Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	191×	body	80	valid
4.0ms	32×	body	640	valid
2.0ms	11×	body	1280	valid
1.0ms	16×	body	320	valid
0.0ms	6×	body	160	valid

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (13.0ms)

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

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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

Merged error: 15.5b

Counts

2 → 2

localize7.0ms

Local error

Found 1 expressions with local error:

2.3b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series58.0ms

Counts

1 → 3

Calls

1 calls:

58.0ms

(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify71.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (23.0ms)

Iter	Nodes	Cost
0	59	83
1	163	71
2	523	68
3	1872	66
4	5001	66

prune40.0ms

Filtered

13 candidates to 12 candidates (92.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	10	3	13
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	11	4	15

Merged error: 9.1b

Counts

15 → 4

localize7.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma (/ x y) (- (/ 1.0 y) 1.0) x)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma (/ x y) (- (/ 1.0 y) 1.0) x)

series44.0ms

Counts

1 → 3

Calls

1 calls:

44.0ms

(fma (/ x y) (- (/ 1.0 y) 1.0) x)

simplify99.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	45	85
1	121	67
2	489	67
3	2630	67
4	5001	67

prune37.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	11	2	13
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	11	6	17

Merged error: 9.1b

Counts

17 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma (/ x y) (- (/ 1.0 y) 1.0) x)) (cbrt (fma (/ x y) (- (/ 1.0 y) 1.0) x)))
14.7b	(cbrt (fma (/ x y) (- (/ 1.0 y) 1.0) x))
14.7b	(cbrt (fma (/ x y) (- (/ 1.0 y) 1.0) x))
14.7b	(cbrt (fma (/ x y) (- (/ 1.0 y) 1.0) x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

6.0ms	(* (cbrt (fma (/ x y) (- (/ 1.0 y) 1.0) x)) (cbrt (fma (/ x y) (- (/ 1.0 y) 1.0) x)))
1.0ms	(cbrt (fma (/ x y) (- (/ 1.0 y) 1.0) x))
1.0ms	(cbrt (fma (/ x y) (- (/ 1.0 y) 1.0) x))
2.0ms	(cbrt (fma (/ x y) (- (/ 1.0 y) 1.0) x))

series989.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (cbrt (fma (/ x y) (- (/ 1.0 y) 1.0) x)) (cbrt (fma (/ x y) (- (/ 1.0 y) 1.0) x)))
174.0ms	(cbrt (fma (/ x y) (- (/ 1.0 y) 1.0) x))
432.0ms	(cbrt (fma (/ x y) (- (/ 1.0 y) 1.0) x))
184.0ms	(cbrt (fma (/ x y) (- (/ 1.0 y) 1.0) x))

simplify57.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	309	1181
1	1095	1095
2	5001	984

prune289.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	88	5	93
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	89	10	99

Merged error: 9.0b

Counts

99 → 10

localize10.0ms

Local error

Found 2 expressions with local error:

2.3b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
3.3b	(log (exp (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod` `*-un-lft-identity` `log-pow`
3×	`pow1` `exp-prod`
2×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`
1×	`rem-log-exp` `exp-sum`

Counts

2 → 28

Calls

2 calls:

1.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
3.0ms	(log (exp (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)))

series121.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
59.0ms	(log (exp (fma (/ y (+ y 1.0)) (- x 1.0) 1.0)))

simplify89.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	96	226
1	245	195
2	676	189
3	2315	185
4	5003	185

prune72.0ms

Filtered

34 candidates to 27 candidates (79.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	34	10	44

Merged error: 9.0b

Counts

44 → 10

regimes118.0ms

Accuracy

98.7% (0.1b remaining)

Error of 7.7b against oracle of 7.6b and baseline of 14.4b

bsearch82.0ms

Steps

Iters	Range		Point
11	1.4731263457460937	2.5158614700293387e+20	5.977622371380283e+19
4	-114621340556398.55	-71135704204377.25	-113262414420397.89

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	8
1	21	8

end0.0ms

sample540.0ms

Algorithm

intervals

Results

189.0ms	6085×	body	80	valid
89.0ms	716×	body	640	valid
57.0ms	379×	body	1280	valid
45.0ms	523×	body	320	valid
18.0ms	297×	body	160	valid