Details

analyze1.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25.7%	74.3%	0%	0%	0%	0
100%	25.7%	0%	74.3%	0%	0%	0%	1

Compiler

Compiled 26 to 19 computations (26.9% saved)

sample2.4s (22.7%)

Results

1.5s	6216×	body	256	valid
595.0ms	995×	body	1024	valid
223.0ms	1018×	body	512	valid
11.0ms	27×	body	2048	valid

Bogosity

preprocess4.0ms (0%)

Algorithm

2×	egg-herbie

Rules

2×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	50
1	14	50
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
(-.f64 (pow.f64 (+.f64 eps x) 2) (pow.f64 eps 2))

Outputs
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
(-.f64 (pow.f64 (+.f64 eps x) 2) (pow.f64 eps 2))
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 eps 2))

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	10	25

Stop Event

1×

saturated

Counts

1 → 1

Calls

Call 1

Inputs
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

Outputs
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

eval0.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

14.8b

Counts

2 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	14.8b	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

Compiler

Compiled 11 to 8 computations (27.3% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 x eps) 2)
✓	3.6b	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

Compiler

Compiled 25 to 13 computations (48% saved)

series3.0ms (0%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
1.0ms	x	@	inf	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
0.0ms	x	@	0	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
0.0ms	eps	@	0	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
0.0ms	eps	@	inf	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

rewrite1.1s (10.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1544×	`rational.json-1`
1544×	`rational.json-2`
1544×	`rational.json-4`
1544×	`rational.json-3`
1480×	`rational.json-simplify-35`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	38
1	57	38
2	120	38
3	246	38
4	468	38
5	1091	38
6	3040	38
7	5606	38
8	7092	38

Stop Event

1×	node limit

Counts

2 → 77

Calls

Call 1

Inputs
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
(pow.f64 (+.f64 x eps) 2)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (+.f64 x eps) 2) (neg.f64 (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (pow.f64 (+.f64 x eps) 2) (-.f64 -1 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (pow.f64 x 2)) (pow.f64 (+.f64 x eps) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 (pow.f64 (+.f64 x eps) 2) (-.f64 1 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 (+.f64 x eps) 2) (-.f64 1 (pow.f64 x 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1/2) (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 (+.f64 x eps) 2) 1/2) (-.f64 (.f64 (pow.f64 (+.f64 x eps) 2) 1/2) (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (pow.f64 x 2)) (+.f64 (pow.f64 (+.f64 x eps) 2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (+.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 (+.f64 x eps) 2) 1) (-.f64 -1 (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2))) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 2 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 16 (-.f64 (pow.f64 (.f64 (+.f64 x eps) 1/4) 2) (pow.f64 (.f64 x 1/4) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -2 (.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) 1/2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/8 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/8 (-.f64 (.f64 (pow.f64 (+.f64 x eps) 2) 8) (.f64 (pow.f64 x 2) 8)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 -1/2 (.f64 2 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/16 (-.f64 (pow.f64 (.f64 (+.f64 x eps) 4) 2) (pow.f64 (.f64 x 4) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) 4) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) 4)) -8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) 4))) -16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8)))) (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (+.f64 x eps) 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (+.f64 x eps) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (pow.f64 (+.f64 x eps) 2) 1/2) (.f64 (pow.f64 (+.f64 x eps) 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (+.f64 x eps) 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 2 (.f64 (pow.f64 (+.f64 x eps) 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (+.f64 x eps) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (pow.f64 (+.f64 x eps) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 2 (pow.f64 (+.f64 x eps) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 4 (.f64 (pow.f64 (+.f64 x eps) 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (+.f64 x eps) 2) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (+.f64 x eps) 2) 8) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/2 (.f64 2 (pow.f64 (+.f64 x eps) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (+.f64 x eps) 2) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 16 (pow.f64 (.f64 (+.f64 x eps) 1/4) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/4 (.f64 (pow.f64 (+.f64 x eps) 2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (+.f64 x eps) 2) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/8 (.f64 (pow.f64 (+.f64 x eps) 2) 8))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/16 (pow.f64 (.f64 (+.f64 x eps) 4) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (+.f64 x eps) 4) 2) 1/16)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (.f64 (+.f64 x eps) 1/4) 2) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (+.f64 x eps) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (pow.f64 (+.f64 x eps) 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (+.f64 x eps) 2) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (pow.f64 (+.f64 x eps) 2) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 (pow.f64 (+.f64 x eps) 2) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 (pow.f64 (+.f64 x eps) 2) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 (+.f64 x eps) 2) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 (+.f64 x eps) 2) 8)))) (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 (+.f64 x eps) 2) 8))))) 128)))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (+.f64 x eps) 2) (neg.f64 (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (pow.f64 (+.f64 x eps) 2) (-.f64 -1 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 (pow.f64 x 2)) (pow.f64 (+.f64 x eps) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (+.f64 (pow.f64 (+.f64 x eps) 2) (-.f64 1 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 (+.f64 x eps) 2) (-.f64 1 (pow.f64 x 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1/2) (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 (+.f64 x eps) 2) 1/2) (-.f64 (*.f64 (pow.f64 (+.f64 x eps) 2) 1/2) (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (-.f64 1 (pow.f64 x 2)) (+.f64 (pow.f64 (+.f64 x eps) 2) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -2 (+.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (pow.f64 (+.f64 x eps) 2) 1) (-.f64 -1 (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2))) -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 2 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 16 (-.f64 (pow.f64 (*.f64 (+.f64 x eps) 1/4) 2) (pow.f64 (*.f64 x 1/4) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -2 (*.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) 1/2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/8 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/8 (-.f64 (*.f64 (pow.f64 (+.f64 x eps) 2) 8) (*.f64 (pow.f64 x 2) 8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1/2 (*.f64 2 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/16 (-.f64 (pow.f64 (*.f64 (+.f64 x eps) 4) 2) (pow.f64 (*.f64 x 4) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2))) -2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) 4) -4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) 4)) -8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) 4))) -16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8)))) (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 (+.f64 x eps) 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (pow.f64 (+.f64 x eps) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (pow.f64 (+.f64 x eps) 2) 1/2) (*.f64 (pow.f64 (+.f64 x eps) 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (pow.f64 (+.f64 x eps) 2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 (pow.f64 (+.f64 x eps) 2) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (+.f64 x eps) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (pow.f64 (+.f64 x eps) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (pow.f64 (+.f64 x eps) 2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (*.f64 (pow.f64 (+.f64 x eps) 2) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (+.f64 x eps) 2) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (+.f64 x eps) 2) 8) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 2 (pow.f64 (+.f64 x eps) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (+.f64 x eps) 2) 1/2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 16 (pow.f64 (*.f64 (+.f64 x eps) 1/4) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (pow.f64 (+.f64 x eps) 2) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (pow.f64 (+.f64 x eps) 2) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/8 (*.f64 (pow.f64 (+.f64 x eps) 2) 8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/16 (pow.f64 (*.f64 (+.f64 x eps) 4) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (+.f64 x eps) 4) 2) 1/16)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 (+.f64 x eps) 1/4) 2) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (+.f64 x eps) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (pow.f64 (+.f64 x eps) 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (+.f64 x eps) 2) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (pow.f64 (+.f64 x eps) 2) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (pow.f64 (+.f64 x eps) 2) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 (+.f64 x eps) 2) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 (+.f64 x eps) 2) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 (+.f64 x eps) 2) 8)))) (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (pow.f64 (+.f64 x eps) 2) 8))))) 128)))))

simplify330.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1792×	`rational.json-simplify-1`
1430×	`rational.json-simplify-52`
1416×	`rational.json-simplify-2`
1286×	`rational.json-simplify-35`
938×	`rational.json-simplify-41`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	156	2945
1	316	2753
2	867	2747
3	1577	2747
4	3176	2747
5	3797	2747
6	4334	2747
7	4632	2747
8	5164	2747
9	5476	2747
10	6589	2747

Stop Event

1×	node limit

Counts

125 → 98

Calls

Call 1

Inputs
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (pow.f64 eps 2) (+.f64 (.f64 2 (.f64 eps x)) (pow.f64 x 2)))
(+.f64 (pow.f64 (+.f64 x eps) 2) (neg.f64 (pow.f64 x 2)))
(+.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 0)
(+.f64 0 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)))
(+.f64 1 (+.f64 (pow.f64 (+.f64 x eps) 2) (-.f64 -1 (pow.f64 x 2))))
(+.f64 (neg.f64 (pow.f64 x 2)) (pow.f64 (+.f64 x eps) 2))
(+.f64 -1 (+.f64 (pow.f64 (+.f64 x eps) 2) (-.f64 1 (pow.f64 x 2))))
(+.f64 (+.f64 (pow.f64 (+.f64 x eps) 2) (-.f64 1 (pow.f64 x 2))) -1)
(+.f64 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1/2) (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1/2))
(+.f64 (.f64 (pow.f64 (+.f64 x eps) 2) 1/2) (-.f64 (.f64 (pow.f64 (+.f64 x eps) 2) 1/2) (pow.f64 x 2)))
(+.f64 (-.f64 1 (pow.f64 x 2)) (+.f64 (pow.f64 (+.f64 x eps) 2) -1))
(+.f64 -2 (+.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 2))
(+.f64 (+.f64 (pow.f64 (+.f64 x eps) 2) 1) (-.f64 -1 (pow.f64 x 2)))
(+.f64 (+.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 2) -2)
(.f64 2 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1/2))
(*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1)
(*.f64 1 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)))
(.f64 (.f64 2 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))) 1/2)
(*.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) -1)
(.f64 4 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1/4))
(.f64 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 4) 1/4)
(*.f64 -1 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)))
(.f64 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8) 1/8)
(.f64 (.f64 2 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2))) -1/2)
(.f64 1/2 (.f64 2 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))))
(.f64 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1/2) 2)
(.f64 16 (-.f64 (pow.f64 (.f64 (+.f64 x eps) 1/4) 2) (pow.f64 (*.f64 x 1/4) 2)))
(.f64 -2 (.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) 1/2))
(.f64 (.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) 1/2) -2)
(.f64 1/4 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 4))
(.f64 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1/4) 4)
(.f64 1/8 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8))
(.f64 1/8 (-.f64 (.f64 (pow.f64 (+.f64 x eps) 2) 8) (*.f64 (pow.f64 x 2) 8)))
(.f64 -1/2 (.f64 2 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2))))
(.f64 1/16 (-.f64 (pow.f64 (.f64 (+.f64 x eps) 4) 2) (pow.f64 (*.f64 x 4) 2)))
(/.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1)
(/.f64 (*.f64 2 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))) 2)
(/.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) -1)
(/.f64 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 4) 4)
(/.f64 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8) 8)
(/.f64 (*.f64 2 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2))) -2)
(/.f64 (*.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) 4) -4)
(/.f64 (.f64 2 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8)) 16)
(/.f64 (.f64 2 (.f64 2 (*.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8))) 32)
(/.f64 (.f64 2 (.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) 4)) -8)
(/.f64 (.f64 2 (.f64 2 (*.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)) 4))) -16)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8)))) 64)
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8)))) (.f64 2 (.f64 2 (.f64 2 (.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 8))))) 128)
(pow.f64 (-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2)) 1)
(neg.f64 (-.f64 (pow.f64 x 2) (pow.f64 (+.f64 x eps) 2)))
(+.f64 (pow.f64 (+.f64 x eps) 2) 0)
(+.f64 0 (pow.f64 (+.f64 x eps) 2))
(+.f64 (.f64 (pow.f64 (+.f64 x eps) 2) 1/2) (.f64 (pow.f64 (+.f64 x eps) 2) 1/2))
(-.f64 (pow.f64 (+.f64 x eps) 2) 0)
(.f64 2 (.f64 (pow.f64 (+.f64 x eps) 2) 1/2))
(*.f64 (pow.f64 (+.f64 x eps) 2) 1)
(*.f64 1 (pow.f64 (+.f64 x eps) 2))
(.f64 (.f64 2 (pow.f64 (+.f64 x eps) 2)) 1/2)
(.f64 4 (.f64 (pow.f64 (+.f64 x eps) 2) 1/4))
(.f64 (.f64 (pow.f64 (+.f64 x eps) 2) 4) 1/4)
(.f64 (.f64 (pow.f64 (+.f64 x eps) 2) 8) 1/8)
(.f64 1/2 (.f64 2 (pow.f64 (+.f64 x eps) 2)))
(.f64 (.f64 (pow.f64 (+.f64 x eps) 2) 1/2) 2)
(.f64 16 (pow.f64 (.f64 (+.f64 x eps) 1/4) 2))
(.f64 1/4 (.f64 (pow.f64 (+.f64 x eps) 2) 4))
(.f64 (.f64 (pow.f64 (+.f64 x eps) 2) 1/4) 4)
(.f64 1/8 (.f64 (pow.f64 (+.f64 x eps) 2) 8))
(.f64 1/16 (pow.f64 (.f64 (+.f64 x eps) 4) 2))
(.f64 (pow.f64 (.f64 (+.f64 x eps) 4) 2) 1/16)
(.f64 (pow.f64 (.f64 (+.f64 x eps) 1/4) 2) 16)
(/.f64 (pow.f64 (+.f64 x eps) 2) 1)
(/.f64 (*.f64 2 (pow.f64 (+.f64 x eps) 2)) 2)
(/.f64 (*.f64 (pow.f64 (+.f64 x eps) 2) 4) 4)
(/.f64 (*.f64 (pow.f64 (+.f64 x eps) 2) 8) 8)
(/.f64 (.f64 2 (.f64 (pow.f64 (+.f64 x eps) 2) 8)) 16)
(/.f64 (.f64 2 (.f64 2 (*.f64 (pow.f64 (+.f64 x eps) 2) 8))) 32)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 (+.f64 x eps) 2) 8)))) 64)
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 (+.f64 x eps) 2) 8)))) (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 (+.f64 x eps) 2) 8))))) 128)

Outputs
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 2 x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 2 x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 2 x)))
(.f64 2 (.f64 eps x))
(.f64 eps (.f64 x 2))
(.f64 eps (.f64 2 x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 2 x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 2 x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 2 x)))
(.f64 2 (.f64 eps x))
(.f64 eps (.f64 x 2))
(.f64 eps (.f64 2 x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 2 x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 2 x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 2 x)))
(.f64 2 (.f64 eps x))
(.f64 eps (.f64 x 2))
(.f64 eps (.f64 2 x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 2 x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 2 x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 2 x)))
(pow.f64 eps 2)
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(pow.f64 (+.f64 eps x) 2)
(.f64 1/2 (.f64 2 (pow.f64 (+.f64 x eps) 2)))
(pow.f64 (+.f64 eps x) 2)
(.f64 (.f64 (pow.f64 (+.f64 x eps) 2) 1/2) 2)
(pow.f64 (+.f64 eps x) 2)
(.f64 16 (pow.f64 (.f64 (+.f64 x eps) 1/4) 2))
(pow.f64 (+.f64 eps x) 2)
(.f64 1/4 (.f64 (pow.f64 (+.f64 x eps) 2) 4))
(pow.f64 (+.f64 eps x) 2)
(.f64 (.f64 (pow.f64 (+.f64 x eps) 2) 1/4) 4)
(pow.f64 (+.f64 eps x) 2)
(.f64 1/8 (.f64 (pow.f64 (+.f64 x eps) 2) 8))
(pow.f64 (+.f64 eps x) 2)
(.f64 1/16 (pow.f64 (.f64 (+.f64 x eps) 4) 2))
(pow.f64 (+.f64 eps x) 2)
(.f64 (pow.f64 (.f64 (+.f64 x eps) 4) 2) 1/16)
(pow.f64 (+.f64 eps x) 2)
(.f64 (pow.f64 (.f64 (+.f64 x eps) 1/4) 2) 16)
(pow.f64 (+.f64 eps x) 2)
(/.f64 (pow.f64 (+.f64 x eps) 2) 1)
(pow.f64 (+.f64 eps x) 2)
(/.f64 (*.f64 2 (pow.f64 (+.f64 x eps) 2)) 2)
(pow.f64 (+.f64 eps x) 2)
(/.f64 (*.f64 (pow.f64 (+.f64 x eps) 2) 4) 4)
(pow.f64 (+.f64 eps x) 2)
(/.f64 (*.f64 (pow.f64 (+.f64 x eps) 2) 8) 8)
(pow.f64 (+.f64 eps x) 2)
(/.f64 (.f64 2 (.f64 (pow.f64 (+.f64 x eps) 2) 8)) 16)
(pow.f64 (+.f64 eps x) 2)
(/.f64 (.f64 2 (.f64 2 (*.f64 (pow.f64 (+.f64 x eps) 2) 8))) 32)
(pow.f64 (+.f64 eps x) 2)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 (+.f64 x eps) 2) 8)))) 64)
(pow.f64 (+.f64 eps x) 2)
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 (+.f64 x eps) 2) 8)))) (.f64 2 (.f64 2 (.f64 2 (.f64 (pow.f64 (+.f64 x eps) 2) 8))))) 128)
(pow.f64 (+.f64 eps x) 2)

eval361.0ms (3.3%)

Compiler: Compiled 1292 to 893 computations (30.9% saved)

prune15.0ms (0.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	94	5	99

Error

0.0b

Counts

99 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	16.3b	(pow.f64 eps 2)
✓	14.8b	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
▶	0.0b	(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
▶	24.3b	(.f64 eps (.f64 x 2))
▶	24.3b	(.f64 2 (.f64 eps x))

Compiler

Compiled 41 to 30 computations (26.8% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 eps x))

Compiler

Compiled 13 to 6 computations (53.8% saved)

series2.0ms (0%)

Counts

1 → 0

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	0	(.f64 2 (.f64 eps x))
0.0ms	x	@	inf	(.f64 2 (.f64 eps x))
0.0ms	eps	@	inf	(.f64 2 (.f64 eps x))
0.0ms	x	@	0	(.f64 2 (.f64 eps x))
0.0ms	eps	@	-inf	(.f64 2 (.f64 eps x))

rewrite222.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2570×	`rational.json-simplify-2`
1730×	`rational.json-simplify-35`
1394×	`rational.json-1`
1394×	`rational.json-2`
1122×	`exponential.json-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	48	13
2	113	13
3	220	13
4	378	13
5	843	13
6	1815	13
7	3192	13
8	3932	13
9	4709	13
10	5815	13
11	6474	13
12	6474	13
13	7805	13

Stop Event

1×	node limit

Counts

1 → 17

Calls

Call 1

Inputs
(.f64 2 (.f64 eps x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 eps x) (.f64 eps x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 2 (.f64 eps x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 2 (.f64 eps x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 eps (.f64 x 1/2)) (.f64 eps (.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 eps (.f64 x 3/2)) (.f64 eps (.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (.f64 2 (.f64 eps x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 eps x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 eps (.f64 x 4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 eps (.f64 x 8)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 16 (.f64 eps x)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 16 (.f64 eps x))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 16 (.f64 eps x)))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 16 (.f64 eps x))))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 16 (.f64 eps x)))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 16 (.f64 eps x))))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 16 (.f64 eps x)))))))) 512)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 2 (*.f64 eps x)) 1)))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 eps x) (*.f64 eps x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 2 (*.f64 eps x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 2 (*.f64 eps x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 eps (*.f64 x 1/2)) (*.f64 eps (*.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 eps (*.f64 x 3/2)) (*.f64 eps (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 2 (*.f64 eps x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 eps x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 eps (*.f64 x 4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 eps (*.f64 x 8)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 16 (*.f64 eps x)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 16 (*.f64 eps x))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 16 (*.f64 eps x)))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 16 (*.f64 eps x))))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 16 (*.f64 eps x)))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 16 (*.f64 eps x))))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 16 (*.f64 eps x)))))))) 512)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 eps x)) 1)))))

simplify532.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

2986×	`rational.json-simplify-35`
2158×	`rational.json-simplify-2`
1058×	`rational.json-simplify-53`
1030×	`rational.json-simplify-49`
1028×	`exponential.json-simplify-26`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	51	323
1	139	221
2	288	221
3	758	221
4	2759	221
5	4584	221
6	5379	221
7	5668	221
8	5857	221
9	6018	221
10	6819	221
11	7018	221
12	7165	221
13	7281	221
14	7290	221
15	7290	221
16	7440	221
17	7707	221
18	7988	221

Stop Event

1×	node limit

Counts

17 → 19

Calls

Call 1

Inputs
(+.f64 (.f64 eps x) (.f64 eps x))
(+.f64 (.f64 2 (.f64 eps x)) 0)
(+.f64 0 (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps (.f64 x 1/2)) (.f64 eps (.f64 x 3/2)))
(+.f64 (.f64 eps (.f64 x 3/2)) (.f64 eps (.f64 x 1/2)))
(-.f64 (.f64 2 (.f64 eps x)) 0)
(/.f64 (.f64 2 (.f64 eps x)) 1)
(/.f64 (.f64 eps (.f64 x 4)) 2)
(/.f64 (.f64 eps (.f64 x 8)) 4)
(/.f64 (.f64 16 (.f64 eps x)) 8)
(/.f64 (.f64 2 (.f64 16 (*.f64 eps x))) 16)
(/.f64 (.f64 2 (.f64 2 (.f64 16 (.f64 eps x)))) 32)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 16 (*.f64 eps x))))) 64)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 16 (.f64 eps x)))))) 128)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 16 (*.f64 eps x))))))) 256)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 16 (.f64 eps x)))))))) 512)
(pow.f64 (.f64 2 (.f64 eps x)) 1)

Outputs
(+.f64 (.f64 eps x) (.f64 eps x))
(*.f64 eps (+.f64 x x))
(.f64 eps (.f64 x 2))
(+.f64 (.f64 2 (.f64 eps x)) 0)
(+.f64 (.f64 eps x) (.f64 eps x))
(*.f64 eps (+.f64 x x))
(.f64 eps (.f64 x 2))
(+.f64 0 (.f64 2 (.f64 eps x)))
(+.f64 (.f64 eps x) (.f64 eps x))
(*.f64 eps (+.f64 x x))
(.f64 eps (.f64 x 2))
(+.f64 (.f64 eps (.f64 x 1/2)) (.f64 eps (.f64 x 3/2)))
(+.f64 (.f64 eps x) (.f64 eps x))
(*.f64 eps (+.f64 x x))
(.f64 eps (.f64 x 2))
(+.f64 (.f64 eps (.f64 x 3/2)) (.f64 eps (.f64 x 1/2)))
(+.f64 (.f64 eps x) (.f64 eps x))
(*.f64 eps (+.f64 x x))
(.f64 eps (.f64 x 2))
(-.f64 (.f64 2 (.f64 eps x)) 0)
(+.f64 (.f64 eps x) (.f64 eps x))
(*.f64 eps (+.f64 x x))
(.f64 eps (.f64 x 2))
(/.f64 (.f64 2 (.f64 eps x)) 1)
(+.f64 (.f64 eps x) (.f64 eps x))
(*.f64 eps (+.f64 x x))
(.f64 eps (.f64 x 2))
(/.f64 (.f64 eps (.f64 x 4)) 2)
(+.f64 (.f64 eps x) (.f64 eps x))
(*.f64 eps (+.f64 x x))
(.f64 eps (.f64 x 2))
(/.f64 (.f64 eps (.f64 x 8)) 4)
(+.f64 (.f64 eps x) (.f64 eps x))
(*.f64 eps (+.f64 x x))
(.f64 eps (.f64 x 2))
(/.f64 (.f64 16 (.f64 eps x)) 8)
(+.f64 (.f64 eps x) (.f64 eps x))
(*.f64 eps (+.f64 x x))
(.f64 eps (.f64 x 2))
(/.f64 (.f64 2 (.f64 16 (*.f64 eps x))) 16)
(+.f64 (.f64 eps x) (.f64 eps x))
(*.f64 eps (+.f64 x x))
(.f64 eps (.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 16 (.f64 eps x)))) 32)
(+.f64 (.f64 eps x) (.f64 eps x))
(*.f64 eps (+.f64 x x))
(.f64 eps (.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 16 (*.f64 eps x))))) 64)
(+.f64 (.f64 eps x) (.f64 eps x))
(*.f64 eps (+.f64 x x))
(.f64 eps (.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 16 (.f64 eps x)))))) 128)
(+.f64 (.f64 eps x) (.f64 eps x))
(*.f64 eps (+.f64 x x))
(.f64 eps (.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 16 (*.f64 eps x))))))) 256)
(+.f64 (.f64 eps x) (.f64 eps x))
(*.f64 eps (+.f64 x x))
(.f64 eps (.f64 x 2))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 16 (.f64 eps x)))))))) 512)
(+.f64 (.f64 eps x) (.f64 eps x))
(*.f64 eps (+.f64 x x))
(.f64 eps (.f64 x 2))
(pow.f64 (.f64 2 (.f64 eps x)) 1)
(+.f64 (.f64 eps x) (.f64 eps x))
(*.f64 eps (+.f64 x x))
(.f64 eps (.f64 x 2))

localize5.0ms (0%)

Compiler: Compiled 13 to 8 computations (38.5% saved)

localize16.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))

Compiler

Compiled 25 to 16 computations (36% saved)

series1.0ms (0%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	eps	@	-inf	(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
0.0ms	eps	@	0	(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
0.0ms	x	@	0	(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
0.0ms	eps	@	inf	(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
0.0ms	x	@	-inf	(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))

rewrite484.0ms (4.5%)

Algorithm

1×	batch-egg-rewrite

Rules

2110×	`rational.json-simplify-35`
1584×	`rational.json-simplify-1`
1240×	`exponential.json-3`
1240×	`rational.json-1`
1240×	`rational.json-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	25
1	61	25
2	135	25
3	271	25
4	486	25
5	1106	25
6	2773	25
7	5112	25
8	6264	25
9	7081	25
10	7081	25
11	7081	25

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

Inputs
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (+.f64 (*.f64 eps x) (*.f64 (pow.f64 eps 2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 eps (*.f64 x 4)) (*.f64 2 (pow.f64 eps 2))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (*.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 8) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (+.f64 (*.f64 eps (*.f64 x 4)) (*.f64 2 (pow.f64 eps 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 eps x) (*.f64 (pow.f64 eps 2) 1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/8 (*.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 8))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 eps (*.f64 x 4)) (*.f64 2 (pow.f64 eps 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 8) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 8)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 8))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 8)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 8))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 8))))) (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 8)))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 1)))))

simplify477.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

3032×	`rational.json-simplify-51`
2698×	`rational.json-simplify-2`
1782×	`rational.json-simplify-35`
1386×	`rational.json-simplify-1`
1238×	`rational.json-simplify-49`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	1121
1	130	1121
2	341	1121
3	1074	1121
4	1874	1121
5	2896	1121
6	3433	1121
7	3507	1121
8	3560	1121
9	3599	1121
10	3638	1121
11	3677	1121
12	3716	1121
13	3755	1121
14	3794	1121
15	3833	1121
16	3872	1121
17	3911	1121
18	3950	1121
19	4792	1121
20	7092	1121
21	7162	1121
22	7197	1121
23	7230	1121
24	7261	1121

Stop Event

1×	node limit

Counts

47 → 28

Calls

Call 1

Inputs
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(-.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 0)
(.f64 2 (+.f64 (.f64 eps x) (*.f64 (pow.f64 eps 2) 1/2)))
(.f64 (+.f64 (pow.f64 eps 2) (.f64 eps (+.f64 x x))) 1)
(.f64 1 (+.f64 (pow.f64 eps 2) (.f64 eps (+.f64 x x))))
(.f64 (+.f64 (.f64 eps (.f64 x 4)) (.f64 2 (pow.f64 eps 2))) 1/2)
(.f64 4 (.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 1/4))
(.f64 (.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 4) 1/4)
(.f64 (.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 8) 1/8)
(.f64 1/2 (+.f64 (.f64 eps (.f64 x 4)) (.f64 2 (pow.f64 eps 2))))
(.f64 (+.f64 (.f64 eps x) (*.f64 (pow.f64 eps 2) 1/2)) 2)
(.f64 1/4 (.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 4))
(.f64 (.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 1/4) 4)
(.f64 1/8 (.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 8))
(/.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 1)
(/.f64 (+.f64 (.f64 eps (.f64 x 4)) (*.f64 2 (pow.f64 eps 2))) 2)
(/.f64 (.f64 (+.f64 (pow.f64 eps 2) (.f64 eps (+.f64 x x))) 4) 4)
(/.f64 (.f64 (+.f64 (pow.f64 eps 2) (.f64 eps (+.f64 x x))) 8) 8)
(/.f64 (.f64 2 (.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 8)) 16)
(/.f64 (.f64 2 (.f64 2 (.f64 (+.f64 (pow.f64 eps 2) (.f64 eps (+.f64 x x))) 8))) 32)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 8)))) 64)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (pow.f64 eps 2) (.f64 eps (+.f64 x x))) 8))))) 128)
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (pow.f64 eps 2) (.f64 eps (+.f64 x x))) 8))))) (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (pow.f64 eps 2) (.f64 eps (+.f64 x x))) 8)))))) 256)
(pow.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 1)

Outputs
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
(.f64 2 (.f64 eps x))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
(+.f64 (pow.f64 eps 2) (.f64 2 (.f64 eps x)))
(+.f64 (.f64 2 (.f64 eps x)) (pow.f64 eps 2))
(-.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 0)
(+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x)))
(.f64 2 (+.f64 (.f64 eps x) (*.f64 (pow.f64 eps 2) 1/2)))
(.f64 (+.f64 (pow.f64 eps 2) (.f64 eps (+.f64 x x))) 1)
(+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x)))
(.f64 1 (+.f64 (pow.f64 eps 2) (.f64 eps (+.f64 x x))))
(+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x)))
(.f64 (+.f64 (.f64 eps (.f64 x 4)) (.f64 2 (pow.f64 eps 2))) 1/2)
(.f64 1/2 (+.f64 (.f64 eps (.f64 x 4)) (.f64 2 (pow.f64 eps 2))))
(.f64 4 (.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 1/4))
(+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x)))
(.f64 (.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 4) 1/4)
(+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x)))
(.f64 (.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 8) 1/8)
(+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x)))
(.f64 1/2 (+.f64 (.f64 eps (.f64 x 4)) (.f64 2 (pow.f64 eps 2))))
(.f64 (+.f64 (.f64 eps x) (*.f64 (pow.f64 eps 2) 1/2)) 2)
(.f64 2 (+.f64 (.f64 eps x) (*.f64 (pow.f64 eps 2) 1/2)))
(.f64 1/4 (.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 4))
(+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x)))
(.f64 (.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 1/4) 4)
(+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x)))
(.f64 1/8 (.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 8))
(+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x)))
(/.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 1)
(+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x)))
(/.f64 (+.f64 (.f64 eps (.f64 x 4)) (*.f64 2 (pow.f64 eps 2))) 2)
(+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x)))
(/.f64 (.f64 (+.f64 (pow.f64 eps 2) (.f64 eps (+.f64 x x))) 4) 4)
(+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x)))
(/.f64 (.f64 (+.f64 (pow.f64 eps 2) (.f64 eps (+.f64 x x))) 8) 8)
(+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x)))
(/.f64 (.f64 2 (.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 8)) 16)
(+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x)))
(/.f64 (.f64 2 (.f64 2 (.f64 (+.f64 (pow.f64 eps 2) (.f64 eps (+.f64 x x))) 8))) 32)
(+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 8)))) 64)
(+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x)))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (pow.f64 eps 2) (.f64 eps (+.f64 x x))) 8))))) 128)
(+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x)))
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (pow.f64 eps 2) (.f64 eps (+.f64 x x))) 8))))) (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (+.f64 (pow.f64 eps 2) (.f64 eps (+.f64 x x))) 8)))))) 256)
(+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x)))
(pow.f64 (+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x))) 1)
(+.f64 (pow.f64 eps 2) (*.f64 eps (+.f64 x x)))

localize3.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

eval9.0ms (0.1%)

Compiler: Compiled 549 to 342 computations (37.7% saved)

prune62.0ms (0.6%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	46	1	47
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	46	6	52

Error

0.0b

Counts

52 → 6

Alt Table

Click to see full alt table

Status	Error	Program
✓	16.3b	(pow.f64 eps 2)
✓	14.8b	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
✓	0.0b	(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
▶	24.3b	(+.f64 (.f64 eps (.f64 x 3/2)) (.f64 eps (.f64 x 1/2)))
✓	24.3b	(.f64 eps (.f64 x 2))
✓	24.3b	(.f64 2 (.f64 eps x))

Compiler

Compiled 54 to 39 computations (27.8% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 eps (.f64 x 3/2)) (.f64 eps (.f64 x 1/2)))
✓	0.2b	(.f64 eps (.f64 x 3/2))

Compiler

Compiled 33 to 21 computations (36.4% saved)

series4.0ms (0%)

Counts

2 → 48

Calls

12 calls:

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

rewrite223.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2448×	`rational.json-simplify-2`
1550×	`rational.json-simplify-35`
1478×	`rational.json-1`
1152×	`rational.json-2`
1152×	`rational.json-3`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	44
1	77	38
2	171	26
3	372	26
4	731	26
5	1827	26
6	3159	26
7	4155	26
8	4958	26
9	6035	26
10	6670	26
11	6670	26
12	7926	26

Stop Event

1×	node limit

Counts

2 → 59

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 eps (*.f64 x 3/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 eps (*.f64 x 1/2)) (*.f64 eps x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 eps (*.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 eps x) (*.f64 eps (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 eps (*.f64 x 3/4)) (*.f64 eps (*.f64 x 3/4)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 eps (*.f64 x 3/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 eps (*.f64 x 3/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 eps (*.f64 x 3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 eps (*.f64 x 6)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 eps (*.f64 x 6))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 eps (*.f64 x 6)))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 eps (*.f64 x 6))))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 eps (*.f64 x 6)))))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 eps (*.f64 x 6))))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 eps (*.f64 x 6)))))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 eps (*.f64 x 3/2)) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 eps (+.f64 x x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 eps (+.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (+.f64 eps eps))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (*.f64 8 (*.f64 eps 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/2 (*.f64 x (*.f64 eps 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 1/2) (*.f64 eps 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 eps (*.f64 x 1/2)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 eps (+.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 eps (+.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 eps 1/2) (*.f64 x 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 2 (*.f64 eps x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (*.f64 eps 4)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 eps eps) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 eps x) 2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 x x) eps)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 4 (*.f64 eps (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 4) (*.f64 eps 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 4) (*.f64 1/8 (*.f64 eps 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (*.f64 8 eps)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 eps 4) (*.f64 x 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 8 (*.f64 x (*.f64 eps 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (*.f64 eps 4)) (*.f64 x 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (*.f64 x 4)) (*.f64 eps 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (*.f64 x 4)) (*.f64 (+.f64 eps eps) 1/8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x (*.f64 eps 1/4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/4 (*.f64 x (*.f64 8 eps)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 1/4) (*.f64 2 (*.f64 eps 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 x 1/4) (*.f64 4 (+.f64 eps eps)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 eps 1/4) (*.f64 2 (*.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 16 (*.f64 eps (/.f64 x 8)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (*.f64 2 (*.f64 eps 4))) (/.f64 x 8))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 2 (*.f64 2 (*.f64 x 4))) (*.f64 1/2 (*.f64 eps 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 eps eps) 1/8) (*.f64 2 (*.f64 x 4)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 eps (+.f64 x x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (*.f64 eps 4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (*.f64 8 eps)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 x (*.f64 8 eps))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 x (*.f64 8 eps)))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 x (*.f64 8 eps))))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 x (*.f64 8 eps)))))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 x (*.f64 8 eps))))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 x (*.f64 8 eps)))))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 eps (+.f64 x x)) 1)))))

simplify204.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

2514×	`rational.json-simplify-2`
1922×	`rational.json-simplify-53`
1818×	`rational.json-simplify-35`
1372×	`rational.json-simplify-41`
1106×	`rational.json-simplify-51`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	147	2195
1	367	1391
2	764	1391
3	1741	1391
4	3795	1391
5	5518	1391
6	5936	1391
7	6292	1391
8	6576	1391
9	6616	1391

Stop Event

1×	node limit

Counts

107 → 66

Calls

Call 1

Inputs
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 eps (+.f64 (.f64 1/2 x) (*.f64 3/2 x)))
(.f64 eps (+.f64 (.f64 1/2 x) (*.f64 3/2 x)))
(.f64 eps (+.f64 (.f64 1/2 x) (*.f64 3/2 x)))
(.f64 eps (+.f64 (.f64 1/2 x) (*.f64 3/2 x)))
(.f64 eps (+.f64 (.f64 1/2 x) (*.f64 3/2 x)))
(.f64 eps (+.f64 (.f64 1/2 x) (*.f64 3/2 x)))
(.f64 eps (+.f64 (.f64 1/2 x) (*.f64 3/2 x)))
(.f64 eps (+.f64 (.f64 1/2 x) (*.f64 3/2 x)))
(.f64 -1 (.f64 eps (+.f64 (.f64 -1/2 x) (.f64 -3/2 x))))
(.f64 -1 (.f64 eps (+.f64 (.f64 -1/2 x) (.f64 -3/2 x))))
(.f64 -1 (.f64 eps (+.f64 (.f64 -1/2 x) (.f64 -3/2 x))))
(.f64 -1 (.f64 eps (+.f64 (.f64 -1/2 x) (.f64 -3/2 x))))
(.f64 (+.f64 (.f64 1/2 eps) (*.f64 3/2 eps)) x)
(.f64 (+.f64 (.f64 1/2 eps) (*.f64 3/2 eps)) x)
(.f64 (+.f64 (.f64 1/2 eps) (*.f64 3/2 eps)) x)
(.f64 (+.f64 (.f64 1/2 eps) (*.f64 3/2 eps)) x)
(.f64 (+.f64 (.f64 1/2 eps) (*.f64 3/2 eps)) x)
(.f64 (+.f64 (.f64 1/2 eps) (*.f64 3/2 eps)) x)
(.f64 (+.f64 (.f64 1/2 eps) (*.f64 3/2 eps)) x)
(.f64 (+.f64 (.f64 1/2 eps) (*.f64 3/2 eps)) x)
(.f64 -1 (.f64 (+.f64 (.f64 -1/2 eps) (.f64 -3/2 eps)) x))
(.f64 -1 (.f64 (+.f64 (.f64 -1/2 eps) (.f64 -3/2 eps)) x))
(.f64 -1 (.f64 (+.f64 (.f64 -1/2 eps) (.f64 -3/2 eps)) x))
(.f64 -1 (.f64 (+.f64 (.f64 -1/2 eps) (.f64 -3/2 eps)) x))
(+.f64 (.f64 eps (.f64 x 3/2)) 0)
(+.f64 (.f64 eps (.f64 x 1/2)) (*.f64 eps x))
(+.f64 0 (.f64 eps (.f64 x 3/2)))
(+.f64 (.f64 eps x) (.f64 eps (*.f64 x 1/2)))
(+.f64 (.f64 eps (.f64 x 3/4)) (.f64 eps (.f64 x 3/4)))
(-.f64 (.f64 eps (.f64 x 3/2)) 0)
(/.f64 (.f64 eps (.f64 x 3/2)) 1)
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(/.f64 (.f64 eps (.f64 x 6)) 4)
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(/.f64 (.f64 2 (.f64 2 (.f64 eps (.f64 x 6)))) 16)
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(pow.f64 (.f64 eps (.f64 x 3/2)) 1)
(-.f64 (*.f64 eps (+.f64 x x)) 0)
(*.f64 eps (+.f64 x x))
(*.f64 x (+.f64 eps eps))
(.f64 x (.f64 8 (*.f64 eps 1/4)))
(.f64 1/2 (.f64 x (*.f64 eps 4)))
(.f64 (.f64 x 1/2) (*.f64 eps 4))
(.f64 (.f64 eps (*.f64 x 1/2)) 4)
(.f64 (.f64 eps (+.f64 x x)) 1)
(.f64 1 (.f64 eps (+.f64 x x)))
(.f64 (.f64 eps 1/2) (*.f64 x 4))
(.f64 2 (.f64 eps x))
(.f64 (.f64 x (*.f64 eps 4)) 1/2)
(*.f64 (+.f64 eps eps) x)
(.f64 (.f64 eps x) 2)
(*.f64 (+.f64 x x) eps)
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(.f64 8 (.f64 x (*.f64 eps 1/4)))
(.f64 (.f64 2 (.f64 eps 4)) (.f64 x 1/4))
(.f64 (.f64 2 (.f64 x 4)) (.f64 eps 1/4))
(.f64 (.f64 2 (.f64 x 4)) (.f64 (+.f64 eps eps) 1/8))
(.f64 (.f64 x (*.f64 eps 1/4)) 8)
(.f64 1/4 (.f64 x (*.f64 8 eps)))
(.f64 (.f64 x 1/4) (.f64 2 (.f64 eps 4)))
(.f64 (.f64 x 1/4) (*.f64 4 (+.f64 eps eps)))
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(/.f64 (.f64 2 (.f64 2 (.f64 x (.f64 8 eps)))) 16)
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(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 x (.f64 8 eps)))))))) 256)
(pow.f64 (*.f64 eps (+.f64 x x)) 1)

Outputs
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 3/2 (.f64 eps x))
(.f64 eps (+.f64 (.f64 1/2 x) (*.f64 3/2 x)))
(.f64 eps (+.f64 (.f64 3/2 x) (*.f64 x 1/2)))
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(*.f64 eps (+.f64 x x))
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(.f64 eps (+.f64 (.f64 3/2 x) (*.f64 x 1/2)))
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(.f64 3/2 (.f64 eps x))
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(.f64 3/2 (.f64 eps x))
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(.f64 3/2 (.f64 eps x))
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(-.f64 (.f64 eps (.f64 x 3/2)) 0)
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(.f64 3/2 (.f64 eps x))
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(.f64 3/2 (.f64 eps x))
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(.f64 3/2 (.f64 eps x))
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(.f64 3/2 (.f64 eps x))
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(.f64 3/2 (.f64 eps x))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 eps (*.f64 x 6))))))) 128)
(.f64 3/2 (.f64 eps x))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 eps (.f64 x 6)))))))) 256)
(.f64 3/2 (.f64 eps x))
(pow.f64 (.f64 eps (.f64 x 3/2)) 1)
(.f64 3/2 (.f64 eps x))
(-.f64 (*.f64 eps (+.f64 x x)) 0)
(.f64 eps (+.f64 (.f64 3/2 x) (*.f64 x 1/2)))
(.f64 eps (.f64 x 2))
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(.f64 eps (+.f64 (.f64 3/2 x) (*.f64 x 1/2)))
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(*.f64 eps (+.f64 x x))
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(*.f64 (+.f64 x x) eps)
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(pow.f64 (*.f64 eps (+.f64 x x)) 1)
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(*.f64 eps (+.f64 x x))

eval13.0ms (0.1%)

Compiler: Compiled 686 to 478 computations (30.3% saved)

prune12.0ms (0.1%)

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	64	8	72

Error

0.0b

Counts

72 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	16.3b	(pow.f64 eps 2)
✓	14.8b	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
✓	0.0b	(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
✓	24.3b	(+.f64 (.f64 eps (.f64 x 3/2)) (.f64 eps (.f64 x 1/2)))
▶	24.3b	(.f64 (.f64 eps (*.f64 x 1/2)) 4)
✓	24.3b	(.f64 eps (.f64 x 2))
▶	24.3b	(.f64 16 (.f64 eps (/.f64 x 8)))
✓	24.3b	(.f64 2 (.f64 eps x))

Compiler

Compiled 72 to 53 computations (26.4% saved)

localize96.0ms (0.9%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 16 (.f64 eps (/.f64 x 8)))

Compiler

Compiled 21 to 14 computations (33.3% saved)

series1.0ms (0%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	eps	@	0	(.f64 16 (.f64 eps (/.f64 x 8)))
0.0ms	x	@	-inf	(.f64 16 (.f64 eps (/.f64 x 8)))
0.0ms	x	@	inf	(.f64 16 (.f64 eps (/.f64 x 8)))
0.0ms	eps	@	inf	(.f64 16 (.f64 eps (/.f64 x 8)))
0.0ms	eps	@	-inf	(.f64 16 (.f64 eps (/.f64 x 8)))

rewrite204.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

2314×	`rational.json-simplify-35`
1492×	`rational.json-simplify-1`
1286×	`exponential.json-3`
1286×	`rational.json-1`
1286×	`rational.json-2`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	63	19
2	146	13
3	321	13
4	622	13
5	1647	13
6	3613	13
7	5243	13
8	6092	13
9	7263	13
10	7263	13
11	7263	13

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

Inputs
(.f64 16 (.f64 eps (/.f64 x 8)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 eps (*.f64 x 1/8)) (+.f64 (*.f64 eps x) (*.f64 (*.f64 eps (*.f64 x 1/8)) 7)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 2 (*.f64 eps x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 2 (*.f64 eps x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (*.f64 eps 1/4)) (+.f64 (*.f64 eps x) (*.f64 (*.f64 x (*.f64 eps 1/4)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 1/2 (*.f64 eps x)) (*.f64 3 (*.f64 1/2 (*.f64 eps x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 eps x) (*.f64 eps x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 eps x) (*.f64 (*.f64 eps (*.f64 x 1/8)) 7)) (*.f64 eps (*.f64 x 1/8)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (*.f64 eps x) (*.f64 (*.f64 x (*.f64 eps 1/4)) 3)) (*.f64 x (*.f64 eps 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 3 (*.f64 1/2 (*.f64 eps x))) (*.f64 1/2 (*.f64 eps x)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 2 (*.f64 eps x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 eps x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 eps (*.f64 x 4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 eps (*.f64 x 8)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 16 (*.f64 eps x)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 32 (*.f64 eps x)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 32 (*.f64 eps x))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 32 (*.f64 eps x)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 32 (*.f64 eps x))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 32 (*.f64 eps x))))) (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 32 (*.f64 eps x)))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 2 (*.f64 eps x)) 1)))))

simplify403.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

2436×	`rational.json-simplify-35`
2296×	`rational.json-simplify-2`
1174×	`exponential.json-simplify-26`
1158×	`rational.json-simplify-53`
1088×	`rational.json-simplify-1`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	644
1	150	644
2	337	620
3	864	608
4	3141	608
5	4833	608
6	5564	608
7	5832	608
8	5992	608
9	6124	608
10	7042	608
11	7441	608
12	7448	608
13	7448	608
14	7692	608
15	7951	608

Stop Event

1×	node limit

Counts

44 → 25

Calls

Call 1

Inputs
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(+.f64 (.f64 eps (.f64 x 1/8)) (+.f64 (.f64 eps x) (.f64 (.f64 eps (.f64 x 1/8)) 7)))
(+.f64 (.f64 2 (.f64 eps x)) 0)
(+.f64 0 (.f64 2 (.f64 eps x)))
(+.f64 (.f64 x (.f64 eps 1/4)) (+.f64 (.f64 eps x) (.f64 (.f64 x (.f64 eps 1/4)) 3)))
(+.f64 (.f64 1/2 (.f64 eps x)) (.f64 3 (.f64 1/2 (*.f64 eps x))))
(+.f64 (.f64 eps x) (.f64 eps x))
(+.f64 (+.f64 (.f64 eps x) (.f64 (.f64 eps (.f64 x 1/8)) 7)) (.f64 eps (.f64 x 1/8)))
(+.f64 (+.f64 (.f64 eps x) (.f64 (.f64 x (.f64 eps 1/4)) 3)) (.f64 x (.f64 eps 1/4)))
(+.f64 (.f64 3 (.f64 1/2 (.f64 eps x))) (.f64 1/2 (*.f64 eps x)))
(-.f64 (.f64 2 (.f64 eps x)) 0)
(/.f64 (.f64 2 (.f64 eps x)) 1)
(/.f64 (.f64 eps (.f64 x 4)) 2)
(/.f64 (.f64 eps (.f64 x 8)) 4)
(/.f64 (.f64 16 (.f64 eps x)) 8)
(/.f64 (.f64 32 (.f64 eps x)) 16)
(/.f64 (.f64 2 (.f64 32 (*.f64 eps x))) 32)
(/.f64 (.f64 2 (.f64 2 (.f64 32 (.f64 eps x)))) 64)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 32 (*.f64 eps x))))) 128)
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 32 (.f64 eps x))))) (.f64 2 (.f64 2 (.f64 2 (.f64 32 (.f64 eps x)))))) 256)
(pow.f64 (.f64 2 (.f64 eps x)) 1)

Outputs
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(+.f64 (.f64 eps (.f64 x 1/8)) (+.f64 (.f64 eps x) (.f64 (.f64 eps (.f64 x 1/8)) 7)))
(+.f64 (.f64 eps x) (+.f64 (.f64 (.f64 eps (.f64 x 1/8)) 7) (.f64 eps (.f64 x 1/8))))
(+.f64 (.f64 eps x) (+.f64 (.f64 eps (.f64 x 1/8)) (.f64 eps (.f64 (.f64 x 1/8) 7))))
(+.f64 (.f64 eps x) (.f64 (.f64 x 1/8) (+.f64 eps (.f64 eps 7))))
(.f64 eps (+.f64 (.f64 x 1/8) (+.f64 x (*.f64 x 7/8))))
(+.f64 (.f64 2 (.f64 eps x)) 0)
(.f64 2 (.f64 eps x))
(+.f64 0 (.f64 2 (.f64 eps x)))
(.f64 2 (.f64 eps x))
(+.f64 (.f64 x (.f64 eps 1/4)) (+.f64 (.f64 eps x) (.f64 (.f64 x (.f64 eps 1/4)) 3)))
(.f64 2 (.f64 eps x))
(+.f64 (.f64 1/2 (.f64 eps x)) (.f64 3 (.f64 1/2 (*.f64 eps x))))
(.f64 2 (.f64 eps x))
(+.f64 (.f64 eps x) (.f64 eps x))
(.f64 2 (.f64 eps x))
(+.f64 (+.f64 (.f64 eps x) (.f64 (.f64 eps (.f64 x 1/8)) 7)) (.f64 eps (.f64 x 1/8)))
(+.f64 (.f64 eps x) (+.f64 (.f64 (.f64 eps (.f64 x 1/8)) 7) (.f64 eps (.f64 x 1/8))))
(+.f64 (.f64 eps x) (+.f64 (.f64 eps (.f64 x 1/8)) (.f64 eps (.f64 (.f64 x 1/8) 7))))
(+.f64 (.f64 eps x) (.f64 (.f64 x 1/8) (+.f64 eps (.f64 eps 7))))
(.f64 eps (+.f64 (.f64 x 1/8) (+.f64 x (*.f64 x 7/8))))
(+.f64 (+.f64 (.f64 eps x) (.f64 (.f64 x (.f64 eps 1/4)) 3)) (.f64 x (.f64 eps 1/4)))
(.f64 2 (.f64 eps x))
(+.f64 (.f64 3 (.f64 1/2 (.f64 eps x))) (.f64 1/2 (*.f64 eps x)))
(.f64 2 (.f64 eps x))
(-.f64 (.f64 2 (.f64 eps x)) 0)
(.f64 2 (.f64 eps x))
(/.f64 (.f64 2 (.f64 eps x)) 1)
(.f64 2 (.f64 eps x))
(/.f64 (.f64 eps (.f64 x 4)) 2)
(.f64 2 (.f64 eps x))
(/.f64 (.f64 eps (.f64 x 8)) 4)
(.f64 2 (.f64 eps x))
(/.f64 (.f64 16 (.f64 eps x)) 8)
(.f64 2 (.f64 eps x))
(/.f64 (.f64 32 (.f64 eps x)) 16)
(.f64 2 (.f64 eps x))
(/.f64 (.f64 2 (.f64 32 (*.f64 eps x))) 32)
(.f64 2 (.f64 eps x))
(/.f64 (.f64 2 (.f64 2 (.f64 32 (.f64 eps x)))) 64)
(.f64 2 (.f64 eps x))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 32 (*.f64 eps x))))) 128)
(.f64 2 (.f64 eps x))
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 32 (.f64 eps x))))) (.f64 2 (.f64 2 (.f64 2 (.f64 32 (.f64 eps x)))))) 256)
(.f64 2 (.f64 eps x))
(pow.f64 (.f64 2 (.f64 eps x)) 1)
(.f64 2 (.f64 eps x))

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 eps (*.f64 x 1/2)) 4)

Compiler

Compiled 21 to 14 computations (33.3% saved)

series0.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite265.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

2456×	`rational.json-simplify-35`
1298×	`rational.json-1`
1298×	`rational.json-2`
1298×	`rational.json-3`
1290×	`exponential.json-3`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	61	19
2	138	19
3	313	13
4	628	13
5	1293	13
6	2509	13
7	4122	13
8	5112	13
9	6267	13
10	7250	13
11	7250	13
12	7250	13

Stop Event

1×	node limit

Counts

1 → 17

Calls

Call 1

Inputs
(.f64 (.f64 eps (*.f64 x 1/2)) 4)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 eps (*.f64 x 1/2)) (*.f64 eps (*.f64 x 3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 x (+.f64 eps eps)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 x (+.f64 eps eps)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 eps x) (*.f64 eps x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 eps (*.f64 x 3/2)) (*.f64 eps (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 x (+.f64 eps eps)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x (+.f64 eps eps)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 eps (*.f64 x 4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 eps (*.f64 x 8)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (*.f64 eps x) 16) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 (*.f64 eps x) 16)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 (*.f64 eps x) 16))) 32)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (*.f64 eps x) 16)))) 64)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (*.f64 eps x) 16))))) 128)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (*.f64 eps x) 16)))))) 256)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (*.f64 eps x) 16)))))) (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 2 (*.f64 (*.f64 eps x) 16))))))) 512)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 x (+.f64 eps eps)) 1)))))

simplify605.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

3118×	`rational.json-simplify-35`
2244×	`rational.json-simplify-2`
1326×	`rational.json-simplify-53`
1092×	`rational.json-simplify-1`
994×	`exponential.json-simplify-26`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	533
1	137	533
2	264	533
3	570	533
4	2141	533
5	4541	533
6	5530	533
7	5970	533
8	6164	533
9	6301	533
10	6436	533
11	7027	533
12	7028	533
13	7156	533
14	7266	533
15	7362	533
16	7529	533
17	7671	533
18	7808	533
19	7943	533

Stop Event

1×	node limit

Counts

41 → 18

Calls

Call 1

Inputs
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(+.f64 (.f64 eps (.f64 x 1/2)) (.f64 eps (.f64 x 3/2)))
(+.f64 (*.f64 x (+.f64 eps eps)) 0)
(+.f64 0 (*.f64 x (+.f64 eps eps)))
(+.f64 (.f64 eps x) (.f64 eps x))
(+.f64 (.f64 eps (.f64 x 3/2)) (.f64 eps (.f64 x 1/2)))
(-.f64 (*.f64 x (+.f64 eps eps)) 0)
(/.f64 (*.f64 x (+.f64 eps eps)) 1)
(/.f64 (.f64 eps (.f64 x 4)) 2)
(/.f64 (.f64 eps (.f64 x 8)) 4)
(/.f64 (.f64 (.f64 eps x) 16) 8)
(/.f64 (.f64 2 (.f64 (*.f64 eps x) 16)) 16)
(/.f64 (.f64 2 (.f64 2 (.f64 (.f64 eps x) 16))) 32)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (*.f64 eps x) 16)))) 64)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (.f64 eps x) 16))))) 128)
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (*.f64 eps x) 16)))))) 256)
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (.f64 eps x) 16)))))) (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (.f64 eps x) 16))))))) 512)
(pow.f64 (*.f64 x (+.f64 eps eps)) 1)

Outputs
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(.f64 2 (.f64 eps x))
(+.f64 (.f64 eps (.f64 x 1/2)) (.f64 eps (.f64 x 3/2)))
(.f64 2 (.f64 eps x))
(+.f64 (*.f64 x (+.f64 eps eps)) 0)
(.f64 2 (.f64 eps x))
(+.f64 0 (*.f64 x (+.f64 eps eps)))
(.f64 2 (.f64 eps x))
(+.f64 (.f64 eps x) (.f64 eps x))
(.f64 2 (.f64 eps x))
(+.f64 (.f64 eps (.f64 x 3/2)) (.f64 eps (.f64 x 1/2)))
(.f64 2 (.f64 eps x))
(-.f64 (*.f64 x (+.f64 eps eps)) 0)
(.f64 2 (.f64 eps x))
(/.f64 (*.f64 x (+.f64 eps eps)) 1)
(.f64 2 (.f64 eps x))
(/.f64 (.f64 eps (.f64 x 4)) 2)
(.f64 2 (.f64 eps x))
(/.f64 (.f64 eps (.f64 x 8)) 4)
(.f64 2 (.f64 eps x))
(/.f64 (.f64 (.f64 eps x) 16) 8)
(.f64 2 (.f64 eps x))
(/.f64 (.f64 2 (.f64 (*.f64 eps x) 16)) 16)
(.f64 2 (.f64 eps x))
(/.f64 (.f64 2 (.f64 2 (.f64 (.f64 eps x) 16))) 32)
(.f64 2 (.f64 eps x))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 (*.f64 eps x) 16)))) 64)
(.f64 2 (.f64 eps x))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (.f64 eps x) 16))))) 128)
(.f64 2 (.f64 eps x))
(/.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (*.f64 eps x) 16)))))) 256)
(.f64 2 (.f64 eps x))
(/.f64 (+.f64 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (.f64 eps x) 16)))))) (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 2 (.f64 (.f64 eps x) 16))))))) 512)
(.f64 2 (.f64 eps x))
(pow.f64 (*.f64 x (+.f64 eps eps)) 1)
(.f64 2 (.f64 eps x))

eval75.0ms (0.7%)

Compiler: Compiled 475 to 294 computations (38.1% saved)

prune10.0ms (0.1%)

Pruning

12 alts after pruning (4 fresh and 8 done)

	Pruned	Kept	Total
New	39	4	43
Fresh	0	0	0
Picked	0	1	1
Done	0	7	7
Total	39	12	51

Error

0.0b

Counts

51 → 12

Alt Table

Click to see full alt table

Status	Error	Program
✓	16.3b	(pow.f64 eps 2)
✓	14.8b	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))
✓	0.0b	(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
	24.3b	(+.f64 (+.f64 (.f64 eps x) (.f64 (.f64 x (.f64 eps 1/4)) 3)) (.f64 x (.f64 eps 1/4)))
	24.3b	(+.f64 (+.f64 (.f64 eps x) (.f64 (.f64 eps (.f64 x 1/8)) 7)) (.f64 eps (.f64 x 1/8)))
✓	24.3b	(+.f64 (.f64 eps (.f64 x 3/2)) (.f64 eps (.f64 x 1/2)))
	24.3b	(+.f64 (.f64 eps x) (+.f64 (.f64 eps (.f64 x 1/8)) (.f64 eps (.f64 (.f64 x 1/8) 7))))
✓	24.3b	(.f64 (.f64 eps (*.f64 x 1/2)) 4)
	24.3b	(.f64 eps (+.f64 (.f64 x 1/8) (+.f64 x (*.f64 x 7/8))))
✓	24.3b	(.f64 eps (.f64 x 2))
✓	24.3b	(.f64 16 (.f64 eps (/.f64 x 8)))
✓	24.3b	(.f64 2 (.f64 eps x))

Compiler

Compiled 142 to 101 computations (28.9% saved)

regimes21.0ms (0.2%)

Counts

12 → 1

Calls

Call 1

Inputs
(.f64 2 (.f64 eps x))
(.f64 eps (.f64 x 2))
(.f64 16 (.f64 eps (/.f64 x 8)))
(.f64 (.f64 eps (*.f64 x 1/2)) 4)
(.f64 eps (+.f64 (.f64 x 1/8) (+.f64 x (*.f64 x 7/8))))
(+.f64 (.f64 eps (.f64 x 3/2)) (.f64 eps (.f64 x 1/2)))
(+.f64 (.f64 eps x) (+.f64 (.f64 eps (.f64 x 1/8)) (.f64 eps (.f64 (.f64 x 1/8) 7))))
(+.f64 (+.f64 (.f64 eps x) (.f64 (.f64 eps (.f64 x 1/8)) 7)) (.f64 eps (.f64 x 1/8)))
(+.f64 (+.f64 (.f64 eps x) (.f64 (.f64 x (.f64 eps 1/4)) 3)) (.f64 x (.f64 eps 1/4)))
(pow.f64 eps 2)
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

Outputs
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))

Calls

3 calls:

8.0ms	eps
6.0ms	x
3.0ms	(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`eps`
0.0b	1	`(-.f64 (pow.f64 (+.f64 x eps) 2) (pow.f64 x 2))`

Compiler

Compiled 137 to 88 computations (35.8% saved)

regimes258.0ms (2.4%)

Counts

10 → 3

Calls

Call 1

Inputs
(.f64 2 (.f64 eps x))
(.f64 eps (.f64 x 2))
(.f64 16 (.f64 eps (/.f64 x 8)))
(.f64 (.f64 eps (*.f64 x 1/2)) 4)
(.f64 eps (+.f64 (.f64 x 1/8) (+.f64 x (*.f64 x 7/8))))
(+.f64 (.f64 eps (.f64 x 3/2)) (.f64 eps (.f64 x 1/2)))
(+.f64 (.f64 eps x) (+.f64 (.f64 eps (.f64 x 1/8)) (.f64 eps (.f64 (.f64 x 1/8) 7))))
(+.f64 (+.f64 (.f64 eps x) (.f64 (.f64 eps (.f64 x 1/8)) 7)) (.f64 eps (.f64 x 1/8)))
(+.f64 (+.f64 (.f64 eps x) (.f64 (.f64 x (.f64 eps 1/4)) 3)) (.f64 x (.f64 eps 1/4)))
(pow.f64 eps 2)

Outputs
(.f64 eps (.f64 x 2))
(pow.f64 eps 2)
(.f64 2 (.f64 eps x))

Calls

2 calls:

239.0ms	eps
16.0ms	x

Results

Error	Segments	Branch
5.1b	3	`x`
7.6b	5	`eps`

Compiler

Compiled 108 to 68 computations (37% saved)

bsearch39.0ms (0.4%)

Algorithm

2×	binary-search

Steps

Time	Left	Right
17.0ms	1.054369488019638e-95	3.117183138766785e-91
22.0ms	-3.644996617885371e-103	-5.526208608709017e-107

Results

22.0ms	119×	body	512	valid
15.0ms	137×	body	256	valid

Compiler

Compiled 240 to 188 computations (21.7% saved)

regimes615.0ms (5.7%)

Accuracy

Total -0.2b remaining (-0.8%)

Threshold costs -0.2b (-0.8%)

Counts

9 → 1

Calls

Call 1

Inputs
(.f64 2 (.f64 eps x))
(.f64 eps (.f64 x 2))
(.f64 16 (.f64 eps (/.f64 x 8)))
(.f64 (.f64 eps (*.f64 x 1/2)) 4)
(.f64 eps (+.f64 (.f64 x 1/8) (+.f64 x (*.f64 x 7/8))))
(+.f64 (.f64 eps (.f64 x 3/2)) (.f64 eps (.f64 x 1/2)))
(+.f64 (.f64 eps x) (+.f64 (.f64 eps (.f64 x 1/8)) (.f64 eps (.f64 (.f64 x 1/8) 7))))
(+.f64 (+.f64 (.f64 eps x) (.f64 (.f64 eps (.f64 x 1/8)) 7)) (.f64 eps (.f64 x 1/8)))
(+.f64 (+.f64 (.f64 eps x) (.f64 (.f64 x (.f64 eps 1/4)) 3)) (.f64 x (.f64 eps 1/4)))

Outputs
(.f64 eps (.f64 x 2))

Calls

2 calls:

608.0ms	x
5.0ms	eps

Results

Error	Segments	Branch
24.3b	1	`x`
24.3b	1	`eps`

Compiler

Compiled 105 to 66 computations (37.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	102

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
(if (<=.f64 x -5487280990934681/322781234760863573706989896500376484291213224103652939103832419567580952752105149328705669160017228929487896496593436672) (.f64 eps (.f64 x 2)) (if (<=.f64 x 4321318352303853/18788340662190665823115844774314696219005460391266558965658327772257672200916867547709591987078149624255479808) (pow.f64 eps 2) (.f64 2 (.f64 eps x))))
(.f64 eps (.f64 x 2))
(.f64 2 (.f64 eps x))

Outputs
(+.f64 (pow.f64 eps 2) (.f64 eps (.f64 x 2)))
(if (<=.f64 x -5487280990934681/322781234760863573706989896500376484291213224103652939103832419567580952752105149328705669160017228929487896496593436672) (.f64 eps (.f64 x 2)) (if (<=.f64 x 4321318352303853/18788340662190665823115844774314696219005460391266558965658327772257672200916867547709591987078149624255479808) (pow.f64 eps 2) (.f64 2 (.f64 eps x))))
(.f64 eps (.f64 x 2))
(.f64 2 (.f64 eps x))

Compiler

Compiled 48 to 34 computations (29.2% saved)

soundness209.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1792×	`rational.json-simplify-1`
1430×	`rational.json-simplify-52`
1416×	`rational.json-simplify-2`
1286×	`rational.json-simplify-35`
938×	`rational.json-simplify-41`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	156	2945
1	316	2753
2	867	2747
3	1577	2747
4	3176	2747
5	3797	2747
6	4334	2747
7	4632	2747
8	5164	2747
9	5476	2747
10	6589	2747

Stop Event

1×	node limit

Compiler

Compiled 20 to 14 computations (30% saved)

end1.4s (12.8%)

Compiler: Compiled 42 to 27 computations (35.7% saved)

Details

analyze1.0ms (0%)

sample2.4s (22.7%)

preprocess4.0ms (0%)

simplify10.0ms (0.1%)

eval0.0ms (0%)

prune1.0ms (0%)

localize9.0ms (0.1%)

series3.0ms (0%)

rewrite1.1s (10.5%)

simplify330.0ms (3.1%)

eval361.0ms (3.3%)

prune15.0ms (0.1%)

localize5.0ms (0%)

series2.0ms (0%)

rewrite222.0ms (2.1%)

simplify532.0ms (4.9%)

localize5.0ms (0%)

localize16.0ms (0.1%)

series1.0ms (0%)

rewrite484.0ms (4.5%)

simplify477.0ms (4.4%)

localize3.0ms (0%)

eval9.0ms (0.1%)

prune62.0ms (0.6%)

localize12.0ms (0.1%)

series4.0ms (0%)

rewrite223.0ms (2.1%)

simplify204.0ms (1.9%)

eval13.0ms (0.1%)

prune12.0ms (0.1%)

localize96.0ms (0.9%)

series1.0ms (0%)

rewrite204.0ms (1.9%)

simplify403.0ms (3.7%)

localize8.0ms (0.1%)

series0.0ms (0%)

rewrite265.0ms (2.5%)

simplify605.0ms (5.6%)

eval75.0ms (0.7%)

prune10.0ms (0.1%)

regimes21.0ms (0.2%)

regimes258.0ms (2.4%)

bsearch39.0ms (0.4%)

regimes615.0ms (5.7%)

simplify3.0ms (0%)

soundness209.0ms (1.9%)

end1.4s (12.8%)

Profiling