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)

sample770.0ms (31.6%)

Results

759.0ms

8256×

body

256

valid

preprocess49.0ms (2%)

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)

simplify6.0ms (0.3%)

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)

eval0.0ms (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
0.0ms	x	@	inf	(+.f64 x 1/3)
0.0ms	x	@	0	(+.f64 x 1/3)
0.0ms	x	@	-inf	(+.f64 x 1/3)

rewrite45.0ms (1.9%)

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 (0.3%)

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)

eval7.0ms (0.3%)

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

prune6.0ms (0.2%)

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

Counts

34 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(+.f64 x 1/3)
▶	13.6b	(-.f64 (/.f64 (*.f64 x x) (+.f64 x -1/3)) (/.f64 1/9 (+.f64 x -1/3)))
▶	13.5b	(/.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))
	32.8b	x
	30.5b	1/3

Compiler

Compiled 32 to 23 computations (28.1% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 35 to 21 computations (40% saved)

series21.0ms (0.9%)

Counts

4 → 48

Calls

12 calls:

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

rewrite100.0ms (4.1%)

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))))))

simplify80.0ms (3.3%)

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)

localize14.0ms (0.6%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 24 to 13 computations (45.8% saved)

series3.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

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

rewrite137.0ms (5.6%)

Algorithm

1×	batch-egg-rewrite

Rules

614×	`unpow-prod-down_binary64`
430×	`log-prod_binary64`
251×	`prod-diff_binary64`
244×	`pow2_binary64`
241×	`pow-prod-down_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	192	15
2	2734	15

Stop Event

1×	node limit

Counts

3 → 278

Calls

Call 1

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

Outputs

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

simplify106.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

667×	`distribute-lft-neg-in_binary64`
648×	`distribute-rgt-neg-in_binary64`
458×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
365×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	194
1	24	158
2	41	158
3	76	158
4	183	158
5	522	158
6	1688	158
7	3517	158
8	4849	158
9	6171	158
10	7020	158

Stop Event

1×	node limit

Counts

314 → 289

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

eval436.0ms (17.9%)

Compiler: Compiled 14500 to 10157 computations (30% saved)

prune126.0ms (5.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	651	2	653
Fresh	1	1	2
Picked	0	1	1
Done	1	1	2
Total	653	5	658

Error

Counts

658 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.1b	(-.f64 (.f64 -3 (.f64 x x)) (/.f64 1/9 (+.f64 x -1/3)))
✓	0.0b	(+.f64 x 1/3)
	32.8b	x
✓	13.5b	(/.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))
	30.5b	1/3

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize16.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 32 to 20 computations (37.5% saved)

series3.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

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

rewrite97.0ms (4%)

Algorithm

1×	batch-egg-rewrite

Rules

493×	`log-prod_binary64`
383×	`exp-prod_binary64`
368×	`fma-def_binary64`
291×	`pow-prod-down_binary64`
289×	`pow2_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	234	21
2	3105	21

Stop Event

1×	node limit

Counts

2 → 148

Calls

Call 1

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

Outputs

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

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

simplify89.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

905×	`fma-def_binary64`
805×	`unswap-sqr_binary64`
585×	`associate-/r*_binary64`
377×	`fma-neg_binary64`
367×	`times-frac_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	266
1	100	252
2	248	252
3	738	252
4	2280	249
5	7322	249

Stop Event

1×	node limit

Counts

172 → 163

Calls

Call 1

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

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

eval168.0ms (6.9%)

Compiler: Compiled 4746 to 3462 computations (27.1% saved)

prune34.0ms (1.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	245	1	246
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	246	5	251

Error

Counts

251 → 5

Alt Table

Click to see full alt table

Status	Error	Program
	30.5b	1/3
✓	0.0b	(+.f64 x 1/3)
✓	30.1b	(-.f64 (.f64 -3 (.f64 x x)) (/.f64 1/9 (+.f64 x -1/3)))
	32.8b	x
✓	13.5b	(/.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))

Compiler

Compiled 30 to 22 computations (26.7% saved)

eval0.0ms (0%)

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

prune2.0ms (0.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

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

Error

Counts

5 → 5

Alt Table

Click to see full alt table

Status	Error	Program
	30.5b	1/3
✓	0.0b	(+.f64 x 1/3)
✓	30.1b	(-.f64 (.f64 -3 (.f64 x x)) (/.f64 1/9 (+.f64 x -1/3)))
	32.8b	x
✓	13.5b	(/.f64 (-.f64 1/9 (*.f64 x x)) (-.f64 1/3 x))

Compiler

Compiled 30 to 22 computations (26.7% saved)

regimes17.0ms (0.7%)

Counts

9 → 1

Calls

Call 1

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

Outputs
(+.f64 x 1/3)

Calls

3 calls:

6.0ms	x
5.0ms	(+.f64 x (/.f64 1 3))
4.0ms	(+.f64 x (/.f64 1 3))

Results

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

Compiler

Compiled 60 to 41 computations (31.7% saved)

regimes12.0ms (0.5%)

Accuracy

Total -60.1b remaining (-3747.8%)

Threshold costs -60.1b (-3747.8%)

Counts

4 → 3

Calls

Call 1

Inputs
1/3
x
x
1/3

Outputs
x
1/3
x

Calls

1 calls:

11.0ms

Results

Error	Segments	Branch
1.6b	3	`x`

Compiler

Compiled 7 to 4 computations (42.9% saved)

bsearch29.0ms (1.2%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
15.0ms	0.10266196555053207	780016502182.3667
14.0ms	-0.8676585674290122	-1.3233892757447837e-7

Compiler

Compiled 10 to 8 computations (20% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	12	20

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 x 1/3)
(if (<=.f64 x -16005475536724449280/18446744073709551616) x (if (<=.f64 x 1893779004614651648/18446744073709551616) 1/3 x))
1/3

Outputs
(+.f64 x 1/3)
(if (<=.f64 x -16005475536724449280/18446744073709551616) x (if (<=.f64 x 1893779004614651648/18446744073709551616) 1/3 x))
(if (<=.f64 x -7815173601916235/9007199254740992) x (if (<=.f64 x 7397574236775983/72057594037927936) 1/3 x))
1/3

Compiler

Compiled 18 to 13 computations (27.8% saved)

soundness11.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	4
1	10	4

Stop Event

1×

saturated

Compiler

Compiled 10 to 8 computations (20% saved)

end22.0ms (0.9%)

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

Details

analyze3.0ms (0.1%)

sample770.0ms (31.6%)

preprocess49.0ms (2%)

simplify6.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

localize3.0ms (0.1%)

series1.0ms (0%)

rewrite45.0ms (1.9%)

simplify7.0ms (0.3%)

eval7.0ms (0.3%)

prune6.0ms (0.2%)

localize13.0ms (0.5%)

series21.0ms (0.9%)

rewrite100.0ms (4.1%)

simplify80.0ms (3.3%)

localize14.0ms (0.6%)

series3.0ms (0.1%)

rewrite137.0ms (5.6%)

simplify106.0ms (4.3%)

eval436.0ms (17.9%)

prune126.0ms (5.2%)

localize16.0ms (0.6%)

series3.0ms (0.1%)

rewrite97.0ms (4%)

simplify89.0ms (3.7%)

eval168.0ms (6.9%)

prune34.0ms (1.4%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes17.0ms (0.7%)

regimes12.0ms (0.5%)

bsearch29.0ms (1.2%)

simplify5.0ms (0.2%)

soundness11.0ms (0.4%)

end22.0ms (0.9%)

Profiling