Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample888.0ms (27.1%)

Results

876.0ms

8256×

body

256

valid

Bogosity

preprocess21.0ms (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)

prune3.0ms (0.1%)

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 1 expressions with local error:

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite47.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

Inputs
(+.f64 x 1/3)

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

Outputs

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

simplify8.0ms (0.2%)

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)

eval37.0ms (1.1%)

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

prune6.0ms (0.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

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

Error

Counts

34 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	13.6b	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))
✓	0.0b	(+.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))))
▶	0.5b	(-.f64 (+.f64 1 (+.f64 x 1/3)) 1)
	33.0b	x
	30.6b	1/3

Compiler

Compiled 43 to 33 computations (23.3% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x -1/3)
✓	0.0b	(fma.f64 x x -1/9)
✓	0.0b	(/.f64 1 (+.f64 x -1/3))
✓	12.7b	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))

Compiler

Compiled 27 to 19 computations (29.6% saved)

series6.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

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

rewrite72.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	194	20
2	2374	20

Stop Event

1×	node limit

Counts

4 → 115

Calls

Call 1

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

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

simplify115.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

719×	`associate-l_binary64`
709×	`fma-neg_binary64`
614×	`associate-/r*_binary64`
585×	`distribute-rgt-neg-in_binary64`
557×	`fma-def_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	42	331
1	107	311
2	229	309
3	546	303
4	1453	300
5	6136	300

Stop Event

1×	node limit

Counts

163 → 140

Calls

Call 1

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

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

localize53.0ms (1.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
	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)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite89.0ms (2.7%)

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	10
1	168	4
2	2419	4

Stop Event

1×	node limit

Counts

1 → 53

Calls

Call 1

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

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

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	39
1	5	39

Stop Event

1×

saturated

Counts

65 → 55

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)

localize24.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x x) (.f64 x 1/3))
✓	0.0b	(+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3)))
✓	0.3b	(*.f64 x 1/3)
✓	17.4b	(/.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)

series6.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

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

rewrite162.0ms (5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 342

Calls

Call 1

Inputs
(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3))))
(*.f64 x 1/3)
(+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3)))
(-.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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fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (+.f64 x -1/3)) (fma.f64 (neg.f64 (cbrt.f64 (.f64 x 1/3))) (pow.f64 (cbrt.f64 (.f64 x 1/3)) 2) (.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (+.f64 x -1/3)) (.f64 (fma.f64 x -1/3 (.f64 x 1/3)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (.f64 (sqrt.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 fma.f64 (sqrt.f64 (.f64 x 1/3)) (neg.f64 (sqrt.f64 (.f64 x 1/3))) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 -1/3 x (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 x 6) (.f64 -1/27 (pow.f64 x 3))) (/.f64 1 (fma.f64 (.f64 x 1/3) (.f64 x (+.f64 x 1/3)) (pow.f64 x 4))) (fma.f64 x -1/3 (.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 x 6) (.f64 -1/27 (pow.f64 x 3))) (/.f64 1 (fma.f64 (.f64 x 1/3) (.f64 x (+.f64 x 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(#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x (sqrt.f64 (.f64 x 1/3))) (-.f64 x (sqrt.f64 (.f64 x 1/3))) (fma.f64 (neg.f64 (cbrt.f64 (.f64 x 1/3))) (pow.f64 (cbrt.f64 (.f64 x 1/3)) 2) (.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x (sqrt.f64 (.f64 x 1/3))) (-.f64 x (sqrt.f64 (.f64 x 1/3))) (.f64 (fma.f64 x -1/3 (.f64 x 1/3)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 x (sqrt.f64 (.f64 x 1/3))) (-.f64 x (sqrt.f64 (.f64 x 1/3))) (+.f64 (fma.f64 x -1/3 (.f64 x 1/3)) (fma.f64 x -1/3 (.f64 x 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (neg.f64 (pow.f64 (cbrt.f64 (.f64 x 1/3)) 2)) (cbrt.f64 (.f64 x 1/3)) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 x -1/3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (.f64 (.f64 x -1/3) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (fma.f64 x -1/3 (fma.f64 x -1/3 (.f64 x 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (neg.f64 (-.f64 (.f64 x 1/3) (fma.f64 x -1/3 (*.f64 x 1/3)))))))))

simplify208.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	269
1	26	250
2	48	238
3	84	238
4	169	238
5	425	238
6	1318	238
7	2553	238
8	2947	238
9	3139	238
10	3349	238
11	3663	238
12	4069	238
13	4554	238
14	5126	238
15	5822	238
16	6668	238
17	7060	238
18	7346	238
19	7628	238
20	7702	238
21	7738	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)
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)))
(*.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))

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

eval425.0ms (13%)

Compiler: Compiled 11349 to 8248 computations (27.3% saved)

prune126.0ms (3.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	578	5	583
Fresh	2	0	2
Picked	1	0	1
Done	2	1	3
Total	583	6	589

Error

Counts

589 → 6

Alt Table

Click to see full alt table

Status	Error	Program
	30.6b	1/3
▶	18.1b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (*.f64 (+.f64 x -1/3) x)))
▶	0.5b	(+.f64 (+.f64 x 4/3) -1)
	33.0b	x
▶	30.4b	(*.f64 -1/9 (/.f64 1 (+.f64 x -1/3)))
✓	0.0b	(+.f64 x 1/3)

Compiler

Compiled 36 to 29 computations (19.4% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 20 to 16 computations (20% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite53.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

795×	`pow1_binary64`
744×	`add-log-exp_binary64`
744×	`log1p-expm1-u_binary64`
744×	`expm1-log1p-u_binary64`
732×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	7
1	173	7
2	2023	7

Stop Event

1×	node limit

Counts

1 → 16

Calls

Call 1

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

Outputs

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

simplify48.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

28 → 29

Calls

Call 1

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

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

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x 4/3)
✓	0.5b	(+.f64 (+.f64 x 4/3) -1)

Compiler

Compiled 12 to 9 computations (25% saved)

series4.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(+.f64 x 4/3)
0.0ms	x	@	0	(+.f64 (+.f64 x 4/3) -1)
0.0ms	x	@	-inf	(+.f64 x 4/3)
0.0ms	x	@	0	(+.f64 x 4/3)
0.0ms	x	@	inf	(+.f64 (+.f64 x 4/3) -1)

rewrite62.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

766×	`pow1_binary64`
722×	`add-log-exp_binary64`
722×	`log1p-expm1-u_binary64`
722×	`expm1-log1p-u_binary64`
712×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	139	8
2	1819	8

Stop Event

1×	node limit

Counts

2 → 66

Calls

Call 1

Inputs
(+.f64 (+.f64 x 4/3) -1)
(+.f64 x 4/3)

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 (pow.f64 (+.f64 x 4/3) 2) (+.f64 x 7/3)) (/.f64 1 (+.f64 x 7/3)))))) (#(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 (pow.f64 (+.f64 x 4/3) 3)) (/.f64 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 (pow.f64 (+.f64 x 4/3) 2) -1) (/.f64 1 (+.f64 x 7/3)))))) (#(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 (+.f64 (pow.f64 (+.f64 x 4/3) 2) (-.f64 1 (*.f64 (+.f64 x 4/3) -1))) (+.f64 -1 (pow.f64 (+.f64 x 4/3) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 x 7/3) (+.f64 (pow.f64 (+.f64 x 4/3) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (pow.f64 (+.f64 x 4/3) 3)) (+.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 (pow.f64 (+.f64 x 4/3) 3)) (+.f64 1 (-.f64 (pow.f64 (+.f64 x 4/3) 2) (*.f64 (+.f64 x 4/3) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (+.f64 x 4/3) 2) -1) (+.f64 x 7/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 -1 (pow.f64 (+.f64 x 4/3) 3))) (neg.f64 (+.f64 (pow.f64 (+.f64 x 4/3) 2) (-.f64 1 (*.f64 (+.f64 x 4/3) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 x 4/3) 2) -1)) (neg.f64 (+.f64 x 7/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 3) 1/27) (+.f64 (*.f64 x x) (-.f64 1/9 (*.f64 x 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 x x) 1/9) (-.f64 x 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 x 4/3) 2)) (-.f64 -1 (+.f64 x 4/3)))))) (#(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 expm1.f64 (log1p.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.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 (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 (sqrt.f64 x) (sqrt.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 -.f64 (+.f64 1 (+.f64 x 4/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (*.f64 x x) (+.f64 x -4/3)) (/.f64 16/9 (+.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 1 (+.f64 x 4/3))))) (#(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 (sqrt.f64 (+.f64 x 4/3)) (sqrt.f64 (+.f64 x 4/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 64/27 (pow.f64 x 3)) (/.f64 1 (fma.f64 x x (-.f64 16/9 (*.f64 x 4/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x x -16/9) (/.f64 1 (+.f64 x -4/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x (-.f64 16/9 (*.f64 x 4/3))) (+.f64 64/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 x -4/3) (fma.f64 x x -16/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 64/27 (pow.f64 x 3)) (fma.f64 x x (-.f64 16/9 (*.f64 x 4/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 64/27 (pow.f64 x 3)) (+.f64 16/9 (-.f64 (*.f64 x x) (*.f64 x 4/3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 x x -16/9) (+.f64 x -4/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 64/27 (pow.f64 x 3))) (neg.f64 (fma.f64 x x (-.f64 16/9 (*.f64 x 4/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 x x -16/9)) (neg.f64 (+.f64 x -4/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 16/9 (*.f64 x x)) (-.f64 4/3 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 expm1.f64 (log1p.f64 (+.f64 x 4/3)))))) (#(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 fma.f64 1 x 4/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) 4/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) 4/3)))))

simplify11.0ms (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

90 → 72

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)

localize20.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 x -1/3)
✓	0.0b	(+.f64 1/9 (*.f64 (+.f64 x -1/3) x))
✓	0.2b	(*.f64 (+.f64 x -1/3) x)
✓	17.4b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (*.f64 (+.f64 x -1/3) x)))

Compiler

Compiled 42 to 31 computations (26.2% saved)

series4.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite93.0ms (2.9%)

Algorithm

1×	batch-egg-rewrite

Rules

577×	`log-prod_binary64`
342×	`pow2_binary64`
309×	`fma-def_binary64`
293×	`prod-diff_binary64`
236×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	285	32
2	3665	32

Stop Event

1×	node limit

Counts

3 → 127

Calls

Call 1

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

Outputs

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

simplify189.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	221
1	24	202
2	46	190
3	78	190
4	151	190
5	362	190
6	1123	190
7	2354	190
8	2748	190
9	2940	190
10	3150	190
11	3462	190
12	3872	190
13	4357	190
14	4929	190
15	5619	190
16	6465	190
17	6860	190
18	7146	190
19	7422	190
20	7498	190
21	7532	190

Stop Event

1×	node limit

Counts

163 → 140

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

eval156.0ms (4.8%)

Compiler: Compiled 5127 to 4050 computations (21% saved)

prune83.0ms (2.5%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	351	2	353
Fresh	2	0	2
Picked	0	1	1
Done	0	3	3
Total	353	6	359

Error

Counts

359 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(+.f64 (+.f64 x 4/3) -1)
	33.0b	x
✓	30.4b	(*.f64 -1/9 (/.f64 1 (+.f64 x -1/3)))
✓	18.1b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (*.f64 (+.f64 x -1/3) x)))
✓	0.0b	(+.f64 x 1/3)
	30.6b	1/3

Compiler

Compiled 36 to 29 computations (19.4% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune5.0ms (0.2%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	0	0
Done	4	4
Total	6	6

Error

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(+.f64 (+.f64 x 4/3) -1)
	33.0b	x
✓	30.4b	(*.f64 -1/9 (/.f64 1 (+.f64 x -1/3)))
✓	18.1b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (*.f64 (+.f64 x -1/3) x)))
✓	0.0b	(+.f64 x 1/3)
	30.6b	1/3

Compiler

Compiled 36 to 29 computations (19.4% saved)

regimes45.0ms (1.4%)

Counts

14 → 1

Calls

Call 1

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

Outputs
(+.f64 x 1/3)

Calls

3 calls:

16.0ms	x
10.0ms	(+.f64 x (/.f64 1 3))
10.0ms	(+.f64 x (/.f64 1 3))

Results

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

Compiler

Compiled 86 to 65 computations (24.4% saved)

regimes31.0ms (0.9%)

Accuracy

Total -59.7b remaining (-3041.9%)

Threshold costs -59.7b (-3041.9%)

Counts

6 → 3

Calls

Call 1

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

Outputs
x
1/3
x

Calls

1 calls:

29.0ms

Results

Error	Segments	Branch
2.0b	3	`x`

Compiler

Compiled 9 to 5 computations (44.4% saved)

bsearch49.0ms (1.5%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
24.0ms	0.13137983386600421	4.597083892091637
25.0ms	-59635613030762.45	-5.203651412372695e-5

Compiler

Compiled 10 to 8 computations (20% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	12	20

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 x 1/3)
(if (<=.f64 x -3816679233968797/64) x (if (<=.f64 x 2366728683371737/18014398509481984) 1/3 x))
x

Outputs
(+.f64 x 1/3)
(if (<=.f64 x -3816679233968797/64) x (if (<=.f64 x 2366728683371737/18014398509481984) 1/3 x))
x

Compiler

Compiled 18 to 12 computations (33.3% saved)

soundness13.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	10	4

Stop Event

1×

saturated

Compiler

Compiled 10 to 8 computations (20% saved)

end43.0ms (1.3%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

Details

analyze3.0ms (0.1%)

sample888.0ms (27.1%)

preprocess21.0ms (0.6%)

simplify7.0ms (0.2%)

eval1.0ms (0%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series1.0ms (0%)

rewrite47.0ms (1.4%)

simplify8.0ms (0.2%)

eval37.0ms (1.1%)

prune6.0ms (0.2%)

localize15.0ms (0.4%)

series6.0ms (0.2%)

rewrite72.0ms (2.2%)

simplify115.0ms (3.5%)

localize53.0ms (1.6%)

series1.0ms (0%)

rewrite89.0ms (2.7%)

simplify9.0ms (0.3%)

localize24.0ms (0.7%)

series6.0ms (0.2%)

rewrite162.0ms (5%)

simplify208.0ms (6.4%)

eval425.0ms (13%)

prune126.0ms (3.9%)

localize10.0ms (0.3%)

series1.0ms (0%)

rewrite53.0ms (1.6%)

simplify48.0ms (1.5%)

localize5.0ms (0.2%)

series4.0ms (0.1%)

rewrite62.0ms (1.9%)

simplify11.0ms (0.3%)

localize20.0ms (0.6%)

series4.0ms (0.1%)

rewrite93.0ms (2.9%)

simplify189.0ms (5.8%)

eval156.0ms (4.8%)

prune83.0ms (2.5%)

eval0.0ms (0%)

prune5.0ms (0.2%)

regimes45.0ms (1.4%)

regimes31.0ms (0.9%)

bsearch49.0ms (1.5%)

simplify7.0ms (0.2%)

soundness13.0ms (0.4%)

end43.0ms (1.3%)

Profiling