Details

sample153.0ms

Algorithm

intervals

Results

90.0ms	108×	body	1280	valid
38.0ms	85×	body	640	valid
8.0ms	42×	body	320	valid
3.0ms	256×	pre	80	true
2.0ms	16×	body	160	valid
0.0ms	5×	body	80	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 62.5b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
4.3b	(log (- 1.0 x))
4.6b	(log (+ 1.0 x))

rewrite29.0ms

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:

16.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.0ms	(log (- 1.0 x))
5.0ms	(log (+ 1.0 x))

series207.0ms

Counts

3 → 9

Calls

3 calls:

122.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
41.0ms	(log (- 1.0 x))
44.0ms	(log (+ 1.0 x))

simplify2.1s

Counts

84 → 84

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	192	1243
1	453	1173
2	1321	1093
3	4650	1039
done	5000	1039

prune209.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 60.2b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))
4.3b	(log (- 1.0 x))

rewrite23.0ms

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:

16.0ms	(/ (log (- 1.0 x)) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))
6.0ms	(log (- 1.0 x))

series169.0ms

Counts

2 → 6

Calls

2 calls:

125.0ms	(/ (log (- 1.0 x)) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))
44.0ms	(log (- 1.0 x))

simplify1.9s

Counts

59 → 59

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	181	1508
1	423	1463
2	1244	1364
3	4524	1346
done	5000	1343

prune212.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

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 -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))

rewrite69.0ms

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:

38.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
22.0ms	(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))

series167.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
114.0ms	(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma -1/2 (/ (pow x 2) (pow 1.0 2)) (fma 1.0 x (log 1.0))))

simplify863.0ms

Counts

162 → 162

Iterations

Useful iterations: done (857.0ms)

Iter	Nodes	Cost
0	313	3610
1	693	3382
2	1657	2980
done	5000	2964

prune489.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b

(* 1/2 (/ (pow x 2) (pow 1.0 2)))

0.0b

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

0.0b

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

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

116×	`times-frac`
106×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
68×	`associate-r`
58×	`add-cube-cbrt`
56×	`unpow-prod-down`
28×	`add-exp-log`
24×	`unpow2` `sqr-pow`
22×	`exp-prod`
17×	`unswap-sqr`
14×	`distribute-lft-out--`
12×	`pow1`
10×	`div-exp` `prod-exp` `add-cbrt-cube`
7×	`log-pow` `difference-of-squares`
6×	`pow-to-exp` `pow-exp` `associate-/l*`
4×	`add-log-exp`
3×	`expm1-log1p-u` `associate-l` `associate-/r*` `log1p-expm1-u` `div-inv`
2×	`cbrt-undiv` `div-sub` `cbrt-unprod` `associate-/l/`
1×	`flip3--` `frac-2neg` `exp-diff` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--` `rem-exp-log`

Counts

3 → 189

Calls

3 calls:

37.0ms

(* 1/2 (/ (pow x 2) (pow 1.0 2)))

25.0ms

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

23.0ms

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

series308.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms

(* 1/2 (/ (pow x 2) (pow 1.0 2)))

142.0ms

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

114.0ms

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

simplify882.0ms

Counts

198 → 198

Iterations

Useful iterations: done (875.0ms)

Iter	Nodes	Cost
0	357	4738
1	774	4485
2	1832	4024
done	5001	4000

prune716.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes52.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	32
1	18	32
done	18	32

end0.0ms

sample4.6s

Algorithm

intervals

Results

3.0s	3507×	body	1280	valid
978.0ms	2448×	body	640	valid
248.0ms	1239×	body	320	valid
93.0ms	8000×	pre	80	true
72.0ms	608×	body	160	valid
9.0ms	198×	body	80	valid