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)

sample674.0ms (14.2%)

Results

660.0ms

8256×

body

256

valid

preprocess15.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	10	4
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	10	4

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

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

Compiler

Compiled 4 to 3 computations (25% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 6 to 4 computations (33.3% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite87.0ms (1.8%)

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	1150	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)))))

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	39
1	5	39

Stop Event

1×

saturated

Counts

42 → 33

Calls

Call 1

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

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

eval11.0ms (0.2%)

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

prune6.0ms (0.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	29	4	33
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	5	34

Error

0.0b

Counts

34 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	19.8b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3))))
	31.8b	1/3
▶	14.3b	(-.f64 (/.f64 (*.f64 x x) (+.f64 x -1/3)) (/.f64 1/9 (+.f64 x -1/3)))
	31.9b	x
✓	0.0b	(+.f64 x 1/3)

Compiler

Compiled 38 to 28 computations (26.3% saved)

localize13.0ms (0.3%)

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))
✓	13.4b	(/.f64 (*.f64 x x) (+.f64 x -1/3))

Compiler

Compiled 35 to 21 computations (40% saved)

series8.0ms (0.2%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(/.f64 (*.f64 x x) (+.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 (*.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	@	inf	(/.f64 (*.f64 x x) (+.f64 x -1/3))

rewrite115.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

512×	`log-prod_binary64`
435×	`fma-def_binary64`
375×	`pow-prod-down_binary64`
284×	`pow2_binary64`
268×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	34
1	221	25
2	3411	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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#<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 (/.f64 1 (+.f64 x -1/3))) 1/9 (/.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 (/.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))))))

simplify70.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

899×	`fma-neg_binary64`
682×	`cancel-sign-sub-inv_binary64`
651×	`associate-/r*_binary64`
584×	`fma-def_binary64`
259×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	57	396
1	146	394
2	336	387
3	948	376
4	2744	376
5	6996	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 -27 (pow.f64 x 4)) (+.f64 (.f64 -3 (pow.f64 x 2)) (*.f64 -9 (pow.f64 x 3))))
(+.f64 (.f64 -27 (pow.f64 x 4)) (+.f64 (.f64 -3 (pow.f64 x 2)) (+.f64 (.f64 -9 (pow.f64 x 3)) (.f64 -81 (pow.f64 x 5)))))
x
(+.f64 1/3 x)
(+.f64 1/3 (+.f64 (*.f64 1/9 (/.f64 1 x)) x))
(+.f64 1/3 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/9 (/.f64 1 x)) x)))
x
(+.f64 1/3 x)
(+.f64 1/3 (+.f64 (*.f64 1/9 (/.f64 1 x)) x))
(+.f64 1/3 (+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 2))) (+.f64 (.f64 1/9 (/.f64 1 x)) x)))
-1/3
(-.f64 (*.f64 -1 x) 1/3)
(-.f64 (+.f64 (.f64 -3 (pow.f64 x 2)) (.f64 -1 x)) 1/3)
(-.f64 (+.f64 (.f64 -3 (pow.f64 x 2)) (+.f64 (.f64 -1 x) (*.f64 -9 (pow.f64 x 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 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (*.f64 1/27 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (.f64 1/243 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (.f64 1/27 (/.f64 1 (pow.f64 x 2))))))
(/.f64 1/9 x)
(+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/9 (/.f64 1 x)))
(+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (*.f64 1/27 (/.f64 1 (pow.f64 x 2)))))
(+.f64 (.f64 1/243 (/.f64 1 (pow.f64 x 4))) (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/9 (/.f64 1 x)) (.f64 1/27 (/.f64 1 (pow.f64 x 2))))))
-1/3
(-.f64 x 1/3)
(-.f64 x 1/3)
(-.f64 x 1/3)
x
(-.f64 x 1/3)
(-.f64 x 1/3)
(-.f64 x 1/3)
x
(-.f64 x 1/3)
(-.f64 x 1/3)
(-.f64 x 1/3)
1/3
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)

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

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/27 (pow.f64 x 3))
✓	0.0b	(-.f64 (.f64 x x) (.f64 x 1/3))
✓	0.3b	(*.f64 x 1/3)
✓	19.1b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3))))

Compiler

Compiled 51 to 32 computations (37.3% saved)

series6.0ms (0.1%)

Counts

4 → 39

Calls

12 calls:

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

rewrite126.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

987×	`prod-diff_binary64`
639×	`fma-def_binary64`
275×	`fma-neg_binary64`
251×	`expm1-udef_binary64`
251×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	37
1	316	35
2	4212	35

Stop Event

1×	node limit

Counts

4 → 293

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x (+.f64 x -1/3) 1/9)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1/27 (pow.f64 x 3)) (/.f64 1 (fma.f64 x (+.f64 x -1/3) 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x (+.f64 x -1/3) 1/9)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x (+.f64 x -1/3) 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 1/27 (pow.f64 x 3))) 2) (.f64 (cbrt.f64 (+.f64 1/27 (pow.f64 x 3))) (/.f64 1 (fma.f64 x (+.f64 x -1/3) 1/9))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x (+.f64 x -1/3) 1/9))) (pow.f64 (cbrt.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x (+.f64 x -1/3) 1/9))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (/.f64 (+.f64 1/27 (pow.f64 x 3)) (fma.f64 x 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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 1/27 (pow.f64 x 3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1/729 (-.f64 1/27 (pow.f64 x 3))) (/.f64 (pow.f64 x 6) (-.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1/27 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 1/27 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 1/27 (pow.f64 x 3))) (pow.f64 (cbrt.f64 (+.f64 1/27 (pow.f64 x 3))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 1/27 (pow.f64 x 3))) 2) (cbrt.f64 (+.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (+.f64 1/27 (pow.f64 x 3))) (sqrt.f64 (+.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 1/19683 (pow.f64 x 9)) (/.f64 1 (fma.f64 (pow.f64 x 3) (-.f64 (pow.f64 x 3) 1/27) 1/729)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 1/729 (pow.f64 x 6)) (/.f64 1 (-.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (fma.f64 (pow.f64 x 3) (-.f64 (pow.f64 x 3) 1/27) 1/729) (+.f64 1/19683 (pow.f64 x 9))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 1/27 (pow.f64 x 3)) (-.f64 1/729 (pow.f64 x 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/19683 (pow.f64 x 9)) (fma.f64 (pow.f64 x 3) (-.f64 (pow.f64 x 3) 1/27) 1/729))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1/19683 (pow.f64 x 9)) (+.f64 (pow.f64 x 6) (-.f64 1/729 (pow.f64 (.f64 x 1/3) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1/729 (pow.f64 x 6)) (-.f64 1/27 (pow.f64 x 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1/19683 (pow.f64 x 9))) (neg.f64 (fma.f64 (pow.f64 x 3) (-.f64 (pow.f64 x 3) 1/27) 1/729)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1/729 (pow.f64 x 6))) (neg.f64 (-.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 6) 1/729) (-.f64 (pow.f64 x 3) 1/27))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 1/27 (pow.f64 x 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 1/27 (pow.f64 x 3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 1/27 (pow.f64 x 3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 1/27 (pow.f64 x 3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 1/27 (pow.f64 x 3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 1/27 (pow.f64 x 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 1/27 (pow.f64 x 3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (+.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 1/27 (pow.f64 x 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (+.f64 1/27 (pow.f64 x 3))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x (.f64 x x) 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3) 1 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x x) x 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 x 3) 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (.f64 (cbrt.f64 x) (.f64 x x)) 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (.f64 (pow.f64 (cbrt.f64 x) 2) x) 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (.f64 x x)) 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 x 3/2) (pow.f64 x 3/2) 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (sqrt.f64 x) 3) (pow.f64 (sqrt.f64 x) 3) 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 x (cbrt.f64 (pow.f64 x 4))) (pow.f64 (cbrt.f64 x) 2) 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (.f64 x x) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) 1/27)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (.f64 (*.f64 x x) (sqrt.f64 x)) (sqrt.f64 x) 1/27)))))

simplify184.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

1192×	`sqr-pow_binary64`
561×	`cube-prod_binary64`
536×	`unswap-sqr_binary64`
536×	`fabs-mul_binary64`
498×	`pow-sqr_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	180
1	30	171
2	50	171
3	94	171
4	214	171
5	743	171
6	1971	171
7	2197	171
8	2435	171
9	2716	171
10	3094	171
11	3593	171
12	4187	171
13	4897	171
14	5368	171
15	5695	171
16	5967	171
17	6137	171
18	6227	171
19	6904	171
20	7938	171

Stop Event

1×	node limit

Counts

332 → 304

Calls

Call 1

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

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

eval345.0ms (7.3%)

Compiler: Compiled 14624 to 10466 computations (28.4% saved)

prune148.0ms (3.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	664	4	668
Fresh	1	1	2
Picked	1	0	1
Done	1	1	2
Total	667	6	673

Error

Counts

673 → 6

Alt Table

Click to see full alt table

Status	Error	Program
	31.8b	1/3
✓	0.0b	(+.f64 x 1/3)
▶	14.5b	(/.f64 (-.f64 (.f64 x (.f64 (+.f64 x -1/3) 9)) (.f64 (/.f64 (+.f64 x -1/3) x) 1)) (.f64 (/.f64 (+.f64 x -1/3) x) (*.f64 (+.f64 x -1/3) 9)))
	31.9b	x
▶	31.3b	(/.f64 1/27 (+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3))))
▶	19.8b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (*.f64 (+.f64 x -1/3) x)))

Compiler

Compiled 62 to 47 computations (24.2% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3)))
	0.0b	(-.f64 (.f64 x x) (.f64 x 1/3))
✓	0.1b	(/.f64 1/27 (+.f64 1/9 (-.f64 (.f64 x x) (.f64 x 1/3))))
	0.3b	(*.f64 x 1/3)

Compiler

Compiled 38 to 22 computations (42.1% saved)

series4.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite77.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

910×	`prod-diff_binary64`
557×	`fma-def_binary64`
499×	`log-prod_binary64`
241×	`fma-neg_binary64`
199×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	240	19
2	3203	19

Stop Event

1×	node limit

Counts

2 → 120

Calls

Call 1

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

Outputs

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

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

simplify68.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

926×	`fma-neg_binary64`
573×	`associate-*r/_binary64`
555×	`associate-*l/_binary64`
492×	`unswap-sqr_binary64`
323×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	46	296
1	113	286
2	283	274
3	739	274
4	2866	274
5	7741	266

Stop Event

1×	node limit

Counts

144 → 142

Calls

Call 1

Inputs
1/3
(+.f64 1/3 x)
(+.f64 1/3 (+.f64 (*.f64 -9 (pow.f64 x 3)) x))
(+.f64 (.f64 -27 (pow.f64 x 4)) (+.f64 1/3 (+.f64 (.f64 -9 (pow.f64 x 3)) x)))
(/.f64 1/27 (pow.f64 x 2))
(+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/81 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))) (*.f64 1/729 (/.f64 1 (pow.f64 x 5))))
(-.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 1/729 (/.f64 1 (pow.f64 x 5))) (.f64 1/2187 (/.f64 1 (pow.f64 x 6)))))
(/.f64 1/27 (pow.f64 x 2))
(+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/81 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))) (*.f64 1/729 (/.f64 1 (pow.f64 x 5))))
(-.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 1/729 (/.f64 1 (pow.f64 x 5))) (.f64 1/2187 (/.f64 1 (pow.f64 x 6)))))
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 1/3 x)
(+.f64 1/3 (+.f64 (*.f64 -9 (pow.f64 x 3)) x))
(+.f64 1/3 (fma.f64 -9 (pow.f64 x 3) x))
(+.f64 (.f64 -27 (pow.f64 x 4)) (+.f64 1/3 (+.f64 (.f64 -9 (pow.f64 x 3)) x)))
(fma.f64 -27 (pow.f64 x 4) (+.f64 1/3 (fma.f64 -9 (pow.f64 x 3) x)))
(+.f64 (fma.f64 -9 (pow.f64 x 3) x) (fma.f64 -27 (pow.f64 x 4) 1/3))
(+.f64 x (fma.f64 -27 (pow.f64 x 4) (fma.f64 -9 (pow.f64 x 3) 1/3)))
(+.f64 x (fma.f64 -9 (pow.f64 x 3) (fma.f64 -27 (pow.f64 x 4) 1/3)))
(+.f64 1/3 (fma.f64 -9 (pow.f64 x 3) (fma.f64 -27 (pow.f64 x 4) x)))
(/.f64 1/27 (pow.f64 x 2))
(/.f64 1/27 (*.f64 x x))
(+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/81 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.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 1/27 (/.f64 1 (pow.f64 x 2)))) (*.f64 1/729 (/.f64 1 (pow.f64 x 5))))
(+.f64 (/.f64 1/81 (pow.f64 x 3)) (-.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/729 (pow.f64 x 5))))
(+.f64 (/.f64 1/27 (*.f64 x x)) (-.f64 (/.f64 1/81 (pow.f64 x 3)) (/.f64 1/729 (pow.f64 x 5))))
(+.f64 (/.f64 1/27 (*.f64 x x)) (+.f64 (/.f64 1/81 (pow.f64 x 3)) (/.f64 -1/729 (pow.f64 x 5))))
(fma.f64 (/.f64 (/.f64 1 x) x) (+.f64 1/27 (/.f64 1/81 x)) (/.f64 -1/729 (pow.f64 x 5)))
(-.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 1/729 (/.f64 1 (pow.f64 x 5))) (.f64 1/2187 (/.f64 1 (pow.f64 x 6)))))
(+.f64 (/.f64 1/81 (pow.f64 x 3)) (-.f64 (/.f64 1/27 (*.f64 x x)) (+.f64 (/.f64 1/729 (pow.f64 x 5)) (/.f64 1/2187 (pow.f64 x 6)))))
(+.f64 (/.f64 1/81 (pow.f64 x 3)) (-.f64 (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 -1/729 (pow.f64 x 5))) (/.f64 1/2187 (pow.f64 x 6))))
(+.f64 (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/81 (pow.f64 x 3))) (+.f64 (/.f64 -1/729 (pow.f64 x 5)) (/.f64 -1/2187 (pow.f64 x 6))))
(+.f64 (/.f64 1/27 (*.f64 x x)) (+.f64 (/.f64 1/81 (pow.f64 x 3)) (-.f64 (/.f64 -1/729 (pow.f64 x 5)) (/.f64 1/2187 (pow.f64 x 6)))))
(+.f64 (fma.f64 (/.f64 (/.f64 1 x) x) (+.f64 1/27 (/.f64 1/81 x)) (/.f64 -1/729 (pow.f64 x 5))) (/.f64 -1/2187 (pow.f64 x 6)))
(/.f64 1/27 (pow.f64 x 2))
(/.f64 1/27 (*.f64 x x))
(+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/81 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.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 1/27 (/.f64 1 (pow.f64 x 2)))) (*.f64 1/729 (/.f64 1 (pow.f64 x 5))))
(+.f64 (/.f64 1/81 (pow.f64 x 3)) (-.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/729 (pow.f64 x 5))))
(+.f64 (/.f64 1/27 (*.f64 x x)) (-.f64 (/.f64 1/81 (pow.f64 x 3)) (/.f64 1/729 (pow.f64 x 5))))
(+.f64 (/.f64 1/27 (*.f64 x x)) (+.f64 (/.f64 1/81 (pow.f64 x 3)) (/.f64 -1/729 (pow.f64 x 5))))
(fma.f64 (/.f64 (/.f64 1 x) x) (+.f64 1/27 (/.f64 1/81 x)) (/.f64 -1/729 (pow.f64 x 5)))
(-.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 1/729 (/.f64 1 (pow.f64 x 5))) (.f64 1/2187 (/.f64 1 (pow.f64 x 6)))))
(+.f64 (/.f64 1/81 (pow.f64 x 3)) (-.f64 (/.f64 1/27 (*.f64 x x)) (+.f64 (/.f64 1/729 (pow.f64 x 5)) (/.f64 1/2187 (pow.f64 x 6)))))
(+.f64 (/.f64 1/81 (pow.f64 x 3)) (-.f64 (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 -1/729 (pow.f64 x 5))) (/.f64 1/2187 (pow.f64 x 6))))
(+.f64 (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/81 (pow.f64 x 3))) (+.f64 (/.f64 -1/729 (pow.f64 x 5)) (/.f64 -1/2187 (pow.f64 x 6))))
(+.f64 (/.f64 1/27 (*.f64 x x)) (+.f64 (/.f64 1/81 (pow.f64 x 3)) (-.f64 (/.f64 -1/729 (pow.f64 x 5)) (/.f64 1/2187 (pow.f64 x 6)))))
(+.f64 (fma.f64 (/.f64 (/.f64 1 x) x) (+.f64 1/27 (/.f64 1/81 x)) (/.f64 -1/729 (pow.f64 x 5))) (/.f64 -1/2187 (pow.f64 x 6)))
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)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 x -1/3)
	0.0b	(+.f64 1/27 (pow.f64 x 3))
✓	0.2b	(*.f64 (+.f64 x -1/3) x)
✓	19.1b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (*.f64 (+.f64 x -1/3) x)))

Compiler

Compiled 42 to 31 computations (26.2% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite90.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

577×	`log-prod_binary64`
342×	`pow2_binary64`
309×	`fma-def_binary64`
293×	`prod-diff_binary64`
236×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	285	24
2	3665	24

Stop Event

1×	node limit

Counts

2 → 80

Calls

Call 1

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

Outputs

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

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

simplify180.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

1082×	`sqr-pow_binary64`
560×	`cube-prod_binary64`
554×	`fabs-mul_binary64`
523×	`pow-sqr_binary64`
497×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	123
1	18	114
2	32	114
3	55	114
4	112	114
5	315	114
6	1046	114
7	2214	114
8	2567	114
9	2759	114
10	2969	114
11	3279	114
12	3689	114
13	4172	114
14	4746	114
15	5436	114
16	6282	114
17	6679	114
18	6965	114
19	7243	114
20	7317	114
21	7351	114

Stop Event

1×	node limit

Counts

104 → 89

Calls

Call 1

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

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

localize34.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x (.f64 (+.f64 x -1/3) 9))
✓	0.1b	(.f64 (/.f64 (+.f64 x -1/3) x) (.f64 (+.f64 x -1/3) 9))
✓	0.2b	(/.f64 (+.f64 x -1/3) x)
✓	13.5b	(/.f64 (-.f64 (.f64 x (.f64 (+.f64 x -1/3) 9)) (.f64 (/.f64 (+.f64 x -1/3) x) 1)) (.f64 (/.f64 (+.f64 x -1/3) x) (*.f64 (+.f64 x -1/3) 9)))

Compiler

Compiled 85 to 62 computations (27.1% saved)

series6.0ms (0.1%)

Counts

4 → 48

Calls

12 calls:

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

rewrite108.0ms (2.3%)

Algorithm

1×	batch-egg-rewrite

Rules

872×	`log-prod_binary64`
568×	`fma-def_binary64`
328×	`fma-neg_binary64`
293×	`log-div_binary64`
254×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	70
1	317	64
2	4661	59

Stop Event

1×	node limit

Counts

4 → 172

Calls

Call 1

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

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

simplify68.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary64`
572×	`associate-/l/_binary64`
535×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
411×	`associate-*l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	320
1	51	320
2	80	311
3	137	293
4	298	293
5	814	293
6	2880	293
7	7118	293

Stop Event

1×	node limit

Counts

220 → 194

Calls

Call 1

Inputs
1/3
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
(/.f64 -1/3 x)
(-.f64 1 (*.f64 1/3 (/.f64 1 x)))
(-.f64 1 (*.f64 1/3 (/.f64 1 x)))
(-.f64 1 (*.f64 1/3 (/.f64 1 x)))
1
(-.f64 1 (*.f64 1/3 (/.f64 1 x)))
(-.f64 1 (*.f64 1/3 (/.f64 1 x)))
(-.f64 1 (*.f64 1/3 (/.f64 1 x)))
1
(-.f64 1 (*.f64 1/3 (/.f64 1 x)))
(-.f64 1 (*.f64 1/3 (/.f64 1 x)))
(-.f64 1 (*.f64 1/3 (/.f64 1 x)))
(/.f64 1 x)
(-.f64 (/.f64 1 x) 6)
(-.f64 (+.f64 (/.f64 1 x) (*.f64 9 x)) 6)
(-.f64 (+.f64 (/.f64 1 x) (*.f64 9 x)) 6)
(*.f64 9 x)
(-.f64 (*.f64 9 x) 6)
(-.f64 (+.f64 (/.f64 1 x) (*.f64 9 x)) 6)
(-.f64 (+.f64 (/.f64 1 x) (*.f64 9 x)) 6)
(*.f64 9 x)
(-.f64 (*.f64 9 x) 6)
(-.f64 (+.f64 (/.f64 1 x) (*.f64 9 x)) 6)
(-.f64 (+.f64 (/.f64 1 x) (*.f64 9 x)) 6)
(*.f64 -3 x)
(+.f64 (.f64 -3 x) (.f64 9 (pow.f64 x 2)))
(+.f64 (.f64 -3 x) (.f64 9 (pow.f64 x 2)))
(+.f64 (.f64 -3 x) (.f64 9 (pow.f64 x 2)))
(*.f64 9 (pow.f64 x 2))
(+.f64 (.f64 -3 x) (.f64 9 (pow.f64 x 2)))
(+.f64 (.f64 -3 x) (.f64 9 (pow.f64 x 2)))
(+.f64 (.f64 -3 x) (.f64 9 (pow.f64 x 2)))
(*.f64 9 (pow.f64 x 2))
(+.f64 (.f64 -3 x) (.f64 9 (pow.f64 x 2)))
(+.f64 (.f64 -3 x) (.f64 9 (pow.f64 x 2)))
(+.f64 (.f64 -3 x) (.f64 9 (pow.f64 x 2)))

Outputs
1/3
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
x
(+.f64 1/3 x)
(+.f64 1/3 x)
(+.f64 1/3 x)
(/.f64 -1/3 x)
(-.f64 1 (*.f64 1/3 (/.f64 1 x)))
(-.f64 1 (/.f64 1/3 x))
(+.f64 1 (/.f64 -1/3 x))
(-.f64 1 (*.f64 1/3 (/.f64 1 x)))
(-.f64 1 (/.f64 1/3 x))
(+.f64 1 (/.f64 -1/3 x))
(-.f64 1 (*.f64 1/3 (/.f64 1 x)))
(-.f64 1 (/.f64 1/3 x))
(+.f64 1 (/.f64 -1/3 x))
1
(-.f64 1 (*.f64 1/3 (/.f64 1 x)))
(-.f64 1 (/.f64 1/3 x))
(+.f64 1 (/.f64 -1/3 x))
(-.f64 1 (*.f64 1/3 (/.f64 1 x)))
(-.f64 1 (/.f64 1/3 x))
(+.f64 1 (/.f64 -1/3 x))
(-.f64 1 (*.f64 1/3 (/.f64 1 x)))
(-.f64 1 (/.f64 1/3 x))
(+.f64 1 (/.f64 -1/3 x))
1
(-.f64 1 (*.f64 1/3 (/.f64 1 x)))
(-.f64 1 (/.f64 1/3 x))
(+.f64 1 (/.f64 -1/3 x))
(-.f64 1 (*.f64 1/3 (/.f64 1 x)))
(-.f64 1 (/.f64 1/3 x))
(+.f64 1 (/.f64 -1/3 x))
(-.f64 1 (*.f64 1/3 (/.f64 1 x)))
(-.f64 1 (/.f64 1/3 x))
(+.f64 1 (/.f64 -1/3 x))
(/.f64 1 x)
(-.f64 (/.f64 1 x) 6)
(+.f64 (/.f64 1 x) -6)
(-.f64 -6 (/.f64 -1 x))
(-.f64 (+.f64 (/.f64 1 x) (*.f64 9 x)) 6)
(+.f64 (/.f64 1 x) (fma.f64 9 x -6))
(+.f64 (/.f64 1 x) (fma.f64 x 9 -6))
(+.f64 (fma.f64 x 9 (/.f64 1 x)) -6)
(-.f64 (+.f64 (/.f64 1 x) (*.f64 9 x)) 6)
(+.f64 (/.f64 1 x) (fma.f64 9 x -6))
(+.f64 (/.f64 1 x) (fma.f64 x 9 -6))
(+.f64 (fma.f64 x 9 (/.f64 1 x)) -6)
(*.f64 9 x)
(*.f64 x 9)
(-.f64 (*.f64 9 x) 6)
(fma.f64 9 x -6)
(fma.f64 x 9 -6)
(-.f64 (+.f64 (/.f64 1 x) (*.f64 9 x)) 6)
(+.f64 (/.f64 1 x) (fma.f64 9 x -6))
(+.f64 (/.f64 1 x) (fma.f64 x 9 -6))
(+.f64 (fma.f64 x 9 (/.f64 1 x)) -6)
(-.f64 (+.f64 (/.f64 1 x) (*.f64 9 x)) 6)
(+.f64 (/.f64 1 x) (fma.f64 9 x -6))
(+.f64 (/.f64 1 x) (fma.f64 x 9 -6))
(+.f64 (fma.f64 x 9 (/.f64 1 x)) -6)
(*.f64 9 x)
(*.f64 x 9)
(-.f64 (*.f64 9 x) 6)
(fma.f64 9 x -6)
(fma.f64 x 9 -6)
(-.f64 (+.f64 (/.f64 1 x) (*.f64 9 x)) 6)
(+.f64 (/.f64 1 x) (fma.f64 9 x -6))
(+.f64 (/.f64 1 x) (fma.f64 x 9 -6))
(+.f64 (fma.f64 x 9 (/.f64 1 x)) -6)
(-.f64 (+.f64 (/.f64 1 x) (*.f64 9 x)) 6)
(+.f64 (/.f64 1 x) (fma.f64 9 x -6))
(+.f64 (/.f64 1 x) (fma.f64 x 9 -6))
(+.f64 (fma.f64 x 9 (/.f64 1 x)) -6)
(*.f64 -3 x)
(*.f64 x -3)
(+.f64 (.f64 -3 x) (.f64 9 (pow.f64 x 2)))
(fma.f64 -3 x (.f64 9 (.f64 x x)))
(fma.f64 x -3 (.f64 x (.f64 x 9)))
(.f64 x (+.f64 -3 (.f64 x 9)))
(*.f64 x (fma.f64 x 9 -3))
(+.f64 (.f64 -3 x) (.f64 9 (pow.f64 x 2)))
(fma.f64 -3 x (.f64 9 (.f64 x x)))
(fma.f64 x -3 (.f64 x (.f64 x 9)))
(.f64 x (+.f64 -3 (.f64 x 9)))
(*.f64 x (fma.f64 x 9 -3))
(+.f64 (.f64 -3 x) (.f64 9 (pow.f64 x 2)))
(fma.f64 -3 x (.f64 9 (.f64 x x)))
(fma.f64 x -3 (.f64 x (.f64 x 9)))
(.f64 x (+.f64 -3 (.f64 x 9)))
(*.f64 x (fma.f64 x 9 -3))
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(.f64 x (.f64 x 9))
(+.f64 (.f64 -3 x) (.f64 9 (pow.f64 x 2)))
(fma.f64 -3 x (.f64 9 (.f64 x x)))
(fma.f64 x -3 (.f64 x (.f64 x 9)))
(.f64 x (+.f64 -3 (.f64 x 9)))
(*.f64 x (fma.f64 x 9 -3))
(+.f64 (.f64 -3 x) (.f64 9 (pow.f64 x 2)))
(fma.f64 -3 x (.f64 9 (.f64 x x)))
(fma.f64 x -3 (.f64 x (.f64 x 9)))
(.f64 x (+.f64 -3 (.f64 x 9)))
(*.f64 x (fma.f64 x 9 -3))
(+.f64 (.f64 -3 x) (.f64 9 (pow.f64 x 2)))
(fma.f64 -3 x (.f64 9 (.f64 x x)))
(fma.f64 x -3 (.f64 x (.f64 x 9)))
(.f64 x (+.f64 -3 (.f64 x 9)))
(*.f64 x (fma.f64 x 9 -3))
(*.f64 9 (pow.f64 x 2))
(.f64 9 (.f64 x x))
(.f64 x (.f64 x 9))
(+.f64 (.f64 -3 x) (.f64 9 (pow.f64 x 2)))
(fma.f64 -3 x (.f64 9 (.f64 x x)))
(fma.f64 x -3 (.f64 x (.f64 x 9)))
(.f64 x (+.f64 -3 (.f64 x 9)))
(*.f64 x (fma.f64 x 9 -3))
(+.f64 (.f64 -3 x) (.f64 9 (pow.f64 x 2)))
(fma.f64 -3 x (.f64 9 (.f64 x x)))
(fma.f64 x -3 (.f64 x (.f64 x 9)))
(.f64 x (+.f64 -3 (.f64 x 9)))
(*.f64 x (fma.f64 x 9 -3))
(+.f64 (.f64 -3 x) (.f64 9 (pow.f64 x 2)))
(fma.f64 -3 x (.f64 9 (.f64 x x)))
(fma.f64 x -3 (.f64 x (.f64 x 9)))
(.f64 x (+.f64 -3 (.f64 x 9)))
(*.f64 x (fma.f64 x 9 -3))

eval750.0ms (15.8%)

Compiler: Compiled 18016 to 13333 computations (26% saved)

prune392.0ms (8.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	770	4	774
Fresh	2	0	2
Picked	1	0	1
Done	1	2	3
Total	774	6	780

Error

Counts

780 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	31.3b	(/.f64 1/27 (+.f64 1/9 (*.f64 (+.f64 x -1/3) x)))
▶	31.1b	(/.f64 (-.f64 (.f64 x -3) (.f64 (/.f64 (+.f64 x -1/3) x) 1)) (.f64 (/.f64 (+.f64 x -1/3) x) (.f64 (+.f64 x -1/3) 9)))
✓	19.8b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (*.f64 (+.f64 x -1/3) x)))
	31.8b	1/3
	31.9b	x
✓	0.0b	(+.f64 x 1/3)

Compiler

Compiled 56 to 43 computations (23.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1/9 (*.f64 (+.f64 x -1/3) x))
	0.0b	(+.f64 x -1/3)
✓	0.1b	(/.f64 1/27 (+.f64 1/9 (*.f64 (+.f64 x -1/3) x)))
	0.2b	(*.f64 (+.f64 x -1/3) x)

Compiler

Compiled 29 to 21 computations (27.6% saved)

series2.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite78.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

565×	`unpow-prod-down_binary64`
417×	`log-prod_binary64`
322×	`exp-prod_binary64`
254×	`pow2_binary64`
242×	`pow-prod-down_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	208	19
2	2644	19

Stop Event

1×	node limit

Counts

2 → 111

Calls

Call 1

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

Outputs

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

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

simplify192.0ms (4%)

Algorithm

1×	egg-herbie

Rules

926×	`fma-neg_binary64`
573×	`associate-*r/_binary64`
555×	`associate-*l/_binary64`
492×	`unswap-sqr_binary64`
323×	`distribute-neg-frac_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	46	296
1	113	286
2	283	274
3	739	274
4	2866	274
5	7741	266

Stop Event

1×	node limit

Counts

135 → 133

Calls

Call 1

Inputs
1/3
(+.f64 1/3 x)
(+.f64 1/3 (+.f64 (*.f64 -9 (pow.f64 x 3)) x))
(+.f64 (.f64 -27 (pow.f64 x 4)) (+.f64 1/3 (+.f64 (.f64 -9 (pow.f64 x 3)) x)))
(/.f64 1/27 (pow.f64 x 2))
(+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/81 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))) (*.f64 1/729 (/.f64 1 (pow.f64 x 5))))
(-.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 1/729 (/.f64 1 (pow.f64 x 5))) (.f64 1/2187 (/.f64 1 (pow.f64 x 6)))))
(/.f64 1/27 (pow.f64 x 2))
(+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/81 (/.f64 1 (pow.f64 x 3))))
(-.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))) (*.f64 1/729 (/.f64 1 (pow.f64 x 5))))
(-.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 1/729 (/.f64 1 (pow.f64 x 5))) (.f64 1/2187 (/.f64 1 (pow.f64 x 6)))))
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 1/3 x)
(+.f64 1/3 (+.f64 (*.f64 -9 (pow.f64 x 3)) x))
(+.f64 1/3 (fma.f64 -9 (pow.f64 x 3) x))
(+.f64 (.f64 -27 (pow.f64 x 4)) (+.f64 1/3 (+.f64 (.f64 -9 (pow.f64 x 3)) x)))
(fma.f64 -27 (pow.f64 x 4) (+.f64 1/3 (fma.f64 -9 (pow.f64 x 3) x)))
(+.f64 (fma.f64 -9 (pow.f64 x 3) x) (fma.f64 -27 (pow.f64 x 4) 1/3))
(+.f64 x (fma.f64 -27 (pow.f64 x 4) (fma.f64 -9 (pow.f64 x 3) 1/3)))
(+.f64 x (fma.f64 -9 (pow.f64 x 3) (fma.f64 -27 (pow.f64 x 4) 1/3)))
(+.f64 1/3 (fma.f64 -9 (pow.f64 x 3) (fma.f64 -27 (pow.f64 x 4) x)))
(/.f64 1/27 (pow.f64 x 2))
(/.f64 1/27 (*.f64 x x))
(+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/81 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.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 1/27 (/.f64 1 (pow.f64 x 2)))) (*.f64 1/729 (/.f64 1 (pow.f64 x 5))))
(+.f64 (/.f64 1/81 (pow.f64 x 3)) (-.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/729 (pow.f64 x 5))))
(+.f64 (/.f64 1/27 (*.f64 x x)) (-.f64 (/.f64 1/81 (pow.f64 x 3)) (/.f64 1/729 (pow.f64 x 5))))
(+.f64 (/.f64 1/27 (*.f64 x x)) (+.f64 (/.f64 1/81 (pow.f64 x 3)) (/.f64 -1/729 (pow.f64 x 5))))
(fma.f64 (/.f64 (/.f64 1 x) x) (+.f64 1/27 (/.f64 1/81 x)) (/.f64 -1/729 (pow.f64 x 5)))
(-.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 1/729 (/.f64 1 (pow.f64 x 5))) (.f64 1/2187 (/.f64 1 (pow.f64 x 6)))))
(+.f64 (/.f64 1/81 (pow.f64 x 3)) (-.f64 (/.f64 1/27 (*.f64 x x)) (+.f64 (/.f64 1/729 (pow.f64 x 5)) (/.f64 1/2187 (pow.f64 x 6)))))
(+.f64 (/.f64 1/81 (pow.f64 x 3)) (-.f64 (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 -1/729 (pow.f64 x 5))) (/.f64 1/2187 (pow.f64 x 6))))
(+.f64 (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/81 (pow.f64 x 3))) (+.f64 (/.f64 -1/729 (pow.f64 x 5)) (/.f64 -1/2187 (pow.f64 x 6))))
(+.f64 (/.f64 1/27 (*.f64 x x)) (+.f64 (/.f64 1/81 (pow.f64 x 3)) (-.f64 (/.f64 -1/729 (pow.f64 x 5)) (/.f64 1/2187 (pow.f64 x 6)))))
(+.f64 (fma.f64 (/.f64 (/.f64 1 x) x) (+.f64 1/27 (/.f64 1/81 x)) (/.f64 -1/729 (pow.f64 x 5))) (/.f64 -1/2187 (pow.f64 x 6)))
(/.f64 1/27 (pow.f64 x 2))
(/.f64 1/27 (*.f64 x x))
(+.f64 (.f64 1/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/81 (/.f64 1 (pow.f64 x 3))))
(+.f64 (/.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 1/27 (/.f64 1 (pow.f64 x 2)))) (*.f64 1/729 (/.f64 1 (pow.f64 x 5))))
(+.f64 (/.f64 1/81 (pow.f64 x 3)) (-.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/729 (pow.f64 x 5))))
(+.f64 (/.f64 1/27 (*.f64 x x)) (-.f64 (/.f64 1/81 (pow.f64 x 3)) (/.f64 1/729 (pow.f64 x 5))))
(+.f64 (/.f64 1/27 (*.f64 x x)) (+.f64 (/.f64 1/81 (pow.f64 x 3)) (/.f64 -1/729 (pow.f64 x 5))))
(fma.f64 (/.f64 (/.f64 1 x) x) (+.f64 1/27 (/.f64 1/81 x)) (/.f64 -1/729 (pow.f64 x 5)))
(-.f64 (+.f64 (.f64 1/81 (/.f64 1 (pow.f64 x 3))) (.f64 1/27 (/.f64 1 (pow.f64 x 2)))) (+.f64 (.f64 1/729 (/.f64 1 (pow.f64 x 5))) (.f64 1/2187 (/.f64 1 (pow.f64 x 6)))))
(+.f64 (/.f64 1/81 (pow.f64 x 3)) (-.f64 (/.f64 1/27 (*.f64 x x)) (+.f64 (/.f64 1/729 (pow.f64 x 5)) (/.f64 1/2187 (pow.f64 x 6)))))
(+.f64 (/.f64 1/81 (pow.f64 x 3)) (-.f64 (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 -1/729 (pow.f64 x 5))) (/.f64 1/2187 (pow.f64 x 6))))
(+.f64 (+.f64 (/.f64 1/27 (*.f64 x x)) (/.f64 1/81 (pow.f64 x 3))) (+.f64 (/.f64 -1/729 (pow.f64 x 5)) (/.f64 -1/2187 (pow.f64 x 6))))
(+.f64 (/.f64 1/27 (*.f64 x x)) (+.f64 (/.f64 1/81 (pow.f64 x 3)) (-.f64 (/.f64 -1/729 (pow.f64 x 5)) (/.f64 1/2187 (pow.f64 x 6)))))
(+.f64 (fma.f64 (/.f64 (/.f64 1 x) x) (+.f64 1/27 (/.f64 1/81 x)) (/.f64 -1/729 (pow.f64 x 5))) (/.f64 -1/2187 (pow.f64 x 6)))
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)

localize30.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 x -1/3) 9)
	0.1b	(.f64 (/.f64 (+.f64 x -1/3) x) (.f64 (+.f64 x -1/3) 9))
	0.2b	(/.f64 (+.f64 x -1/3) x)
✓	0.3b	(/.f64 (-.f64 (.f64 x -3) (.f64 (/.f64 (+.f64 x -1/3) x) 1)) (.f64 (/.f64 (+.f64 x -1/3) x) (.f64 (+.f64 x -1/3) 9)))

Compiler

Compiled 74 to 54 computations (27% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite103.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

857×	`log-prod_binary64`
489×	`fma-def_binary64`
290×	`log-div_binary64`
289×	`fma-neg_binary64`
264×	`expm1-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	38
1	335	35
2	4719	32

Stop Event

1×	node limit

Counts

2 → 109

Calls

Call 1

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

Outputs

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

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

simplify61.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

805×	`unswap-sqr_binary64`
594×	`associate-/r*_binary64`
589×	`fma-neg_binary64`
430×	`times-frac_binary64`
337×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	198
1	108	186
2	285	186
3	870	186
4	2518	186
5	7388	186

Stop Event

1×	node limit

Counts

133 → 126

Calls

Call 1

Inputs
1/3
(+.f64 1/3 x)
(+.f64 1/3 (+.f64 (*.f64 -9 (pow.f64 x 3)) x))
(+.f64 1/3 (+.f64 (.f64 -9 (pow.f64 x 3)) (+.f64 (.f64 -54 (pow.f64 x 4)) x)))
-1/3
(neg.f64 (+.f64 1/3 (*.f64 1/3 (/.f64 1 x))))
(neg.f64 (+.f64 1/3 (+.f64 (.f64 4/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/3 (/.f64 1 x)))))
(neg.f64 (+.f64 (.f64 5/81 (/.f64 1 (pow.f64 x 3))) (+.f64 1/3 (+.f64 (.f64 4/27 (/.f64 1 (pow.f64 x 2))) (*.f64 1/3 (/.f64 1 x))))))
-1/3
(neg.f64 (+.f64 1/3 (*.f64 1/3 (/.f64 1 x))))
(neg.f64 (+.f64 1/3 (+.f64 (.f64 4/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/3 (/.f64 1 x)))))
(neg.f64 (+.f64 (.f64 5/81 (/.f64 1 (pow.f64 x 3))) (+.f64 1/3 (+.f64 (.f64 4/27 (/.f64 1 (pow.f64 x 2))) (*.f64 1/3 (/.f64 1 x))))))
-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)

Outputs
1/3
(+.f64 1/3 x)
(+.f64 1/3 (+.f64 (*.f64 -9 (pow.f64 x 3)) x))
(+.f64 1/3 (fma.f64 -9 (pow.f64 x 3) x))
(+.f64 1/3 (+.f64 (.f64 -9 (pow.f64 x 3)) (+.f64 (.f64 -54 (pow.f64 x 4)) x)))
(+.f64 1/3 (fma.f64 -9 (pow.f64 x 3) (fma.f64 -54 (pow.f64 x 4) x)))
(+.f64 x (fma.f64 -9 (pow.f64 x 3) (fma.f64 -54 (pow.f64 x 4) 1/3)))
(+.f64 (fma.f64 -9 (pow.f64 x 3) x) (fma.f64 -54 (pow.f64 x 4) 1/3))
-1/3
(neg.f64 (+.f64 1/3 (*.f64 1/3 (/.f64 1 x))))
(neg.f64 (+.f64 1/3 (/.f64 1/3 x)))
(+.f64 -1/3 (/.f64 -1/3 x))
(neg.f64 (+.f64 1/3 (+.f64 (.f64 4/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/3 (/.f64 1 x)))))
(+.f64 -1/3 (neg.f64 (+.f64 (/.f64 1/3 x) (/.f64 4/27 (*.f64 x x)))))
(-.f64 -1/3 (+.f64 (/.f64 1/3 x) (/.f64 4/27 (*.f64 x x))))
(+.f64 (+.f64 -1/3 (/.f64 -1/3 x)) (/.f64 -4/27 (*.f64 x x)))
(+.f64 (/.f64 -1/3 x) (+.f64 -1/3 (/.f64 -4/27 (*.f64 x x))))
(neg.f64 (+.f64 (.f64 5/81 (/.f64 1 (pow.f64 x 3))) (+.f64 1/3 (+.f64 (.f64 4/27 (/.f64 1 (pow.f64 x 2))) (*.f64 1/3 (/.f64 1 x))))))
(neg.f64 (+.f64 (+.f64 1/3 (+.f64 (/.f64 1/3 x) (/.f64 4/27 (*.f64 x x)))) (/.f64 5/81 (pow.f64 x 3))))
(+.f64 (-.f64 -1/3 (+.f64 (/.f64 1/3 x) (/.f64 4/27 (*.f64 x x)))) (/.f64 -5/81 (pow.f64 x 3)))
(+.f64 (+.f64 (+.f64 -1/3 (/.f64 -1/3 x)) (/.f64 -4/27 (*.f64 x x))) (/.f64 -5/81 (pow.f64 x 3)))
(-.f64 (+.f64 -1/3 (/.f64 -1/3 x)) (-.f64 (/.f64 4/27 (*.f64 x x)) (/.f64 -5/81 (pow.f64 x 3))))
(+.f64 (+.f64 -1/3 (/.f64 -1/3 x)) (+.f64 (/.f64 -5/81 (pow.f64 x 3)) (/.f64 -4/27 (*.f64 x x))))
-1/3
(neg.f64 (+.f64 1/3 (*.f64 1/3 (/.f64 1 x))))
(neg.f64 (+.f64 1/3 (/.f64 1/3 x)))
(+.f64 -1/3 (/.f64 -1/3 x))
(neg.f64 (+.f64 1/3 (+.f64 (.f64 4/27 (/.f64 1 (pow.f64 x 2))) (.f64 1/3 (/.f64 1 x)))))
(+.f64 -1/3 (neg.f64 (+.f64 (/.f64 1/3 x) (/.f64 4/27 (*.f64 x x)))))
(-.f64 -1/3 (+.f64 (/.f64 1/3 x) (/.f64 4/27 (*.f64 x x))))
(+.f64 (+.f64 -1/3 (/.f64 -1/3 x)) (/.f64 -4/27 (*.f64 x x)))
(+.f64 (/.f64 -1/3 x) (+.f64 -1/3 (/.f64 -4/27 (*.f64 x x))))
(neg.f64 (+.f64 (.f64 5/81 (/.f64 1 (pow.f64 x 3))) (+.f64 1/3 (+.f64 (.f64 4/27 (/.f64 1 (pow.f64 x 2))) (*.f64 1/3 (/.f64 1 x))))))
(neg.f64 (+.f64 (+.f64 1/3 (+.f64 (/.f64 1/3 x) (/.f64 4/27 (*.f64 x x)))) (/.f64 5/81 (pow.f64 x 3))))
(+.f64 (-.f64 -1/3 (+.f64 (/.f64 1/3 x) (/.f64 4/27 (*.f64 x x)))) (/.f64 -5/81 (pow.f64 x 3)))
(+.f64 (+.f64 (+.f64 -1/3 (/.f64 -1/3 x)) (/.f64 -4/27 (*.f64 x x))) (/.f64 -5/81 (pow.f64 x 3)))
(-.f64 (+.f64 -1/3 (/.f64 -1/3 x)) (-.f64 (/.f64 4/27 (*.f64 x x)) (/.f64 -5/81 (pow.f64 x 3))))
(+.f64 (+.f64 -1/3 (/.f64 -1/3 x)) (+.f64 (/.f64 -5/81 (pow.f64 x 3)) (/.f64 -4/27 (*.f64 x x))))
-3
(-.f64 (*.f64 9 x) 3)
(fma.f64 9 x -3)
(fma.f64 x 9 -3)
(-.f64 (*.f64 9 x) 3)
(fma.f64 9 x -3)
(fma.f64 x 9 -3)
(-.f64 (*.f64 9 x) 3)
(fma.f64 9 x -3)
(fma.f64 x 9 -3)
(*.f64 9 x)
(*.f64 x 9)
(-.f64 (*.f64 9 x) 3)
(fma.f64 9 x -3)
(fma.f64 x 9 -3)
(-.f64 (*.f64 9 x) 3)
(fma.f64 9 x -3)
(fma.f64 x 9 -3)
(-.f64 (*.f64 9 x) 3)
(fma.f64 9 x -3)
(fma.f64 x 9 -3)
(*.f64 9 x)
(*.f64 x 9)
(-.f64 (*.f64 9 x) 3)
(fma.f64 9 x -3)
(fma.f64 x 9 -3)
(-.f64 (*.f64 9 x) 3)
(fma.f64 9 x -3)
(fma.f64 x 9 -3)
(-.f64 (*.f64 9 x) 3)
(fma.f64 9 x -3)
(fma.f64 x 9 -3)

eval403.0ms (8.5%)

Compiler: Compiled 10044 to 7722 computations (23.1% saved)

prune60.0ms (1.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	466	1	467
Fresh	0	2	2
Picked	1	0	1
Done	0	3	3
Total	467	6	473

Error

Counts

473 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	19.8b	(/.f64 (+.f64 1/27 (pow.f64 x 3)) (+.f64 1/9 (*.f64 (+.f64 x -1/3) x)))
	2.1b	(/.f64 (-.f64 (.f64 x -3) (.f64 (/.f64 (+.f64 x -1/3) x) 1)) (*.f64 (/.f64 (+.f64 x -1/3) x) -3))
✓	31.3b	(/.f64 1/27 (+.f64 1/9 (*.f64 (+.f64 x -1/3) x)))
	31.8b	1/3
	31.9b	x
✓	0.0b	(+.f64 x 1/3)

Compiler

Compiled 52 to 40 computations (23.1% saved)

regimes27.0ms (0.6%)

Counts

15 → 1

Calls

Call 1

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

Outputs
(+.f64 x 1/3)

Calls

3 calls:

9.0ms	x
6.0ms	(+.f64 x (/.f64 1 3))
6.0ms	(+.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 158 to 115 computations (27.2% saved)

regimes27.0ms (0.6%)

Accuracy

Total -59.9b remaining (-3190.5%)

Threshold costs -59.9b (-3190.5%)

Counts

5 → 3

Calls

Call 1

Inputs
1/3
x
1/3
1/3
x

Outputs
x
1/3
x

Calls

1 calls:

26.0ms

Results

Error	Segments	Branch
1.9b	3	`x`

Compiler

Compiled 8 to 5 computations (37.5% saved)

bsearch28.0ms (0.6%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
14.0ms	9.346374982514411e-7	17085766139.892492
14.0ms	-1.1429382063088882	-0.050911373029014544

Compiler

Compiled 10 to 8 computations (20% saved)

simplify24.0ms (0.5%)

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 -1286834020010053/1125899906842624) x (if (<=.f64 x 2206850397687871/2361183241434822606848) 1/3 x))
1/3

Outputs
(+.f64 x 1/3)
(if (<=.f64 x -1286834020010053/1125899906842624) x (if (<=.f64 x 2206850397687871/2361183241434822606848) 1/3 x))
1/3

Compiler

Compiled 18 to 13 computations (27.8% saved)

soundness7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	10	4

Stop Event

1×

saturated

Compiler

Compiled 10 to 8 computations (20% saved)

end21.0ms (0.4%)

Compiler: Compiled 16 to 11 computations (31.3% saved)

Details

analyze3.0ms (0.1%)

sample674.0ms (14.2%)

preprocess15.0ms (0.3%)

simplify7.0ms (0.1%)

eval1.0ms (0%)

prune1.0ms (0%)

localize3.0ms (0.1%)

series1.0ms (0%)

rewrite87.0ms (1.8%)

simplify7.0ms (0.2%)

eval11.0ms (0.2%)

prune6.0ms (0.1%)

localize13.0ms (0.3%)

series8.0ms (0.2%)

rewrite115.0ms (2.4%)

simplify70.0ms (1.5%)

localize21.0ms (0.4%)

series6.0ms (0.1%)

rewrite126.0ms (2.7%)

simplify184.0ms (3.9%)

eval345.0ms (7.3%)

prune148.0ms (3.1%)

localize14.0ms (0.3%)

series4.0ms (0.1%)

rewrite77.0ms (1.6%)

simplify68.0ms (1.4%)

localize21.0ms (0.4%)

series2.0ms (0%)

rewrite90.0ms (1.9%)

simplify180.0ms (3.8%)

localize34.0ms (0.7%)

series6.0ms (0.1%)

rewrite108.0ms (2.3%)

simplify68.0ms (1.4%)

eval750.0ms (15.8%)

prune392.0ms (8.3%)

localize13.0ms (0.3%)

series2.0ms (0%)

rewrite78.0ms (1.6%)

simplify192.0ms (4%)

localize30.0ms (0.6%)

series3.0ms (0.1%)

rewrite103.0ms (2.2%)

simplify61.0ms (1.3%)

eval403.0ms (8.5%)

prune60.0ms (1.3%)

regimes27.0ms (0.6%)

regimes27.0ms (0.6%)

bsearch28.0ms (0.6%)

simplify24.0ms (0.5%)

soundness7.0ms (0.1%)

end21.0ms (0.4%)

Profiling