Details

analyze5.0ms (0.2%)

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
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample687.0ms (28.6%)

Results

673.0ms

8256×

body

128

valid

preprocess17.0ms (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 6 to 5 computations (16.7% saved)

simplify6.0ms (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 (0.1%)

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 8 to 6 computations (25% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

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)

rewrite59.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

473×	`pow1_binary64`
446×	`add-log-exp_binary64`
446×	`log1p-expm1-u_binary64`
446×	`expm1-log1p-u_binary64`
439×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	91	4
2	1149	4

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

Inputs
(+.f64 x 1/3)

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

Outputs

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

simplify7.0ms (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)

eval7.0ms (0.3%)

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

prune29.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	30	3	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	4	34

Error

Counts

34 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 x 1/3)
	17.4b	(pow.f64 (sqrt.f64 (+.f64 x 1/3)) 2)
▶	15.8b	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))
	27.1b	(pow.f64 (pow.f64 (+.f64 x 1/3) 3) 1/3)

Compiler

Compiled 56 to 45 computations (19.6% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x -1/9)
✓	0.0b	(+.f64 x -1/3)
✓	0.0b	(/.f64 1 (+.f64 x -1/3))
✓	14.8b	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))

series8.0ms (0.3%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(/.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	@	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)))

rewrite51.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

848×	`log1p-expm1-u_binary64`
848×	`expm1-log1p-u_binary64`
94×	`add-sqr-sqrt_binary64`
88×	`add-cbrt-cube_binary64`
88×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	194	20
2	2356	20

Stop Event

1×	node limit

Counts

4 → 124

Calls

Call 1

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

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

simplify26.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

718×	`associate-l_binary64`
596×	`associate-/r*_binary64`
563×	`fma-def_binary64`
255×	`associate-/l/_binary64`
192×	`fma-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	42	331
1	107	311
2	229	309
3	544	303
4	1400	300

Stop Event

1×	node limit

Counts

172 → 149

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

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

eval46.0ms (1.9%)

Compiler: Compiled 1979 to 1441 computations (27.2% saved)

prune281.0ms (11.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	148	5	153

Error

Counts

153 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 x 1/3)
▶	15.8b	(/.f64 1 (/.f64 (+.f64 x -1/3) (fma.f64 x x -1/9)))
✓	15.8b	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))
	17.4b	(pow.f64 (sqrt.f64 (+.f64 x 1/3)) 2)
	15.8b	(.f64 (fma.f64 x x -1/9) (.f64 (/.f64 1 (fma.f64 x x -1/9)) (+.f64 x 1/3)))

Compiler

Compiled 83 to 61 computations (26.5% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x x -1/9)
	0.0b	(+.f64 x -1/3)
✓	0.1b	(/.f64 1 (/.f64 (+.f64 x -1/3) (fma.f64 x x -1/9)))
✓	14.7b	(/.f64 (+.f64 x -1/3) (fma.f64 x x -1/9))

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite48.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

409×	`log-prod_binary64`
235×	`pow2_binary64`
164×	`expm1-udef_binary64`
164×	`log1p-udef_binary64`
163×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	199	11
2	2555	11

Stop Event

1×	node limit

Counts

2 → 95

Calls

Call 1

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

Outputs

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

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

simplify25.0ms (1%)

Algorithm

1×	egg-herbie

Rules

718×	`fma-def_binary64`
415×	`times-frac_binary64`
285×	`associate-/l/_binary64`
275×	`associate-*r/_binary64`
240×	`associate-*l/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	36	220
1	96	216
2	234	216
3	639	210
4	1856	207

Stop Event

1×	node limit

Counts

119 → 112

Calls

Call 1

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

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

eval59.0ms (2.5%)

Compiler: Compiled 2430 to 1842 computations (24.2% saved)

prune378.0ms (15.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	185	5	190

Error

Counts

190 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 x 1/3)
✓	15.8b	(/.f64 1 (/.f64 (+.f64 x -1/3) (fma.f64 x x -1/9)))
✓	15.8b	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))
	17.4b	(pow.f64 (sqrt.f64 (+.f64 x 1/3)) 2)
▶	15.8b	(.f64 (fma.f64 x x -1/9) (.f64 (/.f64 1 (fma.f64 x x -1/9)) (+.f64 x 1/3)))

Compiler

Compiled 72 to 53 computations (26.4% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 x 1/3)
✓	0.4b	(/.f64 1 (fma.f64 x x -1/9))
✓	14.3b	(*.f64 (/.f64 1 (fma.f64 x x -1/9)) (+.f64 x 1/3))
✓	14.8b	(.f64 (fma.f64 x x -1/9) (.f64 (/.f64 1 (fma.f64 x x -1/9)) (+.f64 x 1/3)))

series4.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

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

rewrite54.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

422×	`log-prod_binary64`
218×	`prod-diff_binary64`
164×	`expm1-udef_binary64`
164×	`log1p-udef_binary64`
128×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	220	19
2	2848	19

Stop Event

1×	node limit

Counts

3 → 140

Calls

Call 1

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

Outputs

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

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

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

simplify36.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

847×	`times-frac_binary64`
589×	`fma-neg_binary64`
522×	`fma-def_binary64`
431×	`associate-l_binary64`
431×	`associate-/r*_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	66	434
1	172	430
2	387	426
3	1030	420
4	3923	419

Stop Event

1×	node limit

Counts

176 → 171

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))))
-9
(-.f64 (*.f64 -81 (pow.f64 x 2)) 9)
(-.f64 (+.f64 (.f64 -81 (pow.f64 x 2)) (.f64 -729 (pow.f64 x 4))) 9)
(-.f64 (+.f64 (.f64 -81 (pow.f64 x 2)) (+.f64 (.f64 -6561 (pow.f64 x 6)) (*.f64 -729 (pow.f64 x 4)))) 9)
(/.f64 1 (pow.f64 x 2))
(+.f64 (*.f64 1/9 (/.f64 1 (pow.f64 x 4))) (/.f64 1 (pow.f64 x 2)))
(+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 6))) (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 x 4))) (/.f64 1 (pow.f64 x 2))))
(+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 6))) (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 x 4))) (+.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/729 (/.f64 1 (pow.f64 x 8))))))
(/.f64 1 (pow.f64 x 2))
(+.f64 (*.f64 1/9 (/.f64 1 (pow.f64 x 4))) (/.f64 1 (pow.f64 x 2)))
(+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 6))) (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 x 4))) (/.f64 1 (pow.f64 x 2))))
(+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 6))) (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 x 4))) (+.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/729 (/.f64 1 (pow.f64 x 8))))))

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 -81 (pow.f64 x 3) (.f64 x (.f64 x -27))) (fma.f64 x -9 -3))
(fma.f64 x -9 (fma.f64 x (*.f64 x -27) (fma.f64 -81 (pow.f64 x 3) -3)))
(fma.f64 x (fma.f64 x -27 -9) (fma.f64 -81 (pow.f64 x 3) -3))
(fma.f64 x (+.f64 -9 (*.f64 x (fma.f64 x -81 -27))) -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 (/.f64 1 x) (/.f64 1/9 (pow.f64 x 3))) (+.f64 (/.f64 1/3 (*.f64 x x)) (/.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 x) (+.f64 (/.f64 1/27 (pow.f64 x 4)) (+.f64 (/.f64 1/3 (*.f64 x x)) (/.f64 1/9 (pow.f64 x 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 (/.f64 1 x) (/.f64 1/9 (pow.f64 x 3))) (+.f64 (/.f64 1/3 (*.f64 x x)) (/.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 x) (+.f64 (/.f64 1/27 (pow.f64 x 4)) (+.f64 (/.f64 1/3 (*.f64 x x)) (/.f64 1/9 (pow.f64 x 3)))))
-9
(-.f64 (*.f64 -81 (pow.f64 x 2)) 9)
(fma.f64 -81 (*.f64 x x) -9)
(fma.f64 (*.f64 x x) -81 -9)
(fma.f64 x (*.f64 x -81) -9)
(-.f64 (+.f64 (.f64 -81 (pow.f64 x 2)) (.f64 -729 (pow.f64 x 4))) 9)
(+.f64 (fma.f64 -81 (.f64 x x) (.f64 (pow.f64 x 4) -729)) -9)
(fma.f64 (*.f64 x x) -81 (fma.f64 (pow.f64 x 4) -729 -9))
(fma.f64 x (*.f64 x -81) (fma.f64 (pow.f64 x 4) -729 -9))
(-.f64 (+.f64 (.f64 -81 (pow.f64 x 2)) (+.f64 (.f64 -6561 (pow.f64 x 6)) (*.f64 -729 (pow.f64 x 4)))) 9)
(+.f64 (fma.f64 -81 (.f64 x x) (fma.f64 -6561 (pow.f64 x 6) (.f64 (pow.f64 x 4) -729))) -9)
(+.f64 -9 (fma.f64 (.f64 x x) -81 (fma.f64 -6561 (pow.f64 x 6) (.f64 (pow.f64 x 4) -729))))
(fma.f64 x (*.f64 x -81) (fma.f64 (pow.f64 x 4) -729 (fma.f64 -6561 (pow.f64 x 6) -9)))
(fma.f64 x (*.f64 x -81) (fma.f64 -6561 (pow.f64 x 6) (fma.f64 (pow.f64 x 4) -729 -9)))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 (/.f64 1 x) x)
(+.f64 (*.f64 1/9 (/.f64 1 (pow.f64 x 4))) (/.f64 1 (pow.f64 x 2)))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/9 (pow.f64 x 4)))
(+.f64 (/.f64 (/.f64 1 x) x) (/.f64 1/9 (pow.f64 x 4)))
(+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 6))) (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 x 4))) (/.f64 1 (pow.f64 x 2))))
(+.f64 (+.f64 (/.f64 1/81 (pow.f64 x 6)) (/.f64 1/9 (pow.f64 x 4))) (/.f64 1 (*.f64 x x)))
(+.f64 (/.f64 1/9 (pow.f64 x 4)) (+.f64 (/.f64 (/.f64 1 x) x) (/.f64 1/81 (pow.f64 x 6))))
(+.f64 (/.f64 1/9 (pow.f64 x 4)) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/81 (pow.f64 x 6))))
(+.f64 (/.f64 (/.f64 1 x) x) (+.f64 (/.f64 1/9 (pow.f64 x 4)) (/.f64 1/81 (pow.f64 x 6))))
(+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 6))) (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 x 4))) (+.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/729 (/.f64 1 (pow.f64 x 8))))))
(+.f64 (/.f64 1/81 (pow.f64 x 6)) (+.f64 (/.f64 1/9 (pow.f64 x 4)) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/729 (pow.f64 x 8)))))
(+.f64 (/.f64 1/9 (pow.f64 x 4)) (+.f64 (+.f64 (/.f64 (/.f64 1 x) x) (/.f64 1/729 (pow.f64 x 8))) (/.f64 1/81 (pow.f64 x 6))))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1/9 (pow.f64 x 4)) (+.f64 (/.f64 1/81 (pow.f64 x 6)) (/.f64 1/729 (pow.f64 x 8)))))
(+.f64 (+.f64 (/.f64 (/.f64 1 x) x) (/.f64 1/729 (pow.f64 x 8))) (+.f64 (/.f64 1/9 (pow.f64 x 4)) (/.f64 1/81 (pow.f64 x 6))))
(/.f64 1 (pow.f64 x 2))
(/.f64 1 (*.f64 x x))
(/.f64 (/.f64 1 x) x)
(+.f64 (*.f64 1/9 (/.f64 1 (pow.f64 x 4))) (/.f64 1 (pow.f64 x 2)))
(+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/9 (pow.f64 x 4)))
(+.f64 (/.f64 (/.f64 1 x) x) (/.f64 1/9 (pow.f64 x 4)))
(+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 6))) (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 x 4))) (/.f64 1 (pow.f64 x 2))))
(+.f64 (+.f64 (/.f64 1/81 (pow.f64 x 6)) (/.f64 1/9 (pow.f64 x 4))) (/.f64 1 (*.f64 x x)))
(+.f64 (/.f64 1/9 (pow.f64 x 4)) (+.f64 (/.f64 (/.f64 1 x) x) (/.f64 1/81 (pow.f64 x 6))))
(+.f64 (/.f64 1/9 (pow.f64 x 4)) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/81 (pow.f64 x 6))))
(+.f64 (/.f64 (/.f64 1 x) x) (+.f64 (/.f64 1/9 (pow.f64 x 4)) (/.f64 1/81 (pow.f64 x 6))))
(+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 6))) (+.f64 (.f64 1/9 (/.f64 1 (pow.f64 x 4))) (+.f64 (/.f64 1 (pow.f64 x 2)) (*.f64 1/729 (/.f64 1 (pow.f64 x 8))))))
(+.f64 (/.f64 1/81 (pow.f64 x 6)) (+.f64 (/.f64 1/9 (pow.f64 x 4)) (+.f64 (/.f64 1 (*.f64 x x)) (/.f64 1/729 (pow.f64 x 8)))))
(+.f64 (/.f64 1/9 (pow.f64 x 4)) (+.f64 (+.f64 (/.f64 (/.f64 1 x) x) (/.f64 1/729 (pow.f64 x 8))) (/.f64 1/81 (pow.f64 x 6))))
(+.f64 (/.f64 1 (*.f64 x x)) (+.f64 (/.f64 1/9 (pow.f64 x 4)) (+.f64 (/.f64 1/81 (pow.f64 x 6)) (/.f64 1/729 (pow.f64 x 8)))))
(+.f64 (+.f64 (/.f64 (/.f64 1 x) x) (/.f64 1/729 (pow.f64 x 8))) (+.f64 (/.f64 1/9 (pow.f64 x 4)) (/.f64 1/81 (pow.f64 x 6))))

eval84.0ms (3.5%)

Compiler: Compiled 3716 to 2579 computations (30.6% saved)

prune431.0ms (17.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	1	0	1
Picked	1	0	1
Done	0	3	3
Total	205	4	209

Error

Counts

209 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	15.8b	(/.f64 1 (/.f64 (+.f64 x -1/3) (fma.f64 x x -1/9)))
	15.8b	(*.f64 (fma.f64 x x -1/9) (fma.f64 (/.f64 1 (fma.f64 x x -1/9)) 1/3 (/.f64 x (fma.f64 x x -1/9))))
✓	0.0b	(+.f64 x 1/3)
✓	15.8b	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))

Compiler

Compiled 46 to 32 computations (30.4% saved)

regimes15.0ms (0.6%)

Accuracy

Total -27.1b remaining (-173631.9%)

Threshold costs -27.1b (-173631.9%)

Counts

10 → 1

Calls

Call 1

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

Outputs
(+.f64 x 1/3)

Results

Time	Error	Segments	Branch
7.0ms	0.0b	1	`x`
5.0ms	0.0b	1	`(+.f64 x (/.f64 1 3))`

Compiler

Compiled 96 to 70 computations (27.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	5	4

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 x 1/3)

Outputs
(+.f64 x 1/3)

end11.0ms (0.5%)

Stop Event

1×

fuel

Compiler

Compiled 8 to 6 computations (25% saved)

Details

analyze5.0ms (0.2%)

sample687.0ms (28.6%)

preprocess17.0ms (0.7%)

simplify6.0ms (0.3%)

eval1.0ms (0%)

prune2.0ms (0.1%)

localize2.0ms (0.1%)

series1.0ms (0%)

rewrite59.0ms (2.5%)

simplify7.0ms (0.3%)

eval7.0ms (0.3%)

prune29.0ms (1.2%)

localize6.0ms (0.2%)

series8.0ms (0.3%)

rewrite51.0ms (2.1%)

simplify26.0ms (1.1%)

eval46.0ms (1.9%)

prune281.0ms (11.7%)

localize6.0ms (0.2%)

series2.0ms (0.1%)

rewrite48.0ms (2%)

simplify25.0ms (1%)

eval59.0ms (2.5%)

prune378.0ms (15.7%)

localize9.0ms (0.4%)

series4.0ms (0.2%)

rewrite54.0ms (2.2%)

simplify36.0ms (1.5%)

eval84.0ms (3.5%)

prune431.0ms (17.9%)

regimes15.0ms (0.6%)

simplify2.0ms (0.1%)

end11.0ms (0.5%)

Profiling