Details

sample58.0ms

Algorithm

intervals

Results

20.0ms	47×	body	1280	valid
10.0ms	39×	body	640	valid
7.0ms	166×	body	80	valid
4.0ms	27×	body	320	valid
3.0ms	108×	body	80	nan
1.0ms	15×	body	160	valid

simplify111.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (8.0ms)

Iter	Nodes	Cost
0	15	6
1	24	6
2	51	6
3	108	6
4	310	4
5	792	4
6	4183	4
7	5001	4

prune4.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 12.2b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (pow (/ x (+ x y)) x) x)
0.0b	(/ x (+ x y))
7.8b	(pow (/ x (+ x y)) x)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

6×	`unpow-prod-down` `associate-/r/`
4×	`div-inv` `associate-/l*`
3×	`flip3-+` `flip-+`
2×	`frac-2neg` `clear-num` `sqr-pow`
1×	`pow-to-exp`

Counts

3 → 17

Calls

3 calls:

4.0ms	(/ (pow (/ x (+ x y)) x) x)
3.0ms	(/ x (+ x y))
5.0ms	(pow (/ x (+ x y)) x)

series385.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms	(/ (pow (/ x (+ x y)) x) x)
40.0ms	(/ x (+ x y))
218.0ms	(pow (/ x (+ x y)) x)

simplify62.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	194	128
1	591	125
2	2419	124
3	5001	120

prune63.0ms

Filtered

26 candidates to 21 candidates (80.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	24	2	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	24	3	27

Merged error: 4.3b

Counts

27 → 3

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(/ (exp (* -1 y)) x)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

1×	`exp-neg` `frac-2neg` `mul-1-neg` `clear-num` `div-inv` `associate-/l/`

Counts

1 → 4

Calls

1 calls:

4.0ms

(/ (exp (* -1 y)) x)

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(/ (exp (* -1 y)) x)

simplify38.0ms

Algorithm

egg-herbie

Counts

7 → 7

Iterations

Useful iterations: 3 (10.0ms)

Iter	Nodes	Cost
0	41	23
1	79	22
2	234	22
3	805	21
4	5001	21

prune14.0ms

Filtered

7 candidates to 4 candidates (57.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	5	2	7
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	6	4	10

Merged error: 4.3b

Counts

10 → 4

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (exp y) x)
0.0b	(/ 1 (* (exp y) x))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

2×	`associate-/r` `-commutative`
1×	`frac-2neg` `clear-num` `div-inv` `inv-pow`

Counts

2 → 7

Calls

2 calls:

3.0ms	(* (exp y) x)
3.0ms	(/ 1 (* (exp y) x))

series43.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(* (exp y) x)
20.0ms	(/ 1 (* (exp y) x))

simplify66.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 4 (64.0ms)

Iter	Nodes	Cost
0	60	34
1	149	32
2	502	32
3	1986	32
4	5001	31

prune22.0ms

Filtered

13 candidates to 8 candidates (61.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	12	1	13
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	13	4	17

Merged error: 4.2b

Counts

17 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ 1 (fma x (fma (* 1/2 y) y y) x))
2.6b	(fma x (fma (* 1/2 y) y y) x)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

1×	`frac-2neg` `clear-num` `fma-udef` `div-inv` `inv-pow`

Counts

2 → 5

Calls

2 calls:

2.0ms	(/ 1 (fma x (fma (* 1/2 y) y y) x))
1.0ms	(fma x (fma (* 1/2 y) y y) x)

series99.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ 1 (fma x (fma (* 1/2 y) y y) x))
44.0ms	(fma x (fma (* 1/2 y) y y) x)

simplify63.0ms

Algorithm

egg-herbie

Counts

11 → 11

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	95	63
1	350	52
2	1685	52
3	5001	50

prune16.0ms

Filtered

11 candidates to 6 candidates (54.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	11	0	11
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	11	4	15

Merged error: 4.2b

Counts

15 → 4

regimes63.0ms

bsearch80.0ms

Steps

Iters	Range		Point
7	-6.2786212248486995e+38	-6.017134225162489e+36	-6.714296009098068e+36