Details

sample33.0ms

Algorithm

intervals

Results

11.0ms	257×	body	80	valid
3.0ms	11×	body	640	valid
3.0ms	83×	body	80	overflowed
2.0ms	4×	body	1280	valid
2.0ms	9×	body	320	valid
1.0ms	6×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	19	5
2	23	5
3	23	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 0.8b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.8b	(log (+ 1.0 (exp x)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod`
6×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-div` `fma-neg` `prod-diff` `associate--l+`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `log-pow` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`associate--l-`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `rem-log-exp` `sum-log` `flip--`

Counts

3 → 62

Calls

3 calls:

3.0ms	(+ 1.0 (exp x))
9.0ms	(- (log (+ 1.0 (exp x))) (* x y))
3.0ms	(log (+ 1.0 (exp x)))

series126.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+ 1.0 (exp x))
60.0ms	(- (log (+ 1.0 (exp x))) (* x y))
59.0ms	(log (+ 1.0 (exp x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	236	404
1	702	369
2	2284	367
3	5002	340

prune145.0ms

Filtered

71 candidates to 54 candidates (76.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	4	72

Merged error: 0.5b

Counts

72 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp x)))
0.0b	(sqrt (+ 1.0 (exp x)))
1.4b	(log (sqrt (+ 1.0 (exp x))))
1.4b	(log (sqrt (+ 1.0 (exp x))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`add-sqr-sqrt` `sqrt-prod`
14×	`log-prod`
10×	`pow1` `add-cube-cbrt`
8×	`sqrt-div`
6×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `log-div` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp` `hypot-def`

Counts

4 → 82

Calls

4 calls:

4.0ms	(sqrt (+ 1.0 (exp x)))
4.0ms	(sqrt (+ 1.0 (exp x)))
4.0ms	(log (sqrt (+ 1.0 (exp x))))
4.0ms	(log (sqrt (+ 1.0 (exp x))))

series283.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ 1.0 (exp x)))
40.0ms	(sqrt (+ 1.0 (exp x)))
104.0ms	(log (sqrt (+ 1.0 (exp x))))
108.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify59.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	172	598
1	486	558
2	1684	540
3	5002	522

prune236.0ms

Filtered

94 candidates to 70 candidates (74.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	94	4	98

Merged error: 0.5b

Counts

98 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
0.0b	(fma 1/2 (pow x 2) (+ x 2.0))
7.6b	(log (fma 1/2 (pow x 2) (+ x 2.0)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `log-prod`
4×	`add-exp-log` `fma-neg` `prod-diff` `add-log-exp`
3×	`expm1-log1p-u` `associate--l+` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `fma-udef`

Counts

3 → 49

Calls

3 calls:

4.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
1.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
1.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

series151.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
17.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
55.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify88.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	229	423
1	763	380
2	3267	376
3	5001	356

prune143.0ms

Filtered

58 candidates to 46 candidates (79.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	58	4	62

Merged error: 0.5b

Counts

62 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow x 2) (sqrt 2.0))
0.5b	(/ x (sqrt 2.0))
1.4b	(log (sqrt (+ 1.0 (exp x))))
8.2b	(log (fma (/ (pow x 2) (sqrt 2.0)) (- 1/4 (/ 1/8 2.0)) (fma 1/2 (/ x (sqrt 2.0)) (sqrt 2.0))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
56×	`*-un-lft-identity`
54×	`add-sqr-sqrt` `add-cube-cbrt`
43×	`sqrt-prod`
21×	`unpow-prod-down`
13×	`add-exp-log`
12×	`associate-/r*`
11×	`associate-/l*`
10×	`log-prod`
8×	`add-cbrt-cube`
7×	`pow1` `unpow2` `sqr-pow`
4×	`expm1-log1p-u` `div-exp` `log-pow` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `log-div` `frac-2neg` `sqrt-div` `rem-log-exp` `clear-num` `div-inv`
1×	`pow-to-exp` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `flip-+` `distribute-lft-out`

Counts

4 → 155

Calls

4 calls:

6.0ms	(/ (pow x 2) (sqrt 2.0))
4.0ms	(/ x (sqrt 2.0))
4.0ms	(log (sqrt (+ 1.0 (exp x))))
1.0ms	(log (fma (/ (pow x 2) (sqrt 2.0)) (- 1/4 (/ 1/8 2.0)) (fma 1/2 (/ x (sqrt 2.0)) (sqrt 2.0))))

series434.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (pow x 2) (sqrt 2.0))
58.0ms	(/ x (sqrt 2.0))
102.0ms	(log (sqrt (+ 1.0 (exp x))))
210.0ms	(log (fma (/ (pow x 2) (sqrt 2.0)) (- 1/4 (/ 1/8 2.0)) (fma 1/2 (/ x (sqrt 2.0)) (sqrt 2.0))))

simplify53.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	487	1242
1	1678	1075
2	5002	1058

prune529.0ms

Filtered

167 candidates to 104 candidates (62.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	165	2	167
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	166	5	171

Merged error: 0.5b

Counts

171 → 5

regimes96.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 12.2b

bsearch50.0ms

Steps

Iters	Range		Point
9	-5.855776674212404	-7.74497267090904e-05	-0.0008614003792471078

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	29
1	41	29

end0.0ms

sample882.0ms

Algorithm

intervals

Results

387.0ms	8391×	body	80	valid
95.0ms	2450×	body	80	overflowed
72.0ms	244×	body	640	valid
67.0ms	126×	body	1280	valid
36.0ms	198×	body	320	valid
11.0ms	99×	body	160	valid