Details

sample22.0ms

Algorithm

intervals

Results

4.0ms	189×	body	80	valid
4.0ms	21×	body	320	valid
2.0ms	17×	body	1280	valid
2.0ms	19×	body	640	valid
0.0ms	10×	body	160	valid

simplify78.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (11.0ms)

Iter	Nodes	Cost
0	16	5
1	35	5
2	76	5
3	137	5
4	285	4
5	459	4
6	719	4
7	848	4
8	1064	4
9	1397	4
10	2101	4
11	5002	4

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
3.3b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `distribute-lft-out`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `fma-udef` `div-inv`

Counts

2 → 45

Calls

2 calls:

11.0ms	(/ y (+ y 1.0))
0.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series94.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ y (+ y 1.0))
59.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify108.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	203	263
1	708	238
2	3148	232
3	5002	228

prune141.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
10.6b	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)
0.0ms	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

series648.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(cbrt y)
190.0ms	(cbrt y)
196.0ms	(cbrt y)
70.0ms	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

simplify49.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	104	277
1	282	243
2	1092	232
3	5002	228

prune219.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ y 1.0) y)
0.1b	(/ (- x 1.0) (/ (+ y 1.0) y))
3.3b	(+ (/ (- x 1.0) (/ (+ y 1.0) y)) 1.0)

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

304×	`times-frac`
276×	`*-un-lft-identity`
200×	`add-sqr-sqrt`
134×	`add-cube-cbrt`
85×	`fma-def`
38×	`distribute-lft-out`
33×	`distribute-lft-out--` `difference-of-squares`
19×	`associate-/r*`
14×	`div-inv`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-/l*`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`frac-2neg` `flip3-+` `div-sub` `clear-num` `associate-/r/` `flip-+`
1×	`+-commutative` `associate-+l-` `flip3--` `sum-log` `flip--`

Counts

3 → 256

Calls

3 calls:

18.0ms	(/ (+ y 1.0) y)
30.0ms	(/ (- x 1.0) (/ (+ y 1.0) y))
113.0ms	(+ (/ (- x 1.0) (/ (+ y 1.0) y)) 1.0)

series175.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (+ y 1.0) y)
51.0ms	(/ (- x 1.0) (/ (+ y 1.0) y))
75.0ms	(+ (/ (- x 1.0) (/ (+ y 1.0) y)) 1.0)

simplify76.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	702	1484
1	2723	1425
2	5001	1422

prune806.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- x 1.0) (+ y 1.0))
16.1b	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
20×	`times-frac`
13×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-sub` `div-exp` `clear-num` `flip--` `flip-+` `fma-udef` `div-inv`

Counts

2 → 58

Calls

2 calls:

23.0ms	(/ (- x 1.0) (+ y 1.0))
0.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

series97.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(/ (- x 1.0) (+ y 1.0))
67.0ms	(fma (/ (- x 1.0) (+ y 1.0)) y 1.0)

simplify118.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	276	398
1	840	371
2	4158	364
3	5001	364

prune135.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes60.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 14.6b

bsearch70.0ms

Steps

Iters	Range		Point
9	6031.575547282502	2908035933644.0933	117884680.70271897
7	-15126611761059.418	-210229570708.90164	-213552842032.68936

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	8
1	24	8

end0.0ms

sample478.0ms

Algorithm

intervals

Results

152.0ms	6069×	body	80	valid
64.0ms	779×	body	640	valid
37.0ms	350×	body	1280	valid
33.0ms	516×	body	320	valid
13.0ms	286×	body	160	valid