Details

sample201.0ms

Algorithm

intervals

Results

127.0ms	119×	body	1280	valid
40.0ms	78×	body	640	valid
9.0ms	35×	body	320	valid
5.0ms	256×	pre	80	true
2.0ms	16×	body	160	valid
1.0ms	8×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	10	9
2	11	9
done	11	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.3b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.0b	(log (- 1.0 x))
5.3b	(log (+ 1.0 x))

rewrite84.0ms

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:

58.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
13.0ms	(log (- 1.0 x))
9.0ms	(log (+ 1.0 x))

series353.0ms

Counts

3 → 9

Calls

3 calls:

195.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
83.0ms	(log (- 1.0 x))
74.0ms	(log (+ 1.0 x))

simplify1.3s

Counts

84 → 84

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	192	1243
1	460	1173
2	1824	1095
done	5000	1070

prune428.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 59.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
5.0b	(log (- 1.0 x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 53

Calls

2 calls:

26.0ms	(/ (log (- 1.0 x)) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
7.0ms	(log (- 1.0 x))

series278.0ms

Counts

2 → 6

Calls

2 calls:

187.0ms	(/ (log (- 1.0 x)) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
90.0ms	(log (- 1.0 x))

simplify918.0ms

Counts

59 → 59

Iterations

Useful iterations: done (915.0ms)

Iter	Nodes	Cost
0	181	1508
1	429	1463
2	1645	1366
done	5001	1361

prune329.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 2 expressions with local error:

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

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

98×	`times-frac`
89×	`add-sqr-sqrt`
68×	`associate-r`
59×	`*-un-lft-identity`
56×	`unpow-prod-down`
47×	`add-cube-cbrt`
27×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`div-exp` `prod-exp`
9×	`add-cbrt-cube`
8×	`pow1` `distribute-lft-out--`
6×	`pow-to-exp` `pow-exp` `associate-/l*`
4×	`log-pow` `difference-of-squares`
3×	`associate-l` `associate-/r*`
2×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
1×	`flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--`

Counts

2 → 156

Calls

2 calls:

61.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
47.0ms	(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))

series258.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
186.0ms	(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))

simplify1.9s

Counts

162 → 162

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	313	3610
1	823	3382
2	3732	2980
done	5001	2976

prune765.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

134×	`times-frac`
124×	`add-sqr-sqrt`
100×	`*-un-lft-identity`
70×	`add-cube-cbrt`
68×	`associate-r`
56×	`unpow-prod-down`
44×	`exp-prod`
33×	`log-pow`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
20×	`distribute-lft-out--`
17×	`pow1` `unswap-sqr`
11×	`add-cbrt-cube`
10×	`div-exp` `prod-exp` `difference-of-squares`
6×	`pow-to-exp` `pow-exp` `associate-/l*`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`log-prod` `div-sub` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `exp-diff` `cbrt-unprod` `associate-/l/`
1×	`log-div` `flip3--` `frac-2neg` `associate-r/` `rem-log-exp` `pow-prod-down` `clear-num` `-commutative` `flip--` `rem-exp-log`

Counts

4 → 226

Calls

4 calls:

52.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
31.0ms	(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
35.0ms	(exp (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0)))))
40.0ms	(log (exp (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))))

series641.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
182.0ms	(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))
189.0ms	(exp (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0)))))
202.0ms	(log (exp (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma (/ (pow x 2) (pow 1.0 2)) -1/2 (fma 1.0 x (log 1.0))))))

simplify2.3s

Counts

238 → 238

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	388	6123
1	942	5781
2	4092	5221
done	5001	5212

prune1.3s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	30
1	16	30
done	16	30

end0.0ms

sample7.4s

Algorithm

intervals

Results

4.4s	3362×	body	1280	valid
1.6s	2529×	body	640	valid
795.0ms	1300×	body	320	valid
180.0ms	8000×	pre	80	true
105.0ms	605×	body	160	valid
16.0ms	204×	body	80	valid