Details

analyze3.0ms (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)

sample624.0ms (47.6%)

Results

613.0ms

8256×

body

128

valid

Compiler

Compiled 14 to 12 computations (14.3% saved)

preprocess16.0ms (1.3%)

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 (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	10	4

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

prune2.0ms (0.2%)

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

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

Compiler

Compiled 17 to 13 computations (23.5% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series1.0ms (0.1%)

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)

rewrite33.0ms (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 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 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 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 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 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 expm1.f64 (log1p.f64 (+.f64 x 1/3)))))))

simplify7.0ms (0.5%)

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)

prune18.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	31	2	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	31	3	34

Error

Counts

34 → 3

Alt Table

Status	Error	Program
	17.6b	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))
▶	17.5b	(-.f64 (/.f64 (*.f64 x x) (+.f64 x -1/3)) (/.f64 1/9 (+.f64 x -1/3)))
✓	0.0b	(+.f64 x 1/3)

Compiler

Compiled 319 to 235 computations (26.3% saved)

localize9.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (*.f64 x x) (+.f64 x -1/3)) (/.f64 1/9 (+.f64 x -1/3)))
✓	0.0b	(+.f64 x -1/3)
✓	0.2b	(/.f64 1/9 (+.f64 x -1/3))
✓	16.4b	(/.f64 (*.f64 x x) (+.f64 x -1/3))

series6.0ms (0.5%)

Counts

4 → 48

Calls

12 calls:

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

rewrite81.0ms (6.2%)

Algorithm

1×	batch-egg-rewrite

Rules

435×	`fma-def_binary64`
266×	`fma-neg_binary64`
192×	`expm1-udef_binary64`
192×	`log1p-udef_binary64`
184×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	34
1	221	25
2	3405	25

Stop Event

1×	node limit

Counts

4 → 279

Calls

Call 1

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

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

simplify32.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

798×	`fma-neg_binary64`
451×	`cancel-sign-sub-inv_binary64`
361×	`associate-l_binary64`
258×	`associate-r_binary64`
249×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	404
1	174	396
2	490	389
3	1675	385

Stop Event

1×	node limit

Counts

327 → 310

Calls

Call 1

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

prune233.0ms (17.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	347	0	347
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	347	3	350

Error

Counts

350 → 3

Alt Table

Status	Error	Program
▶	17.6b	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))
✓	17.5b	(-.f64 (/.f64 (*.f64 x x) (+.f64 x -1/3)) (/.f64 1/9 (+.f64 x -1/3)))
✓	0.0b	(+.f64 x 1/3)

Compiler

Compiled 6929 to 5026 computations (27.5% saved)

localize6.0ms (0.4%)

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))
✓	16.4b	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))

series4.0ms (0.3%)

Counts

3 → 36

Calls

9 calls:

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

rewrite57.0ms (4.3%)

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	23
1	194	16
2	2356	16

Stop Event

1×	node limit

Counts

3 → 87

Calls

Call 1

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

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 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 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 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 -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)))))))

simplify31.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

599×	`associate-/r*_binary64`
405×	`fma-def_binary64`
273×	`distribute-rgt-neg-in_binary64`
254×	`associate-/l/_binary64`
241×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	42	300
1	109	276
2	282	272
3	847	267
4	2744	267

Stop Event

1×	node limit

Counts

123 → 109

Calls

Call 1

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

prune72.0ms (5.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Error

Counts

149 → 3

Alt Table

Status	Error	Program
✓	17.6b	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x -1/3)))
✓	17.5b	(-.f64 (/.f64 (*.f64 x x) (+.f64 x -1/3)) (/.f64 1/9 (+.f64 x -1/3)))
✓	0.0b	(+.f64 x 1/3)

Compiler

Compiled 1975 to 1433 computations (27.4% saved)

regimes23.0ms (1.8%)

Accuracy

Total 0.0b remaining (70%)

Threshold costs 0.0b (70%)

Counts

13 → 1

Compiler

Compiled 120 to 88 computations (26.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	9	17

Stop Event

1×

saturated

Calls

Call 1

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

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

end43.0ms (3.2%)

Stop Event

1×

done

Compiler

Compiled 55 to 39 computations (29.1% saved)

Details

analyze3.0ms (0.2%)

sample624.0ms (47.6%)

preprocess16.0ms (1.3%)

simplify6.0ms (0.4%)

prune2.0ms (0.2%)

localize2.0ms (0.1%)

series1.0ms (0.1%)

rewrite33.0ms (2.5%)

simplify7.0ms (0.5%)

prune18.0ms (1.4%)

localize9.0ms (0.7%)

series6.0ms (0.5%)

rewrite81.0ms (6.2%)

simplify32.0ms (2.4%)

prune233.0ms (17.8%)

localize6.0ms (0.4%)

series4.0ms (0.3%)

rewrite57.0ms (4.3%)

simplify31.0ms (2.4%)

prune72.0ms (5.5%)

regimes23.0ms (1.8%)

simplify2.0ms (0.1%)

end43.0ms (3.2%)

Profiling