Details

sample151.0ms

Algorithm

intervals

Results

94.0ms	111×	body	1280	valid
33.0ms	82×	body	640	valid
8.0ms	38×	body	320	valid
3.0ms	256×	pre	80	true
2.0ms	19×	body	160	valid
0.0ms	6×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 61.9b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.1b	(log (- 1.0 x))
6.1b	(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:

8.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
3.0ms	(log (- 1.0 x))
2.0ms	(log (+ 1.0 x))

series215.0ms

Counts

3 → 9

Calls

3 calls:

124.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
46.0ms	(log (- 1.0 x))
45.0ms	(log (+ 1.0 x))

simplify483.0ms

Counts

84 → 84

Iterations

Useful iterations: 2 (135.0ms)

Iter	Nodes	Cost
0	192	1243
1	458	1173
2	1706	1093
done	5000	1093

prune197.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 59.9b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(/ (log (- 1.0 x)) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
6.1b	(log (- 1.0 x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 167

Calls

3 calls:

27.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
9.0ms	(/ (log (- 1.0 x)) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
3.0ms	(log (- 1.0 x))

series232.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
141.0ms	(/ (log (- 1.0 x)) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
43.0ms	(log (- 1.0 x))

simplify1.9s

Counts

176 → 176

Iterations

Useful iterations: 2 (564.0ms)

Iter	Nodes	Cost
0	397	3124
1	970	2862
2	4256	2559
done	5001	2559

prune510.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

178×	`times-frac`
158×	`add-sqr-sqrt`
136×	`associate-r`
112×	`unpow-prod-down`
94×	`*-un-lft-identity`
82×	`add-cube-cbrt`
51×	`add-exp-log`
48×	`unpow2` `sqr-pow`
34×	`unswap-sqr`
20×	`prod-exp`
19×	`div-exp`
15×	`add-cbrt-cube`
12×	`pow-to-exp` `pow-exp`
11×	`pow1`
8×	`distribute-lft-out--`
6×	`associate-l` `associate-/l*`
4×	`log-pow` `cbrt-unprod` `difference-of-squares`
3×	`cbrt-undiv` `expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`flip3--` `associate-r/` `pow-prod-down` `associate-/r/` `-commutative` `flip--` `associate-/l/`
1×	`frac-2neg` `div-sub` `clear-num`

Counts

3 → 270

Calls

3 calls:

26.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
29.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
13.0ms	(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series218.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
50.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
119.0ms	(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify1.5s

Counts

279 → 279

Iterations

Useful iterations: 2 (309.0ms)

Iter	Nodes	Cost
0	320	5262
1	783	4805
2	3462	4264
done	5000	4264

prune855.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(expm1 (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 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 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
0.0b	(log1p (expm1 (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 180

Calls

4 calls:

27.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0ms	(expm1 (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
13.0ms	(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
0.0ms	(log1p (expm1 (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))

series592.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
172.0ms	(expm1 (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
118.0ms	(/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
248.0ms	(log1p (expm1 (/ (- (log 1.0) (fma 1.0 x (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))

simplify1.5s

Counts

192 → 192

Iterations

Useful iterations: 2 (348.0ms)

Iter	Nodes	Cost
0	358	4744
1	861	4466
2	3677	3922
done	5000	3922

prune635.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes29.0ms

Accuracy

0% (0.3b 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	16	33
1	17	33
done	17	33

end0.0ms

sample4.6s

Algorithm

intervals

Results

3.0s	3425×	body	1280	valid
1.0s	2518×	body	640	valid
264.0ms	1257×	body	320	valid
108.0ms	8000×	pre	80	true
71.0ms	582×	body	160	valid
11.0ms	218×	body	80	valid