Details

analyze61.0ms (1.4%)

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)

sample1.1s (25.6%)

Results

1.1s

8256×

body

256

valid

preprocess32.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	10	4

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 4 to 3 computations (25% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite98.0ms (2.2%)

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)))))

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	39
1	5	39

Stop Event

1×

saturated

Counts

42 → 33

Calls

Call 1

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

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

eval14.0ms (0.3%)

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

prune15.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	29	4	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	5	34

Error

Counts

34 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	20.6b	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))
	27.9b	x
	34.6b	1/3
▶	27.0b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3))))
✓	0.0b	(+.f64 x 1/3)

Compiler

Compiled 35 to 26 computations (25.7% saved)

localize25.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x -1/3))
✓	19.1b	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))

Compiler

Compiled 27 to 19 computations (29.6% saved)

series7.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

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

rewrite109.0ms (2.4%)

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	18
1	194	11
2	2374	11

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

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

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 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))))))))

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

716×	`associate-l_binary64`
680×	`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	38	220
1	99	218
2	217	216
3	529	210
4	1433	207
5	6110	207

Stop Event

1×	node limit

Counts

78 → 71

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))))

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

localize42.0ms (0.9%)

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)
✓	26.0b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3))))

Compiler

Compiled 51 to 32 computations (37.3% saved)

series10.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

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

rewrite174.0ms (3.9%)

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 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(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)))))))))

simplify207.0ms (4.6%)

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))

eval606.0ms (13.6%)

Compiler: Compiled 9394 to 6771 computations (27.9% saved)

prune413.0ms (9.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	422	4	426
Fresh	2	0	2
Picked	1	0	1
Done	1	1	2
Total	426	5	431

Error

Counts

431 → 5

Alt Table

Click to see full alt table

Status	Error	Program
	27.9b	x
	34.6b	1/3
▶	35.1b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (*.f64 x -1/3)))
▶	20.6b	(+.f64 (.f64 (/.f64 1 (+.f64 x -1/3)) (.f64 x x)) (*.f64 (/.f64 1 (+.f64 x -1/3)) -1/9))
✓	0.0b	(+.f64 x 1/3)

Compiler

Compiled 38 to 30 computations (21.1% saved)

localize18.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (+.f64 x -1/3))
✓	0.2b	(*.f64 (/.f64 1 (+.f64 x -1/3)) -1/9)
✓	19.2b	(.f64 (/.f64 1 (+.f64 x -1/3)) (.f64 x x))

Compiler

Compiled 49 to 34 computations (30.6% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite70.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

453×	`log-prod_binary64`
370×	`prod-exp_binary64`
352×	`exp-prod_binary64`
274×	`pow-prod-down_binary64`
252×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	215	17
2	2627	17

Stop Event

1×	node limit

Counts

2 → 90

Calls

Call 1

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

Outputs

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

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

simplify52.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

898×	`fma-neg_binary64`
812×	`times-frac_binary64`
675×	`fma-def_binary64`
470×	`cancel-sign-sub-inv_binary64`
269×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	58	324
1	161	312
2	451	309
3	1417	299
4	4170	299

Stop Event

1×	node limit

Counts

114 → 117

Calls

Call 1

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

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/9 (*.f64 x -1/3))
✓	0.3b	(*.f64 x -1/3)
✓	6.0b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (*.f64 x -1/3)))

Compiler

Compiled 33 to 26 computations (21.2% saved)

series3.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite243.0ms (5.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	256	23
2	3178	23

Stop Event

1×	node limit

Counts

3 → 111

Calls

Call 1

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

Outputs

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

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

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

simplify59.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

607×	`fma-def_binary64`
576×	`associate-l_binary64`
536×	`unswap-sqr_binary64`
378×	`associate-r_binary64`
321×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	252
1	79	230
2	192	226
3	512	210
4	1445	209
5	4514	209

Stop Event

1×	node limit

Counts

147 → 129

Calls

Call 1

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

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

eval136.0ms (3%)

Compiler: Compiled 5876 to 4548 computations (22.6% saved)

prune61.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	316	2	318
Fresh	1	1	2
Picked	0	1	1
Done	1	1	2
Total	318	5	323

Error

Counts

323 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	35.0b	(+.f64 (.f64 -3 (.f64 x x)) (*.f64 (/.f64 1 (+.f64 x -1/3)) -1/9))
	27.9b	x
✓	35.1b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (*.f64 x -1/3)))
	34.6b	1/3
✓	0.0b	(+.f64 x 1/3)

Compiler

Compiled 34 to 27 computations (20.6% saved)

localize33.0ms (0.7%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 42 to 29 computations (31% saved)

series60.0ms (1.3%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
58.0ms	x	@	inf	(.f64 -3 (.f64 x x))
1.0ms	x	@	0	(.f64 -3 (.f64 x x))
1.0ms	x	@	-inf	(.f64 -3 (.f64 x x))

rewrite55.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

432×	`pow1_binary64`
421×	`add-sqr-sqrt_binary64`
411×	`*-un-lft-identity_binary64`
402×	`add-log-exp_binary64`
402×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	102	7
2	1149	7

Stop Event

1×	node limit

Counts

1 → 14

Calls

Call 1

Inputs
(.f64 -3 (.f64 x x))

Outputs

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

simplify201.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
617×	`cube-prod_binary64`
554×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`
441×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	12	84
2	23	84
3	44	84
4	105	84
5	331	84
6	1250	84
7	2123	84
8	2287	84
9	2471	84
10	2679	84
11	2976	84
12	3371	84
13	3852	84
14	4418	84
15	5102	84
16	5935	84
17	6327	84
18	6619	84
19	6895	84
20	6969	84
21	7003	84
22	7944	84

Stop Event

1×	node limit

Counts

26 → 16

Calls

Call 1

Inputs
(*.f64 -3 (pow.f64 x 2))
(*.f64 -3 (pow.f64 x 2))
(*.f64 -3 (pow.f64 x 2))
(*.f64 -3 (pow.f64 x 2))
(*.f64 -3 (pow.f64 x 2))
(*.f64 -3 (pow.f64 x 2))
(*.f64 -3 (pow.f64 x 2))
(*.f64 -3 (pow.f64 x 2))
(*.f64 -3 (pow.f64 x 2))
(*.f64 -3 (pow.f64 x 2))
(*.f64 -3 (pow.f64 x 2))
(*.f64 -3 (pow.f64 x 2))

Outputs
(*.f64 -3 (pow.f64 x 2))
(.f64 -3 (.f64 x x))
(.f64 x (.f64 -3 x))
(*.f64 -3 (pow.f64 x 2))
(.f64 -3 (.f64 x x))
(.f64 x (.f64 -3 x))
(*.f64 -3 (pow.f64 x 2))
(.f64 -3 (.f64 x x))
(.f64 x (.f64 -3 x))
(*.f64 -3 (pow.f64 x 2))
(.f64 -3 (.f64 x x))
(.f64 x (.f64 -3 x))
(*.f64 -3 (pow.f64 x 2))
(.f64 -3 (.f64 x x))
(.f64 x (.f64 -3 x))
(*.f64 -3 (pow.f64 x 2))
(.f64 -3 (.f64 x x))
(.f64 x (.f64 -3 x))
(*.f64 -3 (pow.f64 x 2))
(.f64 -3 (.f64 x x))
(.f64 x (.f64 -3 x))
(*.f64 -3 (pow.f64 x 2))
(.f64 -3 (.f64 x x))
(.f64 x (.f64 -3 x))
(*.f64 -3 (pow.f64 x 2))
(.f64 -3 (.f64 x x))
(.f64 x (.f64 -3 x))
(*.f64 -3 (pow.f64 x 2))
(.f64 -3 (.f64 x x))
(.f64 x (.f64 -3 x))
(*.f64 -3 (pow.f64 x 2))
(.f64 -3 (.f64 x x))
(.f64 x (.f64 -3 x))
(*.f64 -3 (pow.f64 x 2))
(.f64 -3 (.f64 x x))
(.f64 x (.f64 -3 x))

eval206.0ms (4.6%)

Compiler: Compiled 1614 to 1178 computations (27% saved)

prune15.0ms (0.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	94	5	99

Error

Counts

99 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	35.0b	(+.f64 (.f64 -3 (.f64 x x)) (*.f64 (/.f64 1 (+.f64 x -1/3)) -1/9))
	27.9b	x
✓	35.1b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (*.f64 x -1/3)))
	34.6b	1/3
✓	0.0b	(+.f64 x 1/3)

Compiler

Compiled 34 to 27 computations (20.6% saved)

regimes21.0ms (0.5%)

Counts

12 → 1

Calls

Call 1

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

Outputs
(+.f64 x 1/3)

Calls

3 calls:

7.0ms	x
6.0ms	(+.f64 x (/.f64 1 3))
5.0ms	(+.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 94 to 69 computations (26.6% saved)

regimes14.0ms (0.3%)

Accuracy

Total -61.2b remaining (-9670.3%)

Threshold costs -61.2b (-9670.3%)

Counts

5 → 3

Calls

Call 1

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

Outputs
x
1/3
x

Calls

1 calls:

13.0ms

Results

Error	Segments	Branch
0.6b	3	`x`

Compiler

Compiled 8 to 5 computations (37.5% saved)

bsearch98.0ms (2.2%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
51.0ms	5.297661538558788e-13	144435.38971176354
48.0ms	-121844.2349791302	-3.2803432052842904e-18

Compiler

Compiled 10 to 8 computations (20% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	12	20

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 x 1/3)
(if (<=.f64 x -8373072071064055/68719476736) x (if (<=.f64 x 5246549866531291/9903520314283042199192993792) 1/3 x))
1/3

Outputs
(+.f64 x 1/3)
(if (<=.f64 x -8373072071064055/68719476736) x (if (<=.f64 x 5246549866531291/9903520314283042199192993792) 1/3 x))
1/3

Compiler

Compiled 18 to 13 computations (27.8% saved)

soundness10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	10	4

Stop Event

1×

saturated

Compiler

Compiled 10 to 8 computations (20% saved)

end23.0ms (0.5%)

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

Details

analyze61.0ms (1.4%)

sample1.1s (25.6%)

preprocess32.0ms (0.7%)

simplify12.0ms (0.3%)

eval1.0ms (0%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series2.0ms (0%)

rewrite98.0ms (2.2%)

simplify14.0ms (0.3%)

eval14.0ms (0.3%)

prune15.0ms (0.3%)

localize25.0ms (0.6%)

series7.0ms (0.2%)

rewrite109.0ms (2.4%)

simplify71.0ms (1.6%)

localize42.0ms (0.9%)

series10.0ms (0.2%)

rewrite174.0ms (3.9%)

simplify207.0ms (4.6%)

eval606.0ms (13.6%)

prune413.0ms (9.2%)

localize18.0ms (0.4%)

series3.0ms (0.1%)

rewrite70.0ms (1.6%)

simplify52.0ms (1.2%)

localize15.0ms (0.3%)

series3.0ms (0.1%)

rewrite243.0ms (5.4%)

simplify59.0ms (1.3%)

eval136.0ms (3%)

prune61.0ms (1.4%)

localize33.0ms (0.7%)

series60.0ms (1.3%)

rewrite55.0ms (1.2%)

simplify201.0ms (4.5%)

eval206.0ms (4.6%)

prune15.0ms (0.3%)

regimes21.0ms (0.5%)

regimes14.0ms (0.3%)

bsearch98.0ms (2.2%)

simplify5.0ms (0.1%)

soundness10.0ms (0.2%)

end23.0ms (0.5%)

Profiling