
561×	`cube-prod_binary64`
553×	`fabs-mul_binary64`
536×	`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	165	238
5	416	238
6	1294	238
7	2536	238
8	2930	238
9	3122	238
10	3332	238
11	3628	238
12	4034	238
13	4514	238
14	5083	238
15	5777	238
16	6621	238
17	7017	238
18	7303	238
19	7579	238
20	7655	238
21	7689	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)

localize25.0ms (0.7%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.3b	(/.f64 1 (fma.f64 x x (-.f64 1/9 (*.f64 x 1/3))))
	0.0b	(-.f64 1/9 (*.f64 x 1/3))
	0.0b	(+.f64 1/27 (pow.f64 x 3))
	0.0b	(fma.f64 x x (-.f64 1/9 (*.f64 x 1/3)))
✓	0.0b	(-.f64 1/9 (*.f64 x 1/3))
✓	0.3b	(/.f64 1 (fma.f64 x x (-.f64 1/9 (*.f64 x 1/3))))
	0.4b	(*.f64 x 1/3)
✓	18.1b	(.f64 (+.f64 1/27 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x (-.f64 1/9 (.f64 x 1/3)))))

Compiler

Compiled 57 to 42 computations (26.3% saved)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/.f64 1 (fma.f64 x x (-.f64 1/9 (*.f64 x 1/3))))
0.0ms	x	@	0	(.f64 (+.f64 1/27 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x (-.f64 1/9 (.f64 x 1/3)))))
0.0ms	x	@	inf	(.f64 (+.f64 1/27 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x (-.f64 1/9 (.f64 x 1/3)))))
0.0ms	x	@	-inf	(/.f64 1 (fma.f64 x x (-.f64 1/9 (*.f64 x 1/3))))
0.0ms	x	@	-inf	(.f64 (+.f64 1/27 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x (-.f64 1/9 (.f64 x 1/3)))))

rewrite106.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

605×	`log-prod_binary64`
376×	`prod-diff_binary64`
351×	`pow2_binary64`
242×	`pow1/3_binary64`
242×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	41
1	310	41
2	3735	35

Stop Event

1×	node limit

Counts

3 → 129

Calls

Call 1

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

Outputs

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

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

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

simplify48.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

565×	`associate-*r/_binary64`
547×	`associate-*l/_binary64`
492×	`unswap-sqr_binary64`
331×	`distribute-neg-frac_binary64`
294×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	45	318
1	110	298
2	270	294
3	747	294
4	2641	294
5	7431	294

Stop Event

1×	node limit

Counts

165 → 151

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)
9
(+.f64 9 (*.f64 27 x))
(+.f64 9 (+.f64 (.f64 27 x) (.f64 -243 (pow.f64 x 3))))
(+.f64 9 (+.f64 (.f64 -729 (pow.f64 x 4)) (+.f64 (.f64 27 x) (*.f64 -243 (pow.f64 x 3)))))
(/.f64 1 (pow.f64 x 2))
(+.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/3 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))) (.f64 1/27 (/.f64 1 (pow.f64 x 5))))
(-.f64 (+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 6))) (*.f64 1/27 (/.f64 1 (pow.f64 x 5)))))
(/.f64 1 (pow.f64 x 2))
(+.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/3 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))) (.f64 1/27 (/.f64 1 (pow.f64 x 5))))
(-.f64 (+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 6))) (*.f64 1/27 (/.f64 1 (pow.f64 x 5)))))
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))

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)
9
(+.f64 9 (*.f64 27 x))
(+.f64 9 (*.f64 x 27))
(fma.f64 x 27 9)
(+.f64 9 (+.f64 (.f64 27 x) (.f64 -243 (pow.f64 x 3))))
(+.f64 9 (fma.f64 27 x (*.f64 -243 (pow.f64 x 3))))
(+.f64 9 (fma.f64 x 27 (*.f64 -243 (pow.f64 x 3))))
(fma.f64 x 27 (fma.f64 -243 (pow.f64 x 3) 9))
(+.f64 9 (+.f64 (.f64 -729 (pow.f64 x 4)) (+.f64 (.f64 27 x) (*.f64 -243 (pow.f64 x 3)))))
(+.f64 9 (fma.f64 -729 (pow.f64 x 4) (fma.f64 27 x (*.f64 -243 (pow.f64 x 3)))))
(+.f64 9 (fma.f64 -729 (pow.f64 x 4) (fma.f64 x 27 (*.f64 -243 (pow.f64 x 3)))))
(fma.f64 -729 (pow.f64 x 4) (fma.f64 x 27 (fma.f64 -243 (pow.f64 x 3) 9)))
(fma.f64 x 27 (fma.f64 -243 (pow.f64 x 3) (fma.f64 -729 (pow.f64 x 4) 9)))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 (/.f64 1 x) x)
(+.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/3 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/3 (pow.f64 x 3)))
(+.f64 (/.f64 (/.f64 1 x) x) (/.f64 1/3 (pow.f64 x 3)))
(-.f64 (+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))) (.f64 1/27 (/.f64 1 (pow.f64 x 5))))
(+.f64 (/.f64 1/3 (pow.f64 x 3)) (-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/27 (pow.f64 x 5))))
(+.f64 (/.f64 (/.f64 1 x) x) (-.f64 (/.f64 1/3 (pow.f64 x 3)) (/.f64 1/27 (pow.f64 x 5))))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1/3 (pow.f64 x 3)) (/.f64 -1/27 (pow.f64 x 5))))
(-.f64 (+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 6))) (*.f64 1/27 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/3 (pow.f64 x 3))) (+.f64 (/.f64 1/27 (pow.f64 x 5)) (/.f64 1/81 (pow.f64 x 6))))
(+.f64 (+.f64 (/.f64 (/.f64 1 x) x) (-.f64 (/.f64 1/3 (pow.f64 x 3)) (/.f64 1/81 (pow.f64 x 6)))) (/.f64 -1/27 (pow.f64 x 5)))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (-.f64 (/.f64 1/3 (pow.f64 x 3)) (/.f64 1/81 (pow.f64 x 6))) (/.f64 -1/27 (pow.f64 x 5))))
(+.f64 (/.f64 1 (*.f64 x x)) (-.f64 (/.f64 1/3 (pow.f64 x 3)) (+.f64 (/.f64 1/27 (pow.f64 x 5)) (/.f64 1/81 (pow.f64 x 6)))))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1/3 (pow.f64 x 3)) (+.f64 (/.f64 -1/27 (pow.f64 x 5)) (/.f64 -1/81 (pow.f64 x 6)))))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 (/.f64 1 x) x)
(+.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/3 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/3 (pow.f64 x 3)))
(+.f64 (/.f64 (/.f64 1 x) x) (/.f64 1/3 (pow.f64 x 3)))
(-.f64 (+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))) (.f64 1/27 (/.f64 1 (pow.f64 x 5))))
(+.f64 (/.f64 1/3 (pow.f64 x 3)) (-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/27 (pow.f64 x 5))))
(+.f64 (/.f64 (/.f64 1 x) x) (-.f64 (/.f64 1/3 (pow.f64 x 3)) (/.f64 1/27 (pow.f64 x 5))))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1/3 (pow.f64 x 3)) (/.f64 -1/27 (pow.f64 x 5))))
(-.f64 (+.f64 (.f64 1/3 (/.f64 1 (pow.f64 x 3))) (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 6))) (*.f64 1/27 (/.f64 1 (pow.f64 x 5)))))
(-.f64 (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/3 (pow.f64 x 3))) (+.f64 (/.f64 1/27 (pow.f64 x 5)) (/.f64 1/81 (pow.f64 x 6))))
(+.f64 (+.f64 (/.f64 (/.f64 1 x) x) (-.f64 (/.f64 1/3 (pow.f64 x 3)) (/.f64 1/81 (pow.f64 x 6)))) (/.f64 -1/27 (pow.f64 x 5)))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (-.f64 (/.f64 1/3 (pow.f64 x 3)) (/.f64 1/81 (pow.f64 x 6))) (/.f64 -1/27 (pow.f64 x 5))))
(+.f64 (/.f64 1 (*.f64 x x)) (-.f64 (/.f64 1/3 (pow.f64 x 3)) (+.f64 (/.f64 1/27 (pow.f64 x 5)) (/.f64 1/81 (pow.f64 x 6)))))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1/3 (pow.f64 x 3)) (+.f64 (/.f64 -1/27 (pow.f64 x 5)) (/.f64 -1/81 (pow.f64 x 6)))))
1/9
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 1/9 (*.f64 x -1/3))
(fma.f64 x -1/3 1/9)
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 1/9 (*.f64 x -1/3))
(fma.f64 x -1/3 1/9)
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 1/9 (*.f64 x -1/3))
(fma.f64 x -1/3 1/9)
(*.f64 -1/3 x)
(*.f64 x -1/3)
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 1/9 (*.f64 x -1/3))
(fma.f64 x -1/3 1/9)
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 1/9 (*.f64 x -1/3))
(fma.f64 x -1/3 1/9)
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 1/9 (*.f64 x -1/3))
(fma.f64 x -1/3 1/9)
(*.f64 -1/3 x)
(*.f64 x -1/3)
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 1/9 (*.f64 x -1/3))
(fma.f64 x -1/3 1/9)
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 1/9 (*.f64 x -1/3))
(fma.f64 x -1/3 1/9)
(+.f64 1/9 (*.f64 -1/3 x))
(+.f64 1/9 (*.f64 x -1/3))
(fma.f64 x -1/3 1/9)

eval664.0ms (19.4%)

Compiler: Compiled 23629 to 17068 computations (27.8% saved)

prune145.0ms (4.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	1162	4	1166
Fresh	2	0	2
Picked	1	0	1
Done	3	2	5
Total	1168	6	1174

Error

Counts

1174 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 x 1/3)
✓	12.5b	(/.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))
▶	30.1b	(/.f64 1 (/.f64 (+.f64 x -1/3) -1/9))
▶	0.5b	(+.f64 1 (+.f64 x -2/3))
	33.9b	x
	30.1b	1/3

Compiler

Compiled 32 to 25 computations (21.9% saved)

localize5.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(+.f64 1 (+.f64 x -2/3))
	0.0b	(+.f64 x -2/3)
✓	0.0b	(+.f64 x -2/3)
✓	0.5b	(+.f64 1 (+.f64 x -2/3))

Compiler

Compiled 12 to 9 computations (25% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(+.f64 1 (+.f64 x -2/3))
0.0ms	x	@	-inf	(+.f64 1 (+.f64 x -2/3))
0.0ms	x	@	0	(+.f64 x -2/3)
0.0ms	x	@	-inf	(+.f64 x -2/3)
0.0ms	x	@	inf	(+.f64 1 (+.f64 x -2/3))

rewrite53.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

731×	`pow1_binary64`
690×	`add-log-exp_binary64`
689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
680×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	135	8
2	1773	8

Stop Event

1×	node limit

Counts

2 → 62

Calls

Call 1

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

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 1 (-.f64 5/3 x)) (/.f64 (pow.f64 (+.f64 x -2/3) 2) (-.f64 5/3 x)))))) (#(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 (pow.f64 (+.f64 x -2/3) 3)) (/.f64 1 (+.f64 1 (-.f64 (pow.f64 (+.f64 x -2/3) 2) (+.f64 x -2/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (+.f64 x -2/3) 2)) (/.f64 1 (-.f64 5/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (-.f64 (pow.f64 (+.f64 x -2/3) 2) (+.f64 x -2/3))) (+.f64 1 (pow.f64 (+.f64 x -2/3) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 5/3 x) (-.f64 1 (pow.f64 (+.f64 x -2/3) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 x -2/3) 3)) (+.f64 1 (-.f64 (pow.f64 (+.f64 x -2/3) 2) (+.f64 x -2/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 x -2/3) 3)) (+.f64 (pow.f64 (+.f64 x -2/3) 2) (-.f64 5/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 x -2/3) 2)) (-.f64 5/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 x -2/3) 3))) (neg.f64 (+.f64 1 (-.f64 (pow.f64 (+.f64 x -2/3) 2) (+.f64 x -2/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (+.f64 x -2/3) 2))) (neg.f64 (-.f64 5/3 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 1 x) 3) -8/27) (+.f64 (*.f64 (+.f64 1 x) (+.f64 1 x)) (-.f64 4/9 (*.f64 (+.f64 1 x) -2/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x -2/3) 2) 1) (-.f64 (+.f64 x -2/3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 1 x) (+.f64 1 x)) 4/9) (-.f64 (+.f64 1 x) -2/3))))) (#(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 fma.f64 1 (+.f64 x -2/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 x -2/3)) 2) (cbrt.f64 (+.f64 x -2/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 x -2/3)) (sqrt.f64 (+.f64 x -2/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log1p.f64 (+.f64 x -2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.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 (/.f64 (*.f64 x x) (+.f64 x 2/3)) (/.f64 4/9 (+.f64 x 2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 x -2/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x -2/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 x -2/3)) (pow.f64 (cbrt.f64 (+.f64 x -2/3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 x -2/3)) 2) (cbrt.f64 (+.f64 x -2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 x -2/3)) (sqrt.f64 (+.f64 x -2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -8/27 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x (-.f64 4/9 (*.f64 x -2/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x x -4/9) (/.f64 1 (+.f64 x 2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (-.f64 4/9 (*.f64 x -2/3))) (+.f64 -8/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 x 2/3) (fma.f64 x x -4/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -8/27 (pow.f64 x 3)) (fma.f64 x x (-.f64 4/9 (*.f64 x -2/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -8/27 (pow.f64 x 3)) (+.f64 4/9 (-.f64 (*.f64 x x) (*.f64 x -2/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 x x -4/9) (+.f64 x 2/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 -8/27 (pow.f64 x 3))) (neg.f64 (fma.f64 x x (-.f64 4/9 (*.f64 x -2/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 x x -4/9)) (neg.f64 (+.f64 x 2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 4/9 (*.f64 x x)) (-.f64 -2/3 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x -2/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x -2/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x -2/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x -2/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x -2/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x -2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x -2/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x -2/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) -2/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) -2/3)))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x -2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x -2/3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x -2/3)))))))

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	78
1	10	78
2	11	78

Stop Event

1×

saturated

Counts

86 → 68

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)
-2/3
(-.f64 x 2/3)
(-.f64 x 2/3)
(-.f64 x 2/3)
x
(-.f64 x 2/3)
(-.f64 x 2/3)
(-.f64 x 2/3)
x
(-.f64 x 2/3)
(-.f64 x 2/3)
(-.f64 x 2/3)

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)
-2/3
(-.f64 x 2/3)
(+.f64 x -2/3)
(-.f64 x 2/3)
(+.f64 x -2/3)
(-.f64 x 2/3)
(+.f64 x -2/3)
x
(-.f64 x 2/3)
(+.f64 x -2/3)
(-.f64 x 2/3)
(+.f64 x -2/3)
(-.f64 x 2/3)
(+.f64 x -2/3)
x
(-.f64 x 2/3)
(+.f64 x -2/3)
(-.f64 x 2/3)
(+.f64 x -2/3)
(-.f64 x 2/3)
(+.f64 x -2/3)

localize9.0ms (0.3%)

Local error

Found 6 expressions with local error:

New	Error	Program
	0.2b	(/.f64 (+.f64 x -1/3) -1/9)
	0.1b	(/.f64 1 (/.f64 (+.f64 x -1/3) -1/9))
	0.0b	(+.f64 x -1/3)
	0.0b	(+.f64 x -1/3)
✓	0.1b	(/.f64 1 (/.f64 (+.f64 x -1/3) -1/9))
✓	0.2b	(/.f64 (+.f64 x -1/3) -1/9)

Compiler

Compiled 20 to 16 computations (20% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite50.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

848×	`pow1_binary64`
798×	`add-log-exp_binary64`
798×	`log1p-expm1-u_binary64`
798×	`expm1-log1p-u_binary64`
785×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	180	14
2	2198	14

Stop Event

1×	node limit

Counts

2 → 48

Calls

Call 1

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

Outputs

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

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

simplify33.0ms (1%)

Algorithm

1×	egg-herbie

Rules

898×	`fma-neg_binary64`
810×	`times-frac_binary64`
464×	`associate-*l/_binary64`
456×	`cancel-sign-sub-inv_binary64`
408×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	240
1	114	228
2	316	228
3	977	224
4	2909	224

Stop Event

1×	node limit

Counts

72 → 67

Calls

Call 1

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

eval61.0ms (1.8%)

Compiler: Compiled 2060 to 1703 computations (17.3% saved)

prune24.0ms (0.7%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	1	1	2
Picked	0	1	1
Done	0	3	3
Total	186	7	193

Error

Counts

193 → 7

Alt Table

Click to see full alt table

Status	Error	Program
	33.9b	x
✓	30.1b	(/.f64 1 (/.f64 (+.f64 x -1/3) -1/9))
✓	0.0b	(+.f64 x 1/3)
✓	12.5b	(/.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))
✓	0.5b	(+.f64 1 (+.f64 x -2/3))
	30.1b	1/3
▶	30.5b	(+.f64 1 -2/3)

Compiler

Compiled 36 to 29 computations (19.4% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	1.0b	(+.f64 1 -2/3)
✓	1.0b	(+.f64 1 -2/3)

Compiler

Compiled 6 to 6 computations (0% saved)

series0.0ms (0%)

Counts: 1 → 0

rewrite68.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

629×	`prod-diff_binary64`
414×	`log1p-udef_binary64`
256×	`add-sqr-sqrt_binary64`
251×	`pow1_binary64`
244×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	1
1	76	1
2	655	1
3	6115	1

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

Inputs
(+.f64 1 -2/3)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x . 1/3)))))

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

Inputs

Outputs

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune3.0ms (0.1%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	2	2
Picked	0	1	1
Done	0	4	4
Total	1	7	8

Error

Counts

8 → 7

Alt Table

Click to see full alt table

Status	Error	Program
	33.9b	x
✓	30.1b	(/.f64 1 (/.f64 (+.f64 x -1/3) -1/9))
✓	0.0b	(+.f64 x 1/3)
✓	12.5b	(/.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))
✓	0.5b	(+.f64 1 (+.f64 x -2/3))
	30.1b	1/3
✓	30.5b	(+.f64 1 -2/3)

Compiler

Compiled 36 to 29 computations (19.4% saved)

regimes7.0ms (0.2%)

Counts

7 → 1

Calls

Call 1

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

Outputs
(+.f64 x 1/3)

Calls

1 calls:

5.0ms

Results

Error	Segments	Branch
0.0b	1	`x`

Compiler

Compiled 32 to 24 computations (25% saved)

regimes11.0ms (0.3%)

Accuracy

Total -59.5b remaining (-2659.8%)

Threshold costs -59.5b (-2659.8%)

Counts

3 → 3

Calls

Call 1

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

Outputs
x
1/3
x

Calls

1 calls:

10.0ms

Results

Error	Segments	Branch
2.2b	3	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

bsearch28.0ms (0.8%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
14.0ms	0.020906970886639117	0.39211478482209317
14.0ms	-4.405786177188472	-0.001343051659460351

Compiler

Compiled 10 to 8 computations (20% saved)

simplify3.0ms (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×

saturated

Calls

Call 1

Inputs
(+.f64 x 1/3)
(if (<=.f64 x -4960474246465021/1125899906842624) x (if (<=.f64 x 385665541302328256/18446744073709551616) 1/3 x))
1/3

Outputs
(+.f64 x 1/3)
(if (<=.f64 x -4960474246465021/1125899906842624) x (if (<=.f64 x 385665541302328256/18446744073709551616) 1/3 x))
(if (<=.f64 x -4960474246465021/1125899906842624) x (if (<=.f64 x 6026024082848879/288230376151711744) 1/3 x))
1/3

end32.0ms (0.9%)

Stop Event

1×

fuel

Compiler

Compiled 34 to 24 computations (29.4% saved)

Details

analyze3.0ms (0.1%)

sample965.0ms (28.2%)

preprocess20.0ms (0.6%)

simplify7.0ms (0.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize3.0ms (0.1%)

series2.0ms (0.1%)

rewrite37.0ms (1.1%)

simplify33.0ms (1%)

eval8.0ms (0.2%)

prune14.0ms (0.4%)

localize9.0ms (0.2%)

series2.0ms (0%)

rewrite69.0ms (2%)

simplify9.0ms (0.3%)

localize13.0ms (0.4%)

series3.0ms (0.1%)

rewrite234.0ms (6.8%)

simplify95.0ms (2.8%)

localize18.0ms (0.5%)

series5.0ms (0.2%)

rewrite70.0ms (2%)

simplify67.0ms (1.9%)

localize23.0ms (0.7%)

series5.0ms (0.2%)

rewrite129.0ms (3.8%)

simplify174.0ms (5.1%)

localize25.0ms (0.7%)

series4.0ms (0.1%)

rewrite106.0ms (3.1%)

simplify48.0ms (1.4%)

eval664.0ms (19.4%)

prune145.0ms (4.2%)

localize5.0ms (0.2%)

series2.0ms (0%)

rewrite53.0ms (1.6%)

simplify10.0ms (0.3%)

localize9.0ms (0.3%)

series3.0ms (0.1%)

rewrite50.0ms (1.5%)

simplify33.0ms (1%)

eval61.0ms (1.8%)

prune24.0ms (0.7%)

localize3.0ms (0.1%)

series0.0ms (0%)

rewrite68.0ms (2%)

simplify6.0ms (0.2%)

eval0.0ms (0%)

prune3.0ms (0.1%)

regimes7.0ms (0.2%)

regimes11.0ms (0.3%)

bsearch28.0ms (0.8%)

simplify3.0ms (0.1%)

end32.0ms (0.9%)

Profiling