Details

sample28.0ms

Algorithm

intervals

Results

10.0ms	202×	body	80	valid
4.0ms	21×	body	640	valid
3.0ms	19×	body	320	valid
2.0ms	9×	body	1280	valid
0.0ms	5×	body	160	valid

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (12.0ms)

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: 12.8b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
2.0b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite7.0ms

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:

5.0ms	(/ y (+ y 1.0))
0.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series102.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(/ y (+ y 1.0))
60.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify112.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (107.0ms)

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

prune146.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ y 1.0))
0.3b	(cbrt (+ y 1.0))
0.3b	(cbrt (+ y 1.0))
8.8b	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

2.0ms	(cbrt (+ y 1.0))
2.0ms	(cbrt (+ y 1.0))
2.0ms	(cbrt (+ y 1.0))
0.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

series351.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(cbrt (+ y 1.0))
97.0ms	(cbrt (+ y 1.0))
97.0ms	(cbrt (+ y 1.0))
61.0ms	(fma (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0))) (- x 1.0) 1.0)

simplify72.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	230	552
1	657	500
2	2252	479
3	5002	448

prune280.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
8.8b	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

rewrite3.0ms

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:

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

series652.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(cbrt y)
188.0ms	(cbrt y)
190.0ms	(cbrt y)
77.0ms	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (45.0ms)

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

prune224.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (+ y 1.0) y)
0.1b	(/ (- x 1.0) (/ (+ y 1.0) y))
2.0b	(+ (/ (- x 1.0) (/ (+ y 1.0) y)) 1.0)

rewrite118.0ms

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:

8.0ms	(/ (+ y 1.0) y)
15.0ms	(/ (- x 1.0) (/ (+ y 1.0) y))
81.0ms	(+ (/ (- x 1.0) (/ (+ y 1.0) y)) 1.0)

series175.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ (+ y 1.0) y)
52.0ms	(/ (- x 1.0) (/ (+ y 1.0) y))
74.0ms	(+ (/ (- x 1.0) (/ (+ y 1.0) y)) 1.0)

simplify81.0ms

Algorithm

egg-herbie

Counts

265 → 265

Iterations

Useful iterations: 2 (63.0ms)

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

prune585.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

regimes57.0ms

Accuracy

99.5% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 7.5b

bsearch110.0ms

Steps

Iters	Range		Point
10	6835871.788935939	2.88914674873619e+20	138811322.44829124
9	-203252004905.3082	-1043668.381521804	-102786700.59358019

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	12
1	26	12

end0.0ms

sample802.0ms

Algorithm

intervals

Results

318.0ms	6093×	body	80	valid
138.0ms	727×	body	640	valid
103.0ms	367×	body	1280	valid
74.0ms	517×	body	320	valid
31.0ms	296×	body	160	valid