Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample727.0ms (33.9%)

Results

710.0ms

8256×

body

256

valid

preprocess19.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	12	4
2	13	4
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	12	4
2	13	4

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 4 to 3 computations (25% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

series4.0ms (0.2%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(+.f64 x -1/3)
0.0ms	x	@	inf	(+.f64 x -1/3)
0.0ms	x	@	-inf	(+.f64 x -1/3)

rewrite46.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	91	4
2	1151	4

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

Inputs
(+.f64 x -1/3)

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

Outputs

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

simplify11.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	39
1	7	39
2	8	39

Stop Event

1×

saturated

Counts

42 → 34

Calls

Call 1

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

Outputs
-1/3
(-.f64 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)

eval8.0ms (0.4%)

Compiler: Compiled 268 to 198 computations (26.1% saved)

prune10.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	29	5	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	6	35

Error

Counts

35 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(-.f64 (+.f64 1 (+.f64 x -1/3)) 1)
	30.7b	x
	33.1b	-1/3
▶	15.3b	(/.f64 1 (/.f64 (+.f64 x 1/3) (fma.f64 x x -1/9)))
▶	32.8b	(log.f64 (exp.f64 (+.f64 x -1/3)))
✓	0.0b	(+.f64 x -1/3)

Compiler

Compiled 33 to 26 computations (21.2% saved)

localize11.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 x -1/3)
✓	0.0b	(exp.f64 (+.f64 x -1/3))
✓	1.0b	(log.f64 (exp.f64 (+.f64 x -1/3)))

Compiler

Compiled 15 to 11 computations (26.7% saved)

series3.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

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

rewrite71.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

545×	`pow1_binary64`
511×	`add-log-exp_binary64`
511×	`log1p-expm1-u_binary64`
511×	`expm1-log1p-u_binary64`
502×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	115	10
2	1346	10

Stop Event

1×	node limit

Counts

2 → 55

Calls

Call 1

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

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

Outputs

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

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

simplify91.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

693×	`times-frac_binary64`
552×	`fma-def_binary64`
516×	`unsub-neg_binary64`
466×	`associate-r_binary64`
379×	`distribute-rgt-neg-out_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	159
1	78	157
2	184	149
3	640	139
4	2699	138
5	7376	138

Stop Event

1×	node limit

Counts

79 → 68

Calls

Call 1

Inputs
-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)
(exp.f64 -1/3)
(+.f64 (exp.f64 -1/3) (*.f64 (exp.f64 -1/3) x))
(+.f64 (exp.f64 -1/3) (+.f64 (.f64 1/2 (.f64 (exp.f64 -1/3) (pow.f64 x 2))) (*.f64 (exp.f64 -1/3) x)))
(+.f64 (exp.f64 -1/3) (+.f64 (.f64 1/2 (.f64 (exp.f64 -1/3) (pow.f64 x 2))) (+.f64 (.f64 (exp.f64 -1/3) x) (.f64 1/6 (*.f64 (exp.f64 -1/3) (pow.f64 x 3))))))
(exp.f64 (-.f64 x 1/3))
(exp.f64 (-.f64 x 1/3))
(exp.f64 (-.f64 x 1/3))
(exp.f64 (-.f64 x 1/3))
(exp.f64 (neg.f64 (+.f64 1/3 (*.f64 -1 x))))
(exp.f64 (neg.f64 (+.f64 1/3 (*.f64 -1 x))))
(exp.f64 (neg.f64 (+.f64 1/3 (*.f64 -1 x))))
(exp.f64 (neg.f64 (+.f64 1/3 (*.f64 -1 x))))

Outputs
-1/3
(-.f64 x 1/3)
(+.f64 x -1/3)
(+.f64 -1/3 x)
(-.f64 x 1/3)
(+.f64 x -1/3)
(+.f64 -1/3 x)
(-.f64 x 1/3)
(+.f64 x -1/3)
(+.f64 -1/3 x)
x
(-.f64 x 1/3)
(+.f64 x -1/3)
(+.f64 -1/3 x)
(-.f64 x 1/3)
(+.f64 x -1/3)
(+.f64 -1/3 x)
(-.f64 x 1/3)
(+.f64 x -1/3)
(+.f64 -1/3 x)
x
(-.f64 x 1/3)
(+.f64 x -1/3)
(+.f64 -1/3 x)
(-.f64 x 1/3)
(+.f64 x -1/3)
(+.f64 -1/3 x)
(-.f64 x 1/3)
(+.f64 x -1/3)
(+.f64 -1/3 x)
(exp.f64 -1/3)
(+.f64 (exp.f64 -1/3) (*.f64 (exp.f64 -1/3) x))
(+.f64 (exp.f64 -1/3) (*.f64 x (exp.f64 -1/3)))
(fma.f64 x (exp.f64 -1/3) (exp.f64 -1/3))
(*.f64 (exp.f64 -1/3) (+.f64 x 1))
(+.f64 (exp.f64 -1/3) (+.f64 (.f64 1/2 (.f64 (exp.f64 -1/3) (pow.f64 x 2))) (*.f64 (exp.f64 -1/3) x)))
(+.f64 (exp.f64 -1/3) (fma.f64 1/2 (.f64 (exp.f64 -1/3) (.f64 x x)) (*.f64 x (exp.f64 -1/3))))
(+.f64 (exp.f64 -1/3) (fma.f64 x (exp.f64 -1/3) (.f64 (.f64 1/2 (*.f64 x x)) (exp.f64 -1/3))))
(.f64 (exp.f64 -1/3) (+.f64 (.f64 1/2 (*.f64 x x)) (+.f64 x 1)))
(.f64 (exp.f64 -1/3) (+.f64 1 (fma.f64 x (.f64 x 1/2) x)))
(+.f64 (exp.f64 -1/3) (+.f64 (.f64 1/2 (.f64 (exp.f64 -1/3) (pow.f64 x 2))) (+.f64 (.f64 (exp.f64 -1/3) x) (.f64 1/6 (*.f64 (exp.f64 -1/3) (pow.f64 x 3))))))
(+.f64 (exp.f64 -1/3) (fma.f64 1/2 (.f64 (exp.f64 -1/3) (.f64 x x)) (fma.f64 (exp.f64 -1/3) x (.f64 1/6 (.f64 (exp.f64 -1/3) (pow.f64 x 3))))))
(+.f64 (exp.f64 -1/3) (fma.f64 1/2 (.f64 x (.f64 x (exp.f64 -1/3))) (fma.f64 x (exp.f64 -1/3) (.f64 1/6 (.f64 (exp.f64 -1/3) (pow.f64 x 3))))))
(+.f64 (.f64 (exp.f64 -1/3) (+.f64 x (.f64 1/2 (.f64 x x)))) (fma.f64 (exp.f64 -1/3) (.f64 1/6 (pow.f64 x 3)) (exp.f64 -1/3)))
(.f64 (exp.f64 -1/3) (+.f64 (+.f64 x 1) (.f64 (.f64 x x) (+.f64 1/2 (.f64 x 1/6)))))
(.f64 (exp.f64 -1/3) (+.f64 (fma.f64 x (.f64 x 1/2) 1) (fma.f64 1/6 (pow.f64 x 3) x)))
(exp.f64 (-.f64 x 1/3))
(exp.f64 (+.f64 x -1/3))
(exp.f64 (+.f64 -1/3 x))
(exp.f64 (-.f64 x 1/3))
(exp.f64 (+.f64 x -1/3))
(exp.f64 (+.f64 -1/3 x))
(exp.f64 (-.f64 x 1/3))
(exp.f64 (+.f64 x -1/3))
(exp.f64 (+.f64 -1/3 x))
(exp.f64 (-.f64 x 1/3))
(exp.f64 (+.f64 x -1/3))
(exp.f64 (+.f64 -1/3 x))
(exp.f64 (neg.f64 (+.f64 1/3 (*.f64 -1 x))))
(exp.f64 (+.f64 x -1/3))
(exp.f64 (+.f64 -1/3 x))
(exp.f64 (neg.f64 (+.f64 1/3 (*.f64 -1 x))))
(exp.f64 (+.f64 x -1/3))
(exp.f64 (+.f64 -1/3 x))
(exp.f64 (neg.f64 (+.f64 1/3 (*.f64 -1 x))))
(exp.f64 (+.f64 x -1/3))
(exp.f64 (+.f64 -1/3 x))
(exp.f64 (neg.f64 (+.f64 1/3 (*.f64 -1 x))))
(exp.f64 (+.f64 x -1/3))
(exp.f64 (+.f64 -1/3 x))

localize18.0ms (0.9%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 19 to 15 computations (21.1% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite95.0ms (4.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	168	8
2	2420	8

Stop Event

1×	node limit

Counts

2 → 89

Calls

Call 1

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

Outputs

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

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

simplify23.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

113 → 95

Calls

Call 1

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

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

localize32.0ms (1.5%)

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)))
✓	14.3b	(/.f64 (+.f64 x 1/3) (fma.f64 x x -1/9))

Compiler

Compiled 30 to 20 computations (33.3% saved)

series10.0ms (0.5%)

Counts

4 → 48

Calls

12 calls:

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

rewrite92.0ms (4.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	34
1	199	20
2	2563	20

Stop Event

1×	node limit

Counts

4 → 205

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 x -1/3)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (/.f64 1 (+.f64 x -1/3))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 x -1/3))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 1 (+.f64 x -1/3))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 1 (+.f64 x -1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 x 1/3) (/.f64 1 (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (+.f64 x -1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 1 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cbrt.f64 (+.f64 x -1/3))) (cbrt.f64 (pow.f64 (+.f64 x -1/3) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (+.f64 x -1/3) -2)) (/.f64 1 (cbrt.f64 (+.f64 x -1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 x 1/3)) 2) (.f64 (cbrt.f64 (+.f64 x 1/3)) (/.f64 1 (fma.f64 x x -1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (+.f64 x -1/3) -1/2) (pow.f64 (+.f64 x -1/3) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 x 1/3)) (.f64 (sqrt.f64 (+.f64 x 1/3)) (/.f64 1 (fma.f64 x x -1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 -1/3 (neg.f64 x)) (/.f64 1 (neg.f64 (fma.f64 x x -1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (fma.f64 x x -1/9)) (+.f64 x 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (+.f64 x 1/3)) 2) 1) (/.f64 (cbrt.f64 (+.f64 x 1/3)) (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (+.f64 x 1/3)) 1) (/.f64 (sqrt.f64 (+.f64 x 1/3)) (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1/9)) -2) (/.f64 (+.f64 x 1/3) (cbrt.f64 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((#(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 (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 (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 (-.f64 (fma.f64 x x 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 pow.f64 (+.f64 x 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1/3) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x 1/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x 1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x 1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (-.f64 (fma.f64 x x 1/9) (.f64 x 1/3)) (+.f64 1/27 (pow.f64 x 3))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (+.f64 x -1/3) (fma.f64 x x -1/9)) -1)))) (#(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 (.f64 (cbrt.f64 (fma.f64 x x -1/9)) (/.f64 1 (cbrt.f64 (+.f64 x -1/3)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 (fma.f64 x x -1/9)) (pow.f64 (+.f64 x -1/3) -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (+.f64 x 1/3))) 2)) (cbrt.f64 (log.f64 (+.f64 x 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (+.f64 x 1/3)))) (sqrt.f64 (log.f64 (+.f64 x 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x 1/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x 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 x -1/3) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (fma.f64 x x -1/9) 3) (/.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 (+.f64 1/27 (pow.f64 x 3)) 3) (pow.f64 (-.f64 (fma.f64 x x 1/9) (.f64 x 1/3)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (fma.f64 x x -1/9) 3) (/.f64 (pow.f64 (+.f64 x 1/3) 3) (pow.f64 (fma.f64 x x -1/9) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 x 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (pow.f64 (+.f64 x 1/3) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (+.f64 x 1/3))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (+.f64 x 1/3))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x 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 (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 +.f64 -1/9 (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (fma.f64 x x -1/9))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 x x) -1/9)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (.f64 x x) 1) -1/9)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1/9))) 2)) (log.f64 (cbrt.f64 (exp.f64 (fma.f64 x x -1/9)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1/9)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 x x -1/9)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 x x) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 x x -1/9)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x x -1/9) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 x x -1/9))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 x x -1/9)) (pow.f64 (cbrt.f64 (fma.f64 x x -1/9)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (fma.f64 x x -1/9)) 2) (cbrt.f64 (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 x x -1/9)) (sqrt.f64 (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1 (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) -1/729) (+.f64 (pow.f64 x 4) (-.f64 1/81 (.f64 (.f64 x x) -1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 4) 1/81) (fma.f64 x x 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 6) 1/729) (+.f64 (pow.f64 x 4) (+.f64 1/81 (.f64 (.f64 x x) 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 x x -1/9) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (E.f64) (log.f64 (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x -1/9) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 x x -1/9) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 x x -1/9)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 x x -1/9)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (fma.f64 x x -1/9)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 x x -1/9))) 2)) (cbrt.f64 (log.f64 (fma.f64 x x -1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 x x -1/9)))) (sqrt.f64 (log.f64 (fma.f64 x x -1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x -1/9) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 x x -1/9) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (neg.f64 (log.f64 (fma.f64 x x -1/9))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (.f64 3 (log.f64 (fma.f64 x x -1/9))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (cbrt.f64 (fma.f64 x x -1/9))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1/9))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (neg.f64 (neg.f64 (log.f64 (fma.f64 x x -1/9)))))))))

simplify58.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	42	331
1	107	311
2	229	309
3	543	303
4	1450	300
5	6136	300

Stop Event

1×	node limit

Counts

253 → 229

Calls

Call 1

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

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

eval155.0ms (7.2%)

Compiler: Compiled 5390 to 4246 computations (21.2% saved)

prune62.0ms (2.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	456	4	460
Fresh	2	0	2
Picked	1	0	1
Done	2	1	3
Total	461	5	466

Error

Counts

466 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(-.f64 (+.f64 x 2/3) 1)
	30.7b	x
	33.1b	-1/3
▶	15.3b	(/.f64 1 (/.f64 (+.f64 x 1/3) (-.f64 (*.f64 x x) 1/9)))
✓	0.0b	(+.f64 x -1/3)

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 12 to 9 computations (25% saved)

series1.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite61.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

720×	`pow1_binary64`
682×	`add-log-exp_binary64`
681×	`log1p-expm1-u_binary64`
681×	`expm1-log1p-u_binary64`
672×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	139	8
2	1805	8

Stop Event

1×	node limit

Counts

2 → 74

Calls

Call 1

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

Outputs

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

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

simplify10.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

98 → 80

Calls

Call 1

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

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

localize14.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 x x) 1/9)
	0.0b	(+.f64 x 1/3)
✓	0.1b	(/.f64 1 (/.f64 (+.f64 x 1/3) (-.f64 (*.f64 x x) 1/9)))
✓	14.3b	(/.f64 (+.f64 x 1/3) (-.f64 (*.f64 x x) 1/9))

Compiler

Compiled 36 to 21 computations (41.7% saved)

series3.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite81.0ms (3.8%)

Algorithm

1×	batch-egg-rewrite

Rules

467×	`log-prod_binary64`
365×	`exp-prod_binary64`
297×	`pow-prod-down_binary64`
270×	`pow2_binary64`
185×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	229	16
2	3040	16

Stop Event

1×	node limit

Counts

3 → 178

Calls

Call 1

Inputs
(/.f64 (+.f64 x 1/3) (-.f64 (*.f64 x x) 1/9))
(/.f64 1 (/.f64 (+.f64 x 1/3) (-.f64 (*.f64 x x) 1/9)))
(-.f64 (*.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 (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 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x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 6) -1/729) (/.f64 1 (+.f64 (pow.f64 x 4) (fma.f64 x (*.f64 x 1/9) 1/81))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 x 4) -1/81) (/.f64 1 (fma.f64 x x 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 1 (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 x 4) (fma.f64 x (*.f64 x 1/9) 1/81)) (+.f64 (pow.f64 x 6) -1/729)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 x x 1/9) (+.f64 (pow.f64 x 4) -1/81)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) -1/729) (+.f64 (pow.f64 x 4) (fma.f64 x (*.f64 x 1/9) 1/81)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 6) -1/729) (+.f64 (pow.f64 x 4) (-.f64 1/81 (*.f64 (*.f64 x x) -1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 x 4) -1/81) (fma.f64 x x 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x 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pow.f64 (/.f64 (fma.f64 x x 1/9) (+.f64 (pow.f64 x 4) -1/81)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log.f64 (fma.f64 x x -1/9))) 2)) (cbrt.f64 (log.f64 (fma.f64 x x -1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (exp.f64 (sqrt.f64 (log.f64 (fma.f64 x x -1/9)))) (sqrt.f64 (log.f64 (fma.f64 x x -1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 x x -1/9) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x 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 expm1.f64 (log1p.f64 (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 x x -1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (fma.f64 x x -1/9)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 3 (log.f64 (fma.f64 x x -1/9))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (cbrt.f64 (fma.f64 x x -1/9))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1/9))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (neg.f64 (log.f64 (fma.f64 x x -1/9))) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 (log.f64 (fma.f64 x x -1/9)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x -1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 1 -1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) -1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 (cbrt.f64 x) x) (pow.f64 (cbrt.f64 x) 2) -1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) x) -1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (pow.f64 x 3/2) -1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (sqrt.f64 x) -1/9)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 5) (cbrt.f64 x) -1/9)))))

simplify65.0ms (3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	41	292
1	105	272
2	227	270
3	539	264
4	1446	261
5	6111	261

Stop Event

1×	node limit

Counts

214 → 198

Calls

Call 1

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

eval138.0ms (6.4%)

Compiler: Compiled 4169 to 3194 computations (23.4% saved)

prune67.0ms (3.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	330	0	330
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	330	5	335

Error

Counts

335 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(-.f64 (+.f64 x 2/3) 1)
	30.7b	x
	33.1b	-1/3
✓	15.3b	(/.f64 1 (/.f64 (+.f64 x 1/3) (-.f64 (*.f64 x x) 1/9)))
✓	0.0b	(+.f64 x -1/3)

Compiler

Compiled 26 to 20 computations (23.1% saved)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	0	0
Done	3	3
Total	5	5

Error

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(-.f64 (+.f64 x 2/3) 1)
	30.7b	x
	33.1b	-1/3
✓	15.3b	(/.f64 1 (/.f64 (+.f64 x 1/3) (-.f64 (*.f64 x x) 1/9)))
✓	0.0b	(+.f64 x -1/3)

Compiler

Compiled 26 to 20 computations (23.1% saved)

regimes21.0ms (1%)

Counts

11 → 1

Calls

Call 1

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

Outputs
(+.f64 x -1/3)

Calls

3 calls:

7.0ms	(-.f64 x (/.f64 1 3))
6.0ms	x
5.0ms	(-.f64 x (/.f64 1 3))

Results

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

Compiler

Compiled 65 to 49 computations (24.6% saved)

regimes20.0ms (0.9%)

Accuracy

Total -59.7b remaining (-2932.6%)

Threshold costs -59.7b (-2932.6%)

Counts

4 → 3

Calls

Call 1

Inputs
x
-1/3
x
-1/3

Outputs
x
-1/3
x

Calls

1 calls:

19.0ms

Results

Error	Segments	Branch
2.0b	3	`x`

Compiler

Compiled 7 to 4 computations (42.9% saved)

bsearch30.0ms (1.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
16.0ms	0.021398597363671983	1.370840529417722
14.0ms	-0.602516291185853	-9.61122865210643e-6

Compiler

Compiled 10 to 8 computations (20% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	12	20

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 x -1/3)
(if (<=.f64 x -11114463823746093056/18446744073709551616) x (if (<=.f64 x 394734449104012992/18446744073709551616) -1/3 x))
x

Outputs
(+.f64 x -1/3)
(if (<=.f64 x -11114463823746093056/18446744073709551616) x (if (<=.f64 x 394734449104012992/18446744073709551616) -1/3 x))
(if (<=.f64 x -2713492144469261/4503599627370496) x (if (<=.f64 x 6167725767250203/288230376151711744) -1/3 x))
x

Compiler

Compiled 18 to 12 computations (33.3% saved)

soundness8.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	12	4
2	13	4

Stop Event

1×

saturated

Compiler

Compiled 22 to 18 computations (18.2% saved)

end52.0ms (2.4%)

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

Details

analyze3.0ms (0.1%)

sample727.0ms (33.9%)

preprocess19.0ms (0.9%)

simplify7.0ms (0.3%)

eval1.0ms (0%)

prune1.0ms (0%)

localize3.0ms (0.1%)

series4.0ms (0.2%)

rewrite46.0ms (2.1%)

simplify11.0ms (0.5%)

eval8.0ms (0.4%)

prune10.0ms (0.5%)

localize11.0ms (0.5%)

series3.0ms (0.2%)

rewrite71.0ms (3.3%)

simplify91.0ms (4.2%)

localize18.0ms (0.9%)

series3.0ms (0.1%)

rewrite95.0ms (4.4%)

simplify23.0ms (1.1%)

localize32.0ms (1.5%)

series10.0ms (0.5%)

rewrite92.0ms (4.3%)

simplify58.0ms (2.7%)

eval155.0ms (7.2%)

prune62.0ms (2.9%)

localize5.0ms (0.2%)

series1.0ms (0.1%)

rewrite61.0ms (2.8%)

simplify10.0ms (0.5%)

localize14.0ms (0.6%)

series3.0ms (0.1%)

rewrite81.0ms (3.8%)

simplify65.0ms (3%)

eval138.0ms (6.4%)

prune67.0ms (3.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes21.0ms (1%)

regimes20.0ms (0.9%)

bsearch30.0ms (1.4%)

simplify4.0ms (0.2%)

soundness8.0ms (0.4%)

end52.0ms (2.4%)

Profiling