Details

analyze4.0ms (0.3%)

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
75%	12.5%	12.5%	5
75%	6.2%	18.8%	6
75%	3.1%	21.9%	7
75%	1.6%	23.5%	8
75%	0.8%	24.3%	9
75%	0.4%	24.6%	10
75%	0.2%	24.8%	11
75%	0.1%	24.9%	12
75%	0%	25%	13
75%	0%	25%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample920.0ms (65.9%)

Results

906.0ms

8256×

body

128

valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

preprocess16.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

3×	`fma-neg_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	15	8
2	21	8
3	24	8
4	26	8
5	27	8
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(/.f64 (-.f64 (*.f64 x x) 3) 6)

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

Compiler

Compiled 8 to 6 computations (25% saved)

simplify10.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

3×	`fma-neg_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	15	8
2	21	8
3	24	8
4	26	8
5	27	8

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(/.f64 (-.f64 (*.f64 x x) 3) 6)

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

prune3.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (/.f64 x 6) x -1/2)
	0.3b	(/.f64 (-.f64 (*.f64 x x) 3) 6)

Compiler

Compiled 44 to 32 computations (27.3% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (/.f64 x 6) x -1/2)

series2.0ms (0.2%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(fma.f64 (/.f64 x 6) x -1/2)
1.0ms	x	@	-inf	(fma.f64 (/.f64 x 6) x -1/2)
1.0ms	x	@	0	(fma.f64 (/.f64 x 6) x -1/2)

rewrite37.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

586×	`pow1_binary64`
553×	`add-log-exp_binary64`
553×	`log1p-expm1-u_binary64`
553×	`expm1-log1p-u_binary64`
544×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	130	8
2	1479	8

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs
(fma.f64 (/.f64 x 6) x -1/2)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 -1/2 (/.f64 x (/.f64 6 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 x (/.f64 6 x)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (/.f64 x (/.f64 6 x)) 1) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 (/.f64 x 6) x -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (/.f64 x 6) x -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (fma.f64 (/.f64 x 6) x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (fma.f64 (/.f64 x 6) x -1/2)) (cbrt.f64 (pow.f64 (fma.f64 (/.f64 x 6) x -1/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 x 6) x -1/2) 2)) (cbrt.f64 (fma.f64 (/.f64 x 6) x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (fma.f64 (/.f64 x 6) x -1/2)) (sqrt.f64 (fma.f64 (/.f64 x 6) x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (/.f64 x (/.f64 6 x)) 3) -1/8) (+.f64 (.f64 (/.f64 x (/.f64 6 x)) (/.f64 x (/.f64 6 x))) (-.f64 1/4 (.f64 (/.f64 x (/.f64 6 x)) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (/.f64 x (/.f64 6 x)) (/.f64 x (/.f64 6 x))) 1/4) (-.f64 (/.f64 x (/.f64 6 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (/.f64 x 6) x -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (/.f64 x 6) x -1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (/.f64 x 6) x -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (/.f64 x 6) x -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (/.f64 x 6) x -1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (/.f64 x 6) x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (/.f64 x 6) x -1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (/.f64 x 6) x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (/.f64 x 6) x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (/.f64 x 6) x -1/2)))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 -1/2 (/.f64 x (/.f64 6 x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 x (/.f64 6 x)) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 x (/.f64 6 x)) 1) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (fma.f64 (/.f64 x 6) x -1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 (/.f64 x 6) x -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (fma.f64 (/.f64 x 6) x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (fma.f64 (/.f64 x 6) x -1/2)) (cbrt.f64 (pow.f64 (fma.f64 (/.f64 x 6) x -1/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (fma.f64 (/.f64 x 6) x -1/2) 2)) (cbrt.f64 (fma.f64 (/.f64 x 6) x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 (/.f64 x 6) x -1/2)) (sqrt.f64 (fma.f64 (/.f64 x 6) x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (/.f64 x (/.f64 6 x)) 3) -1/8) (+.f64 (*.f64 (/.f64 x (/.f64 6 x)) (/.f64 x (/.f64 6 x))) (-.f64 1/4 (*.f64 (/.f64 x (/.f64 6 x)) -1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (/.f64 x (/.f64 6 x)) (/.f64 x (/.f64 6 x))) 1/4) (-.f64 (/.f64 x (/.f64 6 x)) -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (fma.f64 (/.f64 x 6) x -1/2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (fma.f64 (/.f64 x 6) x -1/2) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (fma.f64 (/.f64 x 6) x -1/2)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (fma.f64 (/.f64 x 6) x -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (fma.f64 (/.f64 x 6) x -1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (fma.f64 (/.f64 x 6) x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (fma.f64 (/.f64 x 6) x -1/2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (fma.f64 (/.f64 x 6) x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (fma.f64 (/.f64 x 6) x -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (fma.f64 (/.f64 x 6) x -1/2)))))))

simplify56.0ms (4%)

Algorithm

1×	egg-herbie

Rules

608×	`sqr-pow_binary64`
441×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
276×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	87
1	18	87
2	30	87
3	54	87
4	117	87
5	346	87
6	1211	87
7	2108	87
8	2272	87
9	2456	87
10	2664	87
11	2958	87
12	3351	87
13	3829	87
14	4390	87

Stop Event

1×	node limit

Counts

33 → 26

Calls

Call 1

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

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

prune18.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	25	1	26
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	25	3	28

Error

Counts

28 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (/.f64 x 6) x -1/2)
	0.3b	(/.f64 (-.f64 (*.f64 x x) 3) 6)
▶	0.1b	(+.f64 -1/2 (/.f64 x (/.f64 6 x)))

Compiler

Compiled 300 to 225 computations (25% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 x (/.f64 6 x))

series2.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 x (/.f64 6 x))
0.0ms	x	@	inf	(/.f64 x (/.f64 6 x))
0.0ms	x	@	-inf	(/.f64 x (/.f64 6 x))

rewrite34.0ms (2.4%)

Algorithm

1×	batch-egg-rewrite

Rules

579×	`pow1_binary64`
546×	`add-log-exp_binary64`
546×	`log1p-expm1-u_binary64`
546×	`expm1-log1p-u_binary64`
535×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	113	7
2	1502	7

Stop Event

1×	node limit

Counts

1 → 39

Calls

Call 1

Inputs
(/.f64 x (/.f64 6 x))

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

Outputs

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

simplify56.0ms (4%)

Algorithm

1×	egg-herbie

Rules

607×	`sqr-pow_binary64`
445×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
273×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	84
1	12	84
2	23	84
3	44	84
4	107	84
5	336	84
6	1237	84
7	2113	84
8	2277	84
9	2461	84
10	2669	84
11	2960	84
12	3353	84
13	3833	84
14	4396	84

Stop Event

1×	node limit

Counts

51 → 41

Calls

Call 1

Inputs
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))
(*.f64 1/6 (pow.f64 x 2))

Outputs
(*.f64 1/6 (pow.f64 x 2))
(.f64 1/6 (.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(.f64 1/6 (.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(.f64 1/6 (.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(.f64 1/6 (.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(.f64 1/6 (.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(.f64 1/6 (.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(.f64 1/6 (.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(.f64 1/6 (.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(.f64 1/6 (.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(.f64 1/6 (.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(.f64 1/6 (.f64 x x))
(*.f64 1/6 (pow.f64 x 2))
(.f64 1/6 (.f64 x x))

prune24.0ms (1.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	41	3	44

Error

Counts

44 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (/.f64 x 6) x -1/2)
▶	0.3b	(/.f64 (-.f64 (*.f64 x x) 3) 6)
✓	0.1b	(+.f64 -1/2 (/.f64 x (/.f64 6 x)))

Compiler

Compiled 502 to 370 computations (26.3% saved)

localize4.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (-.f64 (*.f64 x x) 3) 6)

series1.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 (-.f64 (*.f64 x x) 3) 6)
0.0ms	x	@	inf	(/.f64 (-.f64 (*.f64 x x) 3) 6)
0.0ms	x	@	-inf	(/.f64 (-.f64 (*.f64 x x) 3) 6)

rewrite47.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

796×	`pow1_binary64`
756×	`log1p-expm1-u_binary64`
756×	`expm1-log1p-u_binary64`
82×	`add-sqr-sqrt_binary64`
78×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	166	8
2	2033	8

Stop Event

1×	node limit

Counts

1 → 27

Calls

Call 1

Inputs
(/.f64 (-.f64 (*.f64 x x) 3) 6)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (*.f64 x x) 1/6) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (*.f64 x x) 1/6) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (*.f64 (fma.f64 x x -3) 1/6))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (fma.f64 x x -3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (fma.f64 x x -3) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (fma.f64 x x -3) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (fma.f64 x x -3)) 2) (*.f64 (cbrt.f64 (fma.f64 x x -3)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (fma.f64 x x -3) 1/6)) (pow.f64 (cbrt.f64 (*.f64 (fma.f64 x x -3) 1/6)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (fma.f64 x x -3) 1/6)) 2) (cbrt.f64 (*.f64 (fma.f64 x x -3) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (fma.f64 x x -3)) (*.f64 (sqrt.f64 (fma.f64 x x -3)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 (fma.f64 x x -3) 1/6)) (sqrt.f64 (*.f64 (fma.f64 x x -3) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (fma.f64 x x -3)) -1/6)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/6 (fma.f64 x x -3))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (fma.f64 x x -3) 1/6) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (fma.f64 x x -3) 1/6) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (fma.f64 x x -3) 1/6)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (fma.f64 x x -3) 1/6)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 6 (fma.f64 x x -3)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (fma.f64 x x -3) -6))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 (fma.f64 x x -3) 2) 1/36))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 (fma.f64 x x -3) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (*.f64 (fma.f64 x x -3) 1/6))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (fma.f64 x x -3) 1/6) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (fma.f64 x x -3) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (*.f64 (fma.f64 x x -3) 1/6)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (fma.f64 x x -3) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (fma.f64 x x -3) 1/6)))))))

simplify56.0ms (4%)

Algorithm

1×	egg-herbie

Rules

608×	`sqr-pow_binary64`
441×	`associate-l_binary64`
434×	`unswap-sqr_binary64`
281×	`cube-prod_binary64`
276×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	87
1	18	87
2	30	87
3	54	87
4	117	87
5	346	87
6	1211	87
7	2108	87
8	2272	87
9	2456	87
10	2664	87
11	2958	87
12	3351	87
13	3829	87
14	4390	87

Stop Event

1×	node limit

Counts

39 → 32

Calls

Call 1

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

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

prune17.0ms (1.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	32	3	35

Error

Counts

35 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (/.f64 x 6) x -1/2)
✓	0.3b	(/.f64 (-.f64 (*.f64 x x) 3) 6)
✓	0.1b	(+.f64 -1/2 (/.f64 x (/.f64 6 x)))

Compiler

Compiled 305 to 226 computations (25.9% saved)

regimes29.0ms (2.1%)

Accuracy

Total 0.1b remaining (89.3%)

Threshold costs 0.1b (89.3%)

Counts

10 → 1

Compiler

Compiled 95 to 64 computations (32.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	8	10

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 -1/2 (/.f64 x (/.f64 6 x)))

Outputs
(+.f64 -1/2 (/.f64 x (/.f64 6 x)))

end51.0ms (3.7%)

Stop Event

1×

done

Compiler

Compiled 39 to 29 computations (25.6% saved)

Details

analyze4.0ms (0.3%)

sample920.0ms (65.9%)

preprocess16.0ms (1.1%)

simplify10.0ms (0.7%)

prune3.0ms (0.2%)

localize4.0ms (0.3%)

series2.0ms (0.2%)

rewrite37.0ms (2.6%)

simplify56.0ms (4%)

prune18.0ms (1.3%)

localize4.0ms (0.3%)

series2.0ms (0.1%)

rewrite34.0ms (2.4%)

simplify56.0ms (4%)

prune24.0ms (1.7%)

localize4.0ms (0.3%)

series1.0ms (0.1%)

rewrite47.0ms (3.3%)

simplify56.0ms (4%)

prune17.0ms (1.2%)

regimes29.0ms (2.1%)

simplify2.0ms (0.1%)

end51.0ms (3.7%)

Profiling