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)

sample865.0ms (26.2%)

Results

852.0ms

8256×

body

256

valid

preprocess34.0ms (1%)

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)

simplify9.0ms (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 2 expressions with local error:

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

series1.0ms (0%)

Counts

1 → 3

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)

rewrite48.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

479×	`pow1_binary64`
475×	`add-sqr-sqrt_binary64`
452×	`add-log-exp_binary64`
452×	`log1p-expm1-u_binary64`
452×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	93	4
2	1164	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 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) 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 (pow.f64 x 3) -1/27) (/.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 (pow.f64 x 3) -1/27)))))) (#(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 (pow.f64 x 3) -1/27) (fma.f64 x x (+.f64 1/9 (.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 (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 (neg.f64 (+.f64 (pow.f64 x 3) -1/27)) (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 pow.f64 (+.f64 x -1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x -1/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x -1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x -1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x -1/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x -1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x 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 expm1.f64 (log1p.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 (+.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 (pow.f64 x 3) -1/27) (/.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 (pow.f64 x 3) -1/27)))))) (#(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 (pow.f64 x 3) -1/27) (fma.f64 x x (+.f64 1/9 (*.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 (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 (neg.f64 (+.f64 (pow.f64 x 3) -1/27)) (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 pow.f64 (+.f64 x -1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 x -1/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 x -1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 x -1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 x -1/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 x -1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 x -1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 x -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 x) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (sqrt.f64 x) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x 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 expm1.f64 (log1p.f64 (+.f64 x -1/3)))))))

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2	3

Stop Event

1×

saturated

Counts

33 → 32

Calls

Call 1

Inputs
-1/3
x
x

Outputs
-1/3
x
x

eval8.0ms (0.2%)

Compiler: Compiled 247 to 184 computations (25.5% saved)

prune9.0ms (0.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	26	6	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	7	33

Error

Counts

33 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	17.5b	(expm1.f64 (log1p.f64 (+.f64 x -1/3)))
	33.9b	x
✓	0.0b	(-.f64 x 1/3)
	29.9b	-1/3
▶	12.5b	(/.f64 (fma.f64 x x -1/9) (+.f64 x 1/3))
▶	18.8b	(/.f64 (+.f64 (pow.f64 x 3) -1/27) (+.f64 (.f64 x x) (-.f64 1/9 (.f64 x -1/3))))
▶	12.6b	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x 1/3)))

Compiler

Compiled 50 to 37 computations (26% saved)

localize14.0ms (0.4%)

Local error

Found 8 expressions with local error:

New	Error	Program
	11.7b	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x 1/3)))
	0.0b	(/.f64 1 (+.f64 x 1/3))
	0.0b	(+.f64 x 1/3)
	0.0b	(fma.f64 x x -1/9)
✓	0.0b	(fma.f64 x x -1/9)
✓	0.0b	(+.f64 x 1/3)
✓	0.0b	(/.f64 1 (+.f64 x 1/3))
✓	11.7b	(*.f64 (fma.f64 x x -1/9) (/.f64 1 (+.f64 x 1/3)))

Compiler

Compiled 27 to 19 computations (29.6% saved)

series5.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

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

rewrite65.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	194	20
2	2355	20

Stop Event

1×	node limit

Counts

4 → 115

Calls

Call 1

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

simplify51.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

758×	`distribute-neg-frac_binary64`
727×	`associate-l_binary64`
718×	`fma-def_binary64`
466×	`associate-r_binary64`
415×	`times-frac_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	331
1	102	309
2	244	309
3	649	303
4	1875	300
5	7099	300

Stop Event

1×	node limit

Counts

163 → 139

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

localize28.0ms (0.8%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.4b	(*.f64 x -1/3)
	0.0b	(-.f64 1/9 (*.f64 x -1/3))
	0.0b	(+.f64 (.f64 x x) (-.f64 1/9 (.f64 x -1/3)))
	0.0b	(+.f64 (pow.f64 x 3) -1/27)
✓	0.0b	(+.f64 (.f64 x x) (-.f64 1/9 (.f64 x -1/3)))
✓	0.0b	(-.f64 1/9 (*.f64 x -1/3))
✓	0.4b	(*.f64 x -1/3)
✓	18.1b	(/.f64 (+.f64 (pow.f64 x 3) -1/27) (+.f64 (.f64 x x) (-.f64 1/9 (.f64 x -1/3))))

Compiler

Compiled 49 to 33 computations (32.7% saved)

series6.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

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

rewrite80.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

627×	`log-prod_binary64`
412×	`fma-def_binary64`
364×	`pow2_binary64`
249×	`pow1/3_binary64`
247×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	42
1	308	42
2	4065	36

Stop Event

1×	node limit

Counts

4 → 166

Calls

Call 1

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

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

simplify154.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

1104×	`sqr-pow_binary64`
636×	`fma-def_binary64`
561×	`cube-prod_binary64`
548×	`fabs-mul_binary64`
536×	`pow-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	257
1	27	229
2	50	217
3	86	217
4	170	217
5	425	217
6	1310	217
7	2557	217
8	2951	217
9	3143	217
10	3353	217
11	3651	217
12	4059	217
13	4541	217
14	5108	217
15	5798	217
16	6640	217
17	7034	217
18	7320	217
19	7596	217
20	7666	217
21	7700	217

Stop Event

1×	node limit

Counts

214 → 181

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

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

localize10.0ms (0.3%)

Local error

Found 6 expressions with local error:

New	Error	Program
	11.6b	(/.f64 (fma.f64 x x -1/9) (+.f64 x 1/3))
	0.0b	(+.f64 x 1/3)
	0.0b	(fma.f64 x x -1/9)
	0.0b	(fma.f64 x x -1/9)
	0.0b	(+.f64 x 1/3)
✓	11.6b	(/.f64 (fma.f64 x x -1/9) (+.f64 x 1/3))

Compiler

Compiled 19 to 12 computations (36.8% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite64.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

825×	`pow1_binary64`
775×	`add-log-exp_binary64`
775×	`log1p-expm1-u_binary64`
775×	`expm1-log1p-u_binary64`
762×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	158	4
2	2057	4

Stop Event

1×	node limit

Counts

1 → 38

Calls

Call 1

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

Outputs

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

simplify8.0ms (0.2%)

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

50 → 40

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)

localize12.0ms (0.4%)

Local error

Found 6 expressions with local error:

New	Error	Program
	1.8b	(expm1.f64 (log1p.f64 (+.f64 x -1/3)))
	0.0b	(log1p.f64 (+.f64 x -1/3))
	0.0b	(+.f64 x -1/3)
✓	0.0b	(+.f64 x -1/3)
✓	0.0b	(log1p.f64 (+.f64 x -1/3))
✓	1.8b	(expm1.f64 (log1p.f64 (+.f64 x -1/3)))

Compiler

Compiled 15 to 11 computations (26.7% saved)

series3.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(log1p.f64 (+.f64 x -1/3))
0.0ms	x	@	-inf	(log1p.f64 (+.f64 x -1/3))
0.0ms	x	@	0	(log1p.f64 (+.f64 x -1/3))
0.0ms	x	@	0	(expm1.f64 (log1p.f64 (+.f64 x -1/3)))
0.0ms	x	@	inf	(expm1.f64 (log1p.f64 (+.f64 x -1/3)))

rewrite46.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

554×	`pow1_binary64`
522×	`expm1-log1p-u_binary64`
521×	`add-log-exp_binary64`
521×	`log1p-expm1-u_binary64`
512×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	14
1	112	14
2	1360	14

Stop Event

1×	node limit

Counts

3 → 81

Calls

Call 1

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

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

simplify48.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

540×	`sub-neg_binary64`
521×	`associate-l_binary64`
466×	`fma-def_binary64`
357×	`fma-neg_binary64`
332×	`associate--l-_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	269
1	139	241
2	339	238
3	999	231
4	2884	231
5	7390	231

Stop Event

1×	node limit

Counts

117 → 72

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)
(log.f64 2/3)
(+.f64 (log.f64 2/3) (*.f64 3/2 x))
(+.f64 (log.f64 2/3) (+.f64 (.f64 -9/8 (pow.f64 x 2)) (.f64 3/2 x)))
(+.f64 (log.f64 2/3) (+.f64 (.f64 -9/8 (pow.f64 x 2)) (+.f64 (.f64 3/2 x) (*.f64 9/8 (pow.f64 x 3)))))
(*.f64 -1 (log.f64 (/.f64 1 x)))
(+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (.f64 2/3 (/.f64 1 x)))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (.f64 2/3 (/.f64 1 x))) (*.f64 2/9 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (.f64 8/81 (/.f64 1 (pow.f64 x 3))) (.f64 2/3 (/.f64 1 x)))) (.f64 2/9 (/.f64 1 (pow.f64 x 2))))
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))
(+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 -1) (.f64 2/3 (/.f64 1 x))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 -1) (.f64 2/3 (/.f64 1 x)))) (*.f64 2/9 (/.f64 1 (pow.f64 x 2))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 -1) (+.f64 (.f64 8/81 (/.f64 1 (pow.f64 x 3))) (.f64 2/3 (/.f64 1 x))))) (.f64 2/9 (/.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)

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)
(log.f64 2/3)
(+.f64 (log.f64 2/3) (*.f64 3/2 x))
(+.f64 (log.f64 2/3) (*.f64 x 3/2))
(fma.f64 x 3/2 (log.f64 2/3))
(+.f64 (log.f64 2/3) (+.f64 (.f64 -9/8 (pow.f64 x 2)) (.f64 3/2 x)))
(+.f64 (log.f64 2/3) (fma.f64 -9/8 (.f64 x x) (.f64 x 3/2)))
(+.f64 (log.f64 2/3) (fma.f64 x 3/2 (.f64 x (.f64 x -9/8))))
(fma.f64 x 3/2 (fma.f64 x (*.f64 x -9/8) (log.f64 2/3)))
(fma.f64 x (fma.f64 x -9/8 3/2) (log.f64 2/3))
(+.f64 (log.f64 2/3) (+.f64 (.f64 -9/8 (pow.f64 x 2)) (+.f64 (.f64 3/2 x) (*.f64 9/8 (pow.f64 x 3)))))
(+.f64 (log.f64 2/3) (fma.f64 -9/8 (.f64 x x) (fma.f64 3/2 x (.f64 9/8 (pow.f64 x 3)))))
(+.f64 (log.f64 2/3) (fma.f64 -9/8 (.f64 x x) (fma.f64 x 3/2 (.f64 9/8 (pow.f64 x 3)))))
(+.f64 (log.f64 2/3) (fma.f64 9/8 (pow.f64 x 3) (.f64 x (+.f64 3/2 (.f64 x -9/8)))))
(fma.f64 x 3/2 (fma.f64 (*.f64 x x) (fma.f64 x 9/8 -9/8) (log.f64 2/3)))
(fma.f64 x (fma.f64 x -9/8 3/2) (fma.f64 9/8 (pow.f64 x 3) (log.f64 2/3)))
(*.f64 -1 (log.f64 (/.f64 1 x)))
(neg.f64 (neg.f64 (log.f64 x)))
(log.f64 x)
(+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (.f64 2/3 (/.f64 1 x)))
(fma.f64 -1 (neg.f64 (log.f64 x)) (/.f64 2/3 x))
(+.f64 (log.f64 x) (/.f64 2/3 x))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (.f64 2/3 (/.f64 1 x))) (*.f64 2/9 (/.f64 1 (pow.f64 x 2))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (/.f64 2/3 x)) (/.f64 2/9 (*.f64 x x)))
(+.f64 (/.f64 2/3 x) (-.f64 (log.f64 x) (/.f64 2/9 (*.f64 x x))))
(+.f64 (/.f64 2/3 x) (-.f64 (log.f64 x) (/.f64 (/.f64 2/9 x) x)))
(+.f64 (log.f64 x) (+.f64 (/.f64 2/3 x) (/.f64 -2/9 (*.f64 x x))))
(+.f64 (log.f64 x) (-.f64 (/.f64 2/3 x) (/.f64 2/9 (*.f64 x x))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 1 x))) (+.f64 (.f64 8/81 (/.f64 1 (pow.f64 x 3))) (.f64 2/3 (/.f64 1 x)))) (.f64 2/9 (/.f64 1 (pow.f64 x 2))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (+.f64 (/.f64 2/3 x) (/.f64 8/81 (pow.f64 x 3)))) (/.f64 2/9 (*.f64 x x)))
(+.f64 (+.f64 (/.f64 2/3 x) (/.f64 8/81 (pow.f64 x 3))) (-.f64 (log.f64 x) (/.f64 2/9 (*.f64 x x))))
(+.f64 (log.f64 x) (+.f64 (/.f64 2/3 x) (-.f64 (/.f64 8/81 (pow.f64 x 3)) (/.f64 (/.f64 2/9 x) x))))
(+.f64 (+.f64 (log.f64 x) (/.f64 2/3 x)) (+.f64 (/.f64 8/81 (pow.f64 x 3)) (/.f64 -2/9 (*.f64 x x))))
(+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))
(neg.f64 (neg.f64 (log.f64 x)))
(log.f64 x)
(+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 -1) (.f64 2/3 (/.f64 1 x))))
(fma.f64 -1 (neg.f64 (log.f64 x)) (/.f64 2/3 x))
(+.f64 (log.f64 x) (/.f64 2/3 x))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 -1) (.f64 2/3 (/.f64 1 x)))) (*.f64 2/9 (/.f64 1 (pow.f64 x 2))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (/.f64 2/3 x)) (/.f64 2/9 (*.f64 x x)))
(+.f64 (/.f64 2/3 x) (-.f64 (log.f64 x) (/.f64 2/9 (*.f64 x x))))
(+.f64 (/.f64 2/3 x) (-.f64 (log.f64 x) (/.f64 (/.f64 2/9 x) x)))
(+.f64 (log.f64 x) (+.f64 (/.f64 2/3 x) (/.f64 -2/9 (*.f64 x x))))
(+.f64 (log.f64 x) (-.f64 (/.f64 2/3 x) (/.f64 2/9 (*.f64 x x))))
(-.f64 (+.f64 (.f64 -1 (log.f64 (/.f64 -1 x))) (+.f64 (log.f64 -1) (+.f64 (.f64 8/81 (/.f64 1 (pow.f64 x 3))) (.f64 2/3 (/.f64 1 x))))) (.f64 2/9 (/.f64 1 (pow.f64 x 2))))
(-.f64 (fma.f64 -1 (neg.f64 (log.f64 x)) (+.f64 (/.f64 2/3 x) (/.f64 8/81 (pow.f64 x 3)))) (/.f64 2/9 (*.f64 x x)))
(+.f64 (+.f64 (/.f64 2/3 x) (/.f64 8/81 (pow.f64 x 3))) (-.f64 (log.f64 x) (/.f64 2/9 (*.f64 x x))))
(+.f64 (log.f64 x) (+.f64 (/.f64 2/3 x) (-.f64 (/.f64 8/81 (pow.f64 x 3)) (/.f64 (/.f64 2/9 x) x))))
(+.f64 (+.f64 (log.f64 x) (/.f64 2/3 x)) (+.f64 (/.f64 8/81 (pow.f64 x 3)) (/.f64 -2/9 (*.f64 x x))))
-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)

eval265.0ms (8%)

Compiler: Compiled 7426 to 5384 computations (27.5% saved)

prune102.0ms (3.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	497	4	501
Fresh	2	0	2
Picked	1	0	1
Done	2	2	4
Total	502	6	508

Error

Counts

508 → 6

Alt Table

Click to see full alt table

Status	Error	Program
	33.9b	x
✓	0.0b	(-.f64 x 1/3)
▶	0.5b	(+.f64 (+.f64 2/3 x) -1)
✓	18.8b	(/.f64 (+.f64 (pow.f64 x 3) -1/27) (+.f64 (.f64 x x) (-.f64 1/9 (.f64 x -1/3))))
	29.9b	-1/3
▶	12.5b	(/.f64 (+.f64 (*.f64 x x) -1/9) (+.f64 x 1/3))

Compiler

Compiled 40 to 30 computations (25% saved)

localize10.0ms (0.3%)

Local error

Found 6 expressions with local error:

New	Error	Program
	11.6b	(/.f64 (+.f64 (*.f64 x x) -1/9) (+.f64 x 1/3))
	0.0b	(+.f64 x 1/3)
	0.0b	(+.f64 (*.f64 x x) -1/9)
✓	0.0b	(+.f64 (*.f64 x x) -1/9)
	0.0b	(+.f64 x 1/3)
✓	11.6b	(/.f64 (+.f64 (*.f64 x x) -1/9) (+.f64 x 1/3))

Compiler

Compiled 24 to 13 computations (45.8% saved)

series2.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite63.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

550×	`unpow-prod-down_binary64`
395×	`log-prod_binary64`
305×	`exp-prod_binary64`
241×	`pow-prod-down_binary64`
236×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	189	9
2	2572	9

Stop Event

1×	node limit

Counts

2 → 141

Calls

Call 1

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

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

simplify130.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

1428×	`sqr-pow_binary64`
743×	`pow-sqr_binary64`
618×	`cube-prod_binary64`
605×	`fabs-mul_binary64`
434×	`unswap-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	111
1	19	93
2	30	93
3	42	93
4	71	93
5	158	93
6	580	93
7	1454	93
8	1644	93
9	1828	93
10	2036	93
11	2321	93
12	2715	93
13	3195	93
14	3756	93
15	4440	93
16	5275	93
17	5665	93
18	5953	93
19	6229	93
20	6303	93
21	6339	93
22	7280	93

Stop Event

1×	node limit

Counts

165 → 147

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)
-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 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)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 12 to 9 computations (25% saved)

series2.0ms (0%)

Counts

2 → 15

Calls

6 calls:

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

rewrite77.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

784×	`pow1_binary64`
738×	`add-log-exp_binary64`
738×	`log1p-expm1-u_binary64`
738×	`expm1-log1p-u_binary64`
728×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	138	8
2	1839	8

Stop Event

1×	node limit

Counts

2 → 63

Calls

Call 1

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

Outputs

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

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

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	42
1	8	42
2	9	42

Stop Event

1×

saturated

Counts

78 → 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)
2/3
x
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
x
x

eval153.0ms (4.6%)

Compiler: Compiled 3236 to 2411 computations (25.5% saved)

prune32.0ms (1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	249	4	253
Fresh	2	0	2
Picked	0	1	1
Done	1	2	3
Total	252	7	259

Error

Counts

259 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(-.f64 x 1/3)
▶	30.4b	(+.f64 2/3 -1)
	33.9b	x
✓	0.5b	(+.f64 (+.f64 2/3 x) -1)
	29.9b	-1/3
✓	12.5b	(/.f64 (+.f64 (*.f64 x x) -1/9) (+.f64 x 1/3))
▶	13.0b	(/.f64 (-.f64 4/9 (*.f64 (+.f64 x -1) (+.f64 x -1))) (-.f64 2/3 (+.f64 x -1)))

Compiler

Compiled 44 to 35 computations (20.5% saved)

localize58.0ms (1.8%)

Local error

Found 8 expressions with local error:

New	Error	Program
	11.6b	(/.f64 (-.f64 4/9 (*.f64 (+.f64 x -1) (+.f64 x -1))) (-.f64 2/3 (+.f64 x -1)))
	0.5b	(-.f64 2/3 (+.f64 x -1))
	0.0b	(-.f64 4/9 (*.f64 (+.f64 x -1) (+.f64 x -1)))
	0.0b	(*.f64 (+.f64 x -1) (+.f64 x -1))
✓	0.0b	(*.f64 (+.f64 x -1) (+.f64 x -1))
✓	0.0b	(-.f64 4/9 (*.f64 (+.f64 x -1) (+.f64 x -1)))
✓	0.5b	(-.f64 2/3 (+.f64 x -1))
✓	11.6b	(/.f64 (-.f64 4/9 (*.f64 (+.f64 x -1) (+.f64 x -1))) (-.f64 2/3 (+.f64 x -1)))

Compiler

Compiled 44 to 34 computations (22.7% saved)

series5.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/.f64 (-.f64 4/9 (*.f64 (+.f64 x -1) (+.f64 x -1))) (-.f64 2/3 (+.f64 x -1)))
1.0ms	x	@	0	(/.f64 (-.f64 4/9 (*.f64 (+.f64 x -1) (+.f64 x -1))) (-.f64 2/3 (+.f64 x -1)))
1.0ms	x	@	inf	(/.f64 (-.f64 4/9 (*.f64 (+.f64 x -1) (+.f64 x -1))) (-.f64 2/3 (+.f64 x -1)))
0.0ms	x	@	0	(-.f64 4/9 (*.f64 (+.f64 x -1) (+.f64 x -1)))
0.0ms	x	@	-inf	(-.f64 4/9 (*.f64 (+.f64 x -1) (+.f64 x -1)))

rewrite212.0ms (6.4%)

Algorithm

1×	batch-egg-rewrite

Rules

537×	`log-prod_binary64`
520×	`prod-diff_binary64`
327×	`fma-def_binary64`
311×	`pow2_binary64`
213×	`pow1/3_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	43
1	245	25
2	3650	25

Stop Event

1×	node limit

Counts

4 → 301

Calls

Call 1

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

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

simplify99.0ms (3%)

Algorithm

1×	egg-herbie

Rules

894×	`fma-neg_binary64`
503×	`distribute-rgt-neg-in_binary64`
468×	`fma-def_binary64`
381×	`distribute-lft-neg-in_binary64`
285×	`sub-neg_binary64`

Iterations

Useful iterations: 8 (0.0ms)

Iter	Nodes	Cost
0	24	318
1	52	286
2	94	250
3	180	238
4	473	238
5	1261	238
6	2888	238
7	4911	238
8	6165	230
9	7414	230
10	7999	230

Stop Event

1×	node limit

Counts

349 → 325

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)
5/3
(+.f64 5/3 (*.f64 -1 x))
(+.f64 5/3 (*.f64 -1 x))
(+.f64 5/3 (*.f64 -1 x))
(*.f64 -1 x)
(+.f64 5/3 (*.f64 -1 x))
(+.f64 5/3 (*.f64 -1 x))
(+.f64 5/3 (*.f64 -1 x))
(*.f64 -1 x)
(+.f64 5/3 (*.f64 -1 x))
(+.f64 5/3 (*.f64 -1 x))
(+.f64 5/3 (*.f64 -1 x))
-5/9
(-.f64 (*.f64 2 x) 5/9)
(-.f64 (+.f64 (.f64 2 x) (.f64 -1 (pow.f64 x 2))) 5/9)
(-.f64 (+.f64 (.f64 2 x) (.f64 -1 (pow.f64 x 2))) 5/9)
(*.f64 -1 (pow.f64 x 2))
(+.f64 (.f64 2 x) (.f64 -1 (pow.f64 x 2)))
(-.f64 (+.f64 (.f64 2 x) (.f64 -1 (pow.f64 x 2))) 5/9)
(-.f64 (+.f64 (.f64 2 x) (.f64 -1 (pow.f64 x 2))) 5/9)
(*.f64 -1 (pow.f64 x 2))
(+.f64 (.f64 2 x) (.f64 -1 (pow.f64 x 2)))
(-.f64 (+.f64 (.f64 2 x) (.f64 -1 (pow.f64 x 2))) 5/9)
(-.f64 (+.f64 (.f64 2 x) (.f64 -1 (pow.f64 x 2))) 5/9)
1
(+.f64 1 (*.f64 -2 x))
(+.f64 1 (+.f64 (*.f64 -2 x) (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 -2 x) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 -2 x) (pow.f64 x 2))
(+.f64 1 (+.f64 (*.f64 -2 x) (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 -2 x) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (*.f64 -2 x) (pow.f64 x 2))
(+.f64 1 (+.f64 (*.f64 -2 x) (pow.f64 x 2)))
(+.f64 1 (+.f64 (*.f64 -2 x) (pow.f64 x 2)))

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)
5/3
(+.f64 5/3 (*.f64 -1 x))
(+.f64 5/3 (neg.f64 x))
(-.f64 5/3 x)
(+.f64 x 5/3)
(+.f64 5/3 (*.f64 -1 x))
(+.f64 5/3 (neg.f64 x))
(-.f64 5/3 x)
(+.f64 x 5/3)
(+.f64 5/3 (*.f64 -1 x))
(+.f64 5/3 (neg.f64 x))
(-.f64 5/3 x)
(+.f64 x 5/3)
(*.f64 -1 x)
x
(+.f64 5/3 (*.f64 -1 x))
(+.f64 5/3 (neg.f64 x))
(-.f64 5/3 x)
(+.f64 x 5/3)
(+.f64 5/3 (*.f64 -1 x))
(+.f64 5/3 (neg.f64 x))
(-.f64 5/3 x)
(+.f64 x 5/3)
(+.f64 5/3 (*.f64 -1 x))
(+.f64 5/3 (neg.f64 x))
(-.f64 5/3 x)
(+.f64 x 5/3)
(*.f64 -1 x)
x
(+.f64 5/3 (*.f64 -1 x))
(+.f64 5/3 (neg.f64 x))
(-.f64 5/3 x)
(+.f64 x 5/3)
(+.f64 5/3 (*.f64 -1 x))
(+.f64 5/3 (neg.f64 x))
(-.f64 5/3 x)
(+.f64 x 5/3)
(+.f64 5/3 (*.f64 -1 x))
(+.f64 5/3 (neg.f64 x))
(-.f64 5/3 x)
(+.f64 x 5/3)
-5/9
(-.f64 (*.f64 2 x) 5/9)
(fma.f64 2 x -5/9)
(fma.f64 x 2 -5/9)
(-.f64 (+.f64 (.f64 2 x) (.f64 -1 (pow.f64 x 2))) 5/9)
(+.f64 (fma.f64 2 x (neg.f64 (*.f64 x x))) -5/9)
(fma.f64 x 2 (fma.f64 -1 (*.f64 x x) -5/9))
(+.f64 (*.f64 x (-.f64 2 x)) -5/9)
(fma.f64 x (-.f64 2 x) -5/9)
(fma.f64 x (+.f64 x -2) -5/9)
(-.f64 (+.f64 (.f64 2 x) (.f64 -1 (pow.f64 x 2))) 5/9)
(+.f64 (fma.f64 2 x (neg.f64 (*.f64 x x))) -5/9)
(fma.f64 x 2 (fma.f64 -1 (*.f64 x x) -5/9))
(+.f64 (*.f64 x (-.f64 2 x)) -5/9)
(fma.f64 x (-.f64 2 x) -5/9)
(fma.f64 x (+.f64 x -2) -5/9)
(*.f64 -1 (pow.f64 x 2))
(neg.f64 (*.f64 x x))
(*.f64 x (neg.f64 x))
(*.f64 x x)
(+.f64 (.f64 2 x) (.f64 -1 (pow.f64 x 2)))
(fma.f64 2 x (neg.f64 (*.f64 x x)))
(-.f64 (.f64 x 2) (.f64 x x))
(*.f64 x (-.f64 2 x))
(*.f64 x (+.f64 x -2))
(-.f64 (+.f64 (.f64 2 x) (.f64 -1 (pow.f64 x 2))) 5/9)
(+.f64 (fma.f64 2 x (neg.f64 (*.f64 x x))) -5/9)
(fma.f64 x 2 (fma.f64 -1 (*.f64 x x) -5/9))
(+.f64 (*.f64 x (-.f64 2 x)) -5/9)
(fma.f64 x (-.f64 2 x) -5/9)
(fma.f64 x (+.f64 x -2) -5/9)
(-.f64 (+.f64 (.f64 2 x) (.f64 -1 (pow.f64 x 2))) 5/9)
(+.f64 (fma.f64 2 x (neg.f64 (*.f64 x x))) -5/9)
(fma.f64 x 2 (fma.f64 -1 (*.f64 x x) -5/9))
(+.f64 (*.f64 x (-.f64 2 x)) -5/9)
(fma.f64 x (-.f64 2 x) -5/9)
(fma.f64 x (+.f64 x -2) -5/9)
(*.f64 -1 (pow.f64 x 2))
(neg.f64 (*.f64 x x))
(*.f64 x (neg.f64 x))
(*.f64 x x)
(+.f64 (.f64 2 x) (.f64 -1 (pow.f64 x 2)))
(fma.f64 2 x (neg.f64 (*.f64 x x)))
(-.f64 (.f64 x 2) (.f64 x x))
(*.f64 x (-.f64 2 x))
(*.f64 x (+.f64 x -2))
(-.f64 (+.f64 (.f64 2 x) (.f64 -1 (pow.f64 x 2))) 5/9)
(+.f64 (fma.f64 2 x (neg.f64 (*.f64 x x))) -5/9)
(fma.f64 x 2 (fma.f64 -1 (*.f64 x x) -5/9))
(+.f64 (*.f64 x (-.f64 2 x)) -5/9)
(fma.f64 x (-.f64 2 x) -5/9)
(fma.f64 x (+.f64 x -2) -5/9)
(-.f64 (+.f64 (.f64 2 x) (.f64 -1 (pow.f64 x 2))) 5/9)
(+.f64 (fma.f64 2 x (neg.f64 (*.f64 x x))) -5/9)
(fma.f64 x 2 (fma.f64 -1 (*.f64 x x) -5/9))
(+.f64 (*.f64 x (-.f64 2 x)) -5/9)
(fma.f64 x (-.f64 2 x) -5/9)
(fma.f64 x (+.f64 x -2) -5/9)
1
(+.f64 1 (*.f64 -2 x))
(+.f64 1 (*.f64 x -2))
(fma.f64 x -2 1)
(fma.f64 x 2 1)
(+.f64 1 (+.f64 (*.f64 -2 x) (pow.f64 x 2)))
(+.f64 1 (fma.f64 -2 x (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x -2)))
(fma.f64 x (+.f64 x -2) 1)
(+.f64 1 (+.f64 (*.f64 -2 x) (pow.f64 x 2)))
(+.f64 1 (fma.f64 -2 x (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x -2)))
(fma.f64 x (+.f64 x -2) 1)
(pow.f64 x 2)
(neg.f64 (*.f64 x x))
(*.f64 x (neg.f64 x))
(*.f64 x x)
(+.f64 (*.f64 -2 x) (pow.f64 x 2))
(fma.f64 2 x (neg.f64 (*.f64 x x)))
(-.f64 (.f64 x 2) (.f64 x x))
(*.f64 x (-.f64 2 x))
(*.f64 x (+.f64 x -2))
(+.f64 1 (+.f64 (*.f64 -2 x) (pow.f64 x 2)))
(+.f64 1 (fma.f64 -2 x (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x -2)))
(fma.f64 x (+.f64 x -2) 1)
(+.f64 1 (+.f64 (*.f64 -2 x) (pow.f64 x 2)))
(+.f64 1 (fma.f64 -2 x (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x -2)))
(fma.f64 x (+.f64 x -2) 1)
(pow.f64 x 2)
(neg.f64 (*.f64 x x))
(*.f64 x (neg.f64 x))
(*.f64 x x)
(+.f64 (*.f64 -2 x) (pow.f64 x 2))
(fma.f64 2 x (neg.f64 (*.f64 x x)))
(-.f64 (.f64 x 2) (.f64 x x))
(*.f64 x (-.f64 2 x))
(*.f64 x (+.f64 x -2))
(+.f64 1 (+.f64 (*.f64 -2 x) (pow.f64 x 2)))
(+.f64 1 (fma.f64 -2 x (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x -2)))
(fma.f64 x (+.f64 x -2) 1)
(+.f64 1 (+.f64 (*.f64 -2 x) (pow.f64 x 2)))
(+.f64 1 (fma.f64 -2 x (*.f64 x x)))
(+.f64 1 (*.f64 x (+.f64 x -2)))
(fma.f64 x (+.f64 x -2) 1)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	1.0b	(+.f64 2/3 -1)
✓	1.0b	(+.f64 2/3 -1)

Compiler

Compiled 6 to 6 computations (0% saved)

series0.0ms (0%)

Counts: 1 → 0

rewrite99.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

629×	`prod-diff_binary64`
444×	`log1p-udef_binary64`
274×	`add-sqr-sqrt_binary64`
268×	`pow1_binary64`
261×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	1
1	78	1
2	693	1
3	6490	1

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

Inputs
(+.f64 2/3 -1)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x . -1/3)))))

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

Inputs

Outputs

eval254.0ms (7.7%)

Compiler: Compiled 9673 to 8020 computations (17.1% saved)

prune45.0ms (1.4%)

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	324	2	326
Fresh	2	0	2
Picked	0	1	1
Done	0	4	4
Total	326	7	333

Error

Counts

333 → 7

Alt Table

Click to see full alt table

Status	Error	Program
✓	13.0b	(/.f64 (-.f64 4/9 (*.f64 (+.f64 x -1) (+.f64 x -1))) (-.f64 2/3 (+.f64 x -1)))
	33.9b	x
	29.9b	-1/3
✓	0.0b	(-.f64 x 1/3)
✓	30.4b	(+.f64 2/3 -1)
✓	0.5b	(+.f64 (+.f64 2/3 x) -1)
✓	12.5b	(/.f64 (+.f64 (*.f64 x x) -1/9) (+.f64 x 1/3))

Compiler

Compiled 44 to 35 computations (20.5% saved)

regimes8.0ms (0.2%)

Counts

7 → 1

Calls

Call 1

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

Outputs
(-.f64 x 1/3)

Calls

1 calls:

6.0ms

Results

Error	Segments	Branch
0.0b	1	`x`

Compiler

Compiled 40 to 30 computations (25% saved)

regimes14.0ms (0.4%)

Accuracy

Total -59.3b remaining (-2647.2%)

Threshold costs -59.3b (-2647.2%)

Counts

3 → 3

Calls

Call 1

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

Outputs
x
-1/3
x

Calls

1 calls:

13.0ms

Results

Error	Segments	Branch
2.2b	3	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

bsearch32.0ms (1%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
16.0ms	0.020906970886639117	0.39211478482209317
16.0ms	-4.405786177188472	-0.001343051659460351

Compiler

Compiled 10 to 8 computations (20% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	14	20
2	15	20

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 x 1/3)
(if (<=.f64 x -4960474246465021/1125899906842624) x (if (<=.f64 x 385665541302328256/18446744073709551616) -1/3 x))
-1/3

Outputs
(-.f64 x 1/3)
(+.f64 x -1/3)
(if (<=.f64 x -4960474246465021/1125899906842624) x (if (<=.f64 x 385665541302328256/18446744073709551616) -1/3 x))
(if (<=.f64 x -4960474246465021/1125899906842624) x (if (<=.f64 x 6026024082848879/288230376151711744) -1/3 x))
-1/3

end34.0ms (1%)

Stop Event

1×

fuel

Compiler

Compiled 34 to 24 computations (29.4% saved)

Details

analyze3.0ms (0.1%)

sample865.0ms (26.2%)

preprocess34.0ms (1%)

simplify9.0ms (0.3%)

eval1.0ms (0%)

prune1.0ms (0%)

localize3.0ms (0.1%)

series1.0ms (0%)

rewrite48.0ms (1.5%)

simplify7.0ms (0.2%)

eval8.0ms (0.2%)

prune9.0ms (0.3%)

localize14.0ms (0.4%)

series5.0ms (0.2%)

rewrite65.0ms (2%)

simplify51.0ms (1.5%)

localize28.0ms (0.8%)

series6.0ms (0.2%)

rewrite80.0ms (2.4%)

simplify154.0ms (4.7%)

localize10.0ms (0.3%)

series1.0ms (0%)

rewrite64.0ms (1.9%)

simplify8.0ms (0.2%)

localize12.0ms (0.4%)

series3.0ms (0.1%)

rewrite46.0ms (1.4%)

simplify48.0ms (1.5%)

eval265.0ms (8%)

prune102.0ms (3.1%)

localize10.0ms (0.3%)

series2.0ms (0.1%)

rewrite63.0ms (1.9%)

simplify130.0ms (3.9%)

localize6.0ms (0.2%)

series2.0ms (0%)

rewrite77.0ms (2.3%)

simplify8.0ms (0.2%)

eval153.0ms (4.6%)

prune32.0ms (1%)

localize58.0ms (1.8%)

series5.0ms (0.2%)

rewrite212.0ms (6.4%)

simplify99.0ms (3%)

localize3.0ms (0.1%)

series0.0ms (0%)

rewrite99.0ms (3%)

simplify6.0ms (0.2%)

eval254.0ms (7.7%)

prune45.0ms (1.4%)

regimes8.0ms (0.2%)

regimes14.0ms (0.4%)

bsearch32.0ms (1%)

simplify3.0ms (0.1%)

end34.0ms (1%)

Profiling