Details

sample139.0ms

Algorithm

intervals

Results

80.0ms	92×	body	1280	valid
34.0ms	87×	body	640	valid
8.0ms	41×	body	320	valid
4.0ms	256×	pre	80	true
3.0ms	28×	body	160	valid
0.0ms	8×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	5
1	11	5
2	11	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.8b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
7.1b	(log (+ 1.0 x))
7.4b	(log (- 1.0 x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
16×	`times-frac`
15×	`pow1` `add-cube-cbrt`
12×	`log-pow`
9×	`log-prod`
7×	`add-exp-log`
6×	`log-div`
5×	`add-cbrt-cube`
4×	`associate-/r` `associate-/l`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`flip3--` `div-sub` `rem-log-exp` `flip--`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 75

Calls

3 calls:

6.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
3.0ms	(log (+ 1.0 x))
4.0ms	(log (- 1.0 x))

series220.0ms

Counts

3 → 9

Calls

3 calls:

130.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
41.0ms	(log (+ 1.0 x))
49.0ms	(log (- 1.0 x))

simplify47.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	452	686
1	1669	638
2	5001	623

prune231.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 57.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1.0 1.0) (* x x))
0.0b	(/ (log (- (* 1.0 1.0) (* x x))) (log (+ 1.0 x)))
3.6b	(log (- (* 1.0 1.0) (* x x)))
7.1b	(log (+ 1.0 x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `times-frac`
12×	`log-pow`
8×	`add-exp-log` `log-prod`
6×	`log-div` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
3×	`flip3--` `flip--`
2×	`div-sub` `rem-log-exp` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `fma-neg` `diff-log` `div-exp` `prod-diff` `clear-num` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 91

Calls

4 calls:

4.0ms	(- (* 1.0 1.0) (* x x))
6.0ms	(/ (log (- (* 1.0 1.0) (* x x))) (log (+ 1.0 x)))
4.0ms	(log (- (* 1.0 1.0) (* x x)))
3.0ms	(log (+ 1.0 x))

series337.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* 1.0 1.0) (* x x))
140.0ms	(/ (log (- (* 1.0 1.0) (* x x))) (log (+ 1.0 x)))
108.0ms	(log (- (* 1.0 1.0) (* x x)))
45.0ms	(log (+ 1.0 x))

simplify59.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	566	984
1	2205	917
2	5002	914

prune263.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* 1.0 1.0) (* x x))
0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(/ (log (- (* 1.0 1.0) (* x x))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
3.6b	(log (- (* 1.0 1.0) (* x x)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

92×	`times-frac`
82×	`add-sqr-sqrt`
68×	`associate-r`
56×	`unpow-prod-down`
48×	`add-cube-cbrt` `*-un-lft-identity`
30×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
11×	`pow1` `add-cbrt-cube`
10×	`div-exp` `prod-exp`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
5×	`log-pow`
4×	`expm1-log1p-u` `log-div` `log-prod` `log1p-expm1-u` `associate-/l*`
3×	`flip3--` `associate-l` `associate-/r*` `flip--`
2×	`cbrt-undiv` `div-sub` `cbrt-unprod` `div-inv` `difference-of-squares`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `associate-r/` `rem-log-exp` `prod-diff` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 181

Calls

4 calls:

4.0ms	(- (* 1.0 1.0) (* x x))
19.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
6.0ms	(/ (log (- (* 1.0 1.0) (* x x))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
4.0ms	(log (- (* 1.0 1.0) (* x x)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* 1.0 1.0) (* x x))
55.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
134.0ms	(/ (log (- (* 1.0 1.0) (* x x))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
116.0ms	(log (- (* 1.0 1.0) (* x x)))

simplify99.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	967	1777
1	4700	1515
2	5001	1513

prune607.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow x 4) (pow 1.0 2)))
0.0b	(+ (* 1.0 (pow x 2)) (* 1/2 (/ (pow x 4) (pow 1.0 2))))
0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
24.9b	(/ (- (log 1.0) (+ (* 1.0 (pow x 2)) (* 1/2 (/ (pow x 4) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

166×	`times-frac`
151×	`add-sqr-sqrt`
128×	`associate-r`
108×	`unpow-prod-down`
93×	`*-un-lft-identity`
81×	`add-cube-cbrt`
52×	`add-exp-log`
46×	`sqr-pow`
34×	`unpow2`
30×	`unswap-sqr`
20×	`prod-exp`
19×	`div-exp`
16×	`add-cbrt-cube`
12×	`pow1` `pow-to-exp` `pow-exp`
8×	`distribute-lft-out--`
6×	`associate-l` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `log-pow` `cbrt-unprod` `log1p-expm1-u` `difference-of-squares`
3×	`cbrt-undiv` `associate-/r*` `div-inv`
2×	`associate-r/` `pow-prod-down` `-commutative` `associate-/l/`
1×	`+-commutative` `flip3--` `fma-def` `frac-2neg` `flip3-+` `div-sub` `clear-num` `sum-log` `flip--` `flip-+`

Counts

4 → 270

Calls

4 calls:

18.0ms	(* 1/2 (/ (pow x 4) (pow 1.0 2)))
4.0ms	(+ (* 1.0 (pow x 2)) (* 1/2 (/ (pow x 4) (pow 1.0 2))))
19.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
14.0ms	(/ (- (log 1.0) (+ (* 1.0 (pow x 2)) (* 1/2 (/ (pow x 4) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

series393.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* 1/2 (/ (pow x 4) (pow 1.0 2)))
134.0ms	(+ (* 1.0 (pow x 2)) (* 1/2 (/ (pow x 4) (pow 1.0 2))))
55.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
137.0ms	(/ (- (log 1.0) (+ (* 1.0 (pow x 2)) (* 1/2 (/ (pow x 4) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

simplify62.0ms

Algorithm

egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1227	2609
1	5001	2342

prune921.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes47.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	18
1	27	18

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.9s	3409×	body	1280	valid
966.0ms	2456×	body	640	valid
249.0ms	1258×	body	320	valid
96.0ms	8000×	pre	80	true
69.0ms	642×	body	160	valid
11.0ms	235×	body	80	valid