Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
50%	50%	50%	0%	0%	0%	0%	3
75%	75%	25%	0%	0%	0%	0%	4
87.5%	87.5%	12.5%	0%	0%	0%	0%	5
93.8%	93.7%	6.2%	0%	0%	0%	0%	6
96.9%	96.8%	3.1%	0%	0%	0%	0%	7
98.4%	98.4%	1.6%	0%	0%	0%	0%	8
99.2%	99.2%	0.8%	0%	0%	0%	0%	9
99.6%	99.6%	0.4%	0%	0%	0%	0%	10
99.8%	99.8%	0.2%	0%	0%	0%	0%	11
99.9%	99.9%	0.1%	0%	0%	0%	0%	12

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample1.3s (39.2%)

Results

1.3s

8256×

body

256

valid

Bogosity

preprocess25.0ms (0.7%)

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)

simplify12.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

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)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite66.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

Inputs
(+.f64 x -1/3)

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

Outputs

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

simplify13.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

42 → 34

Calls

Call 1

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

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

eval86.0ms (2.6%)

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

prune9.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	30	4	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	5	35

Error

Counts

35 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	13.6b	(/.f64 1 (/.f64 (+.f64 x 1/3) (fma.f64 x x -1/9)))
✓	0.0b	(+.f64 x -1/3)
▶	13.6b	(-.f64 (/.f64 (*.f64 x x) (+.f64 x 1/3)) (/.f64 1/9 (+.f64 x 1/3)))
	32.9b	x
	30.7b	-1/3

Compiler

Compiled 33 to 24 computations (27.3% saved)

localize25.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (*.f64 x x) (+.f64 x 1/3)) (/.f64 1/9 (+.f64 x 1/3)))
✓	0.0b	(+.f64 x 1/3)
✓	0.2b	(/.f64 1/9 (+.f64 x 1/3))
✓	12.7b	(/.f64 (*.f64 x x) (+.f64 x 1/3))

Compiler

Compiled 35 to 21 computations (40% saved)

series9.0ms (0.3%)

Counts

4 → 48

Calls

12 calls:

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

rewrite171.0ms (5.1%)

Algorithm

1×	batch-egg-rewrite

Rules

512×	`log-prod_binary64`
435×	`fma-def_binary64`
376×	`pow-prod-down_binary64`
283×	`pow2_binary64`
268×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	34
1	219	25
2	3391	25

Stop Event

1×	node limit

Counts

4 → 293

Calls

Call 1

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

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

simplify111.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

626×	`fma-def_binary64`
486×	`fma-neg_binary64`
423×	`cancel-sign-sub-inv_binary64`
417×	`times-frac_binary64`
287×	`associate-*r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	57	397
1	154	392
2	388	388
3	1115	376
4	3344	376

Stop Event

1×	node limit

Counts

341 → 324

Calls

Call 1

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

localize52.0ms (1.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x -1/9)
	0.0b	(+.f64 x 1/3)
✓	0.1b	(/.f64 1 (/.f64 (+.f64 x 1/3) (fma.f64 x x -1/9)))
✓	12.6b	(/.f64 (+.f64 x 1/3) (fma.f64 x x -1/9))

Compiler

Compiled 30 to 20 computations (33.3% saved)

series6.0ms (0.2%)

Counts

3 → 36

Calls

9 calls:

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

rewrite115.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	30
1	199	16
2	2563	16

Stop Event

1×	node limit

Counts

3 → 156

Calls

Call 1

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

Outputs

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

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

simplify82.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×	node limit

Counts

192 → 177

Calls

Call 1

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

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

eval652.0ms (19.4%)

Compiler: Compiled 9941 to 7312 computations (26.4% saved)

prune139.0ms (4.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	579	2	581
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	581	5	586

Error

Counts

586 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.4b	(/.f64 1 (/.f64 (+.f64 x 1/3) -1/9))
	32.9b	x
✓	0.0b	(+.f64 x -1/3)
✓	13.6b	(-.f64 (/.f64 (*.f64 x x) (+.f64 x 1/3)) (/.f64 1/9 (+.f64 x 1/3)))
	30.7b	-1/3

Compiler

Compiled 30 to 23 computations (23.3% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 20 to 16 computations (20% saved)

series4.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite150.0ms (4.5%)

Algorithm

1×	batch-egg-rewrite

Rules

848×	`pow1_binary64`
798×	`add-log-exp_binary64`
798×	`log1p-expm1-u_binary64`
798×	`expm1-log1p-u_binary64`
785×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	180	14
2	2200	14

Stop Event

1×	node limit

Counts

2 → 48

Calls

Call 1

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

Outputs

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

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

simplify64.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

720×	`associate-l_binary64`
691×	`fma-def_binary64`
512×	`associate-r_binary64`
410×	`times-frac_binary64`
377×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	43	228
1	110	228
2	251	228
3	656	223
4	1977	223
5	7682	223

Stop Event

1×	node limit

Counts

72 → 66

Calls

Call 1

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

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

eval32.0ms (1%)

Compiler: Compiled 1161 to 966 computations (16.8% saved)

prune44.0ms (1.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	106	5	111

Error

Counts

111 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	30.4b	(/.f64 1 (/.f64 (+.f64 x 1/3) -1/9))
	32.9b	x
✓	0.0b	(+.f64 x -1/3)
✓	13.6b	(-.f64 (/.f64 (*.f64 x x) (+.f64 x 1/3)) (/.f64 1/9 (+.f64 x 1/3)))
	30.7b	-1/3

Compiler

Compiled 30 to 23 computations (23.3% saved)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

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

Error

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	30.4b	(/.f64 1 (/.f64 (+.f64 x 1/3) -1/9))
	32.9b	x
✓	0.0b	(+.f64 x -1/3)
✓	13.6b	(-.f64 (/.f64 (*.f64 x x) (+.f64 x 1/3)) (/.f64 1/9 (+.f64 x 1/3)))
	30.7b	-1/3

Compiler

Compiled 30 to 23 computations (23.3% saved)

regimes48.0ms (1.4%)

Counts

8 → 1

Calls

Call 1

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

Outputs
(+.f64 x -1/3)

Calls

3 calls:

37.0ms	x
4.0ms	(-.f64 x (/.f64 1 3))
4.0ms	(-.f64 x (/.f64 1 3))

Results

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

Compiler

Compiled 56 to 41 computations (26.8% saved)

regimes13.0ms (0.4%)

Counts

3 → 3

Calls

Call 1

Inputs
x
x
-1/3

Outputs
x
-1/3
x

Calls

1 calls:

12.0ms

Results

Error	Segments	Branch
2.0b	3	`x`

Compiler

Compiled 6 to 3 computations (50% saved)

bsearch50.0ms (1.5%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
35.0ms	0.13137983386600421	4.597083892091637
14.0ms	-59635613030762.45	-5.203651412372695e-5

Compiler

Compiled 10 to 8 computations (20% saved)

regimes4.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0.0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
x
x

Outputs
x

Calls

1 calls:

3.0ms

Results

Error	Segments	Branch
32.9b	1	`x`

Compiler

Compiled 5 to 2 computations (60% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	12	20

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 x -1/3)
(if (<=.f64 x -3816679233968797/64) x (if (<=.f64 x 2366728683371737/18014398509481984) -1/3 x))
x

Outputs
(+.f64 x -1/3)
(if (<=.f64 x -3816679233968797/64) x (if (<=.f64 x 2366728683371737/18014398509481984) -1/3 x))
x

Compiler

Compiled 18 to 12 computations (33.3% saved)

soundness10.0ms (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

Compiler

Compiled 22 to 18 computations (18.2% saved)

end23.0ms (0.7%)

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

Details

analyze5.0ms (0.1%)

sample1.3s (39.2%)

preprocess25.0ms (0.7%)

simplify12.0ms (0.4%)

eval1.0ms (0%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series2.0ms (0%)

rewrite66.0ms (2%)

simplify13.0ms (0.4%)

eval86.0ms (2.6%)

prune9.0ms (0.3%)

localize25.0ms (0.7%)

series9.0ms (0.3%)

rewrite171.0ms (5.1%)

simplify111.0ms (3.3%)

localize52.0ms (1.5%)

series6.0ms (0.2%)

rewrite115.0ms (3.4%)

simplify82.0ms (2.4%)

eval652.0ms (19.4%)

prune139.0ms (4.1%)

localize9.0ms (0.3%)

series4.0ms (0.1%)

rewrite150.0ms (4.5%)

simplify64.0ms (1.9%)

eval32.0ms (1%)

prune44.0ms (1.3%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes48.0ms (1.4%)

regimes13.0ms (0.4%)

bsearch50.0ms (1.5%)

regimes4.0ms (0.1%)

simplify5.0ms (0.1%)

soundness10.0ms (0.3%)

end23.0ms (0.7%)

Profiling