Details

sample71.0ms

Algorithm

intervals

Results

43.0ms	237×	body	10240	exit
9.0ms	190×	body	80	valid
3.0ms	29×	body	320	valid
2.0ms	14×	body	640	valid
1.0ms	23×	body	160	valid

simplify47.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (7.0ms)

Iter	Nodes	Cost
0	21	9
1	52	9
2	113	9
3	240	8
4	1625	8
5	5001	8

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ wj (+ wj 1))
0.0b	(/ x (+ wj 1))
0.2b	(/ (/ x (+ wj 1)) (exp wj))
5.8b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

231×	`*-un-lft-identity`
175×	`times-frac`
129×	`add-sqr-sqrt`
124×	`add-cube-cbrt`
72×	`prod-diff`
52×	`distribute-lft-out`
24×	`associate-/l*`
20×	`associate-/r/`
13×	`add-cbrt-cube`
11×	`add-exp-log` `flip3-+` `associate-/r*` `flip-+` `div-inv`
9×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `fma-neg` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`diff-log` `frac-sub` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--` `associate-/l/`

Counts

4 → 260

Calls

4 calls:

5.0ms	(/ wj (+ wj 1))
8.0ms	(/ x (+ wj 1))
9.0ms	(/ (/ x (+ wj 1)) (exp wj))
32.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series143.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ wj (+ wj 1))
22.0ms	(/ x (+ wj 1))
46.0ms	(/ (/ x (+ wj 1)) (exp wj))
54.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify127.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	1015	4090
1	4555	3249
2	5001	3243

prune525.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (pow wj 2))
0.0b	(- (+ x (pow wj 2)) (* 2 (* wj x)))
0.0b	(* 2 (* wj x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`fma-neg` `prod-diff`
3×	`expm1-log1p-u` `fma-def` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out`
2×	`diff-log` `sum-log`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `associate-r` `associate--l+` `*-commutative` `flip--` `flip-+`

Counts

3 → 61

Calls

3 calls:

5.0ms	(+ x (pow wj 2))
7.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
5.0ms	(* 2 (* wj x))

series80.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ x (pow wj 2))
29.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
19.0ms	(* 2 (* wj x))

simplify36.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	237	344
1	922	293
2	5001	274

prune147.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (fma wj wj x) (* 2 (* wj x)))
0.0b	(* 2 (* wj x))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 41

Calls

2 calls:

3.0ms	(- (fma wj wj x) (* 2 (* wj x)))
5.0ms	(* 2 (* wj x))

series46.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(- (fma wj wj x) (* 2 (* wj x)))
19.0ms	(* 2 (* wj x))

simplify132.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (128.0ms)

Iter	Nodes	Cost
0	185	232
1	729	206
2	4842	196
3	5001	191

prune103.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (pow wj 2))
0.0b	(- x (pow wj 2))
0.1b	(* (- x (pow wj 2)) (fma wj wj x))
26.0b	(/ (* (- x (pow wj 2)) (fma wj wj x)) (- x (pow wj 2)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
48×	`*-un-lft-identity` `prod-diff`
38×	`add-cube-cbrt`
23×	`unpow-prod-down`
20×	`difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube` `unpow2` `sqr-pow`
8×	`times-frac` `associate-l` `associate-/r*` `add-log-exp`
6×	`pow1` `fma-neg`
5×	`flip3--` `flip--` `distribute-lft-out--`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u`
3×	`associate-r`
2×	`cbrt-undiv` `sub-neg` `diff-log` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `fma-udef` `associate-/l/`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 158

Calls

4 calls:

6.0ms	(- x (pow wj 2))
6.0ms	(- x (pow wj 2))
8.0ms	(* (- x (pow wj 2)) (fma wj wj x))
13.0ms	(/ (* (- x (pow wj 2)) (fma wj wj x)) (- x (pow wj 2)))

series190.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- x (pow wj 2))
38.0ms	(- x (pow wj 2))
89.0ms	(* (- x (pow wj 2)) (fma wj wj x))
29.0ms	(/ (* (- x (pow wj 2)) (fma wj wj x)) (- x (pow wj 2)))

simplify81.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	443	1412
1	2209	973
2	5001	940

prune328.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

regimes77.0ms

Accuracy

52.7% (0.9b remaining)

Error of 1.3b against oracle of 0.4b and baseline of 2.3b

bsearch42.0ms

Steps

Iters	Range		Point
10	4.8723734835607145e-12	0.22405535791780642	7.787217220559818e-07

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	32
1	32	32

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.4s	7489×	body	10240	exit
198.0ms	6331×	body	80	valid
77.0ms	785×	body	320	valid
71.0ms	422×	body	640	valid
33.0ms	536×	body	160	valid