Details

sample95.0ms

Algorithm

intervals

Results

34.0ms	746×	body	80	nan
9.0ms	30×	body	640	valid
9.0ms	180×	body	80	valid
5.0ms	9×	body	1280	valid
4.0ms	26×	body	320	valid
1.0ms	13×	body	160	valid

simplify172.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	13
1	21	13
2	29	13
3	35	13
4	41	13
5	56	13
6	83	13
7	119	13
8	145	13
9	152	13
10	169	13
11	171	13
done	171	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.8b

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(* x (log y))
6.4b	(log (- 1.0 y))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `log-prod`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`pow1`
5×	`add-exp-log`
4×	`associate-r` `add-cbrt-cube`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
2×	`log-div` `log-pow` `add-log-exp`
1×	`flip3--` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

2 → 41

Calls

2 calls:

4.0ms	(* x (log y))
2.0ms	(log (- 1.0 y))

series82.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(* x (log y))
43.0ms	(log (- 1.0 y))

simplify919.0ms

Counts

47 → 47

Iterations

Useful iterations: 3 (285.0ms)

Iter	Nodes	Cost
0	112	394
1	214	378
2	579	334
3	1889	327
done	5001	327

prune141.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0b	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.3b	(* x (log y))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt`
80×	`times-frac`
78×	`associate-r`
56×	`unpow-prod-down`
53×	`*-un-lft-identity`
50×	`add-cube-cbrt`
31×	`add-exp-log`
24×	`log-prod` `unpow2` `sqr-pow`
19×	`unswap-sqr`
16×	`distribute-rgt-in` `distribute-lft-in`
13×	`add-cbrt-cube`
12×	`pow1` `prod-exp` `associate--l+`
10×	`associate-+r+`
9×	`div-exp` `associate-l`
6×	`pow-to-exp` `associate-+l+` `pow-exp` `add-log-exp`
4×	`sub-neg` `cbrt-unprod`
3×	`associate-r/` `pow-prod-down` `-commutative`
2×	`log-pow` `distribute-lft-out--`
1×	`cbrt-undiv` `+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `div-inv` `difference-of-squares`

Counts

4 → 195

Calls

4 calls:

28.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
32.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
6.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
4.0ms	(* x (log y))

series327.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
55.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
127.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
44.0ms	(* x (log y))

simplify1.3s

Counts

207 → 207

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	376	3213
1	865	2934
2	3396	2604
done	5000	2600

prune728.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt y) (cbrt y))
0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (cbrt y) (cbrt y))
0.0ms	(cbrt y)
0.0ms	(cbrt y)
1.0ms	(cbrt y)

series919.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(* (cbrt y) (cbrt y))
173.0ms	(cbrt y)
175.0ms	(cbrt y)
373.0ms	(cbrt y)

simplify1.4s

Counts

85 → 85

Iterations

Useful iterations: 3 (330.0ms)

Iter	Nodes	Cost
0	61	524
1	115	417
2	381	397
3	1865	379
done	5000	379

prune416.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x (log y)) (* (* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.2b	(* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.2b	(* (* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.3b	(* x (log y))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
20×	`associate-r`
16×	`pow1`
13×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
12×	`log-prod` `sqrt-prod`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`associate-*r/`
7×	`associate-l`
6×	`associate-+l+` `add-log-exp`
5×	`flip3-+` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`
4×	`frac-times` `sub-neg` `associate-+r+` `difference-of-squares`
3×	`flip3--` `log-pow` `*-commutative` `flip--` `distribute-lft-out` `distribute-lft-out--`
2×	`associate-*l/` `unswap-sqr`
1×	`+-commutative` `sum-log`

Counts

4 → 108

Calls

4 calls:

7.0ms	(+ (* x (log y)) (* (* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
39.0ms	(* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
74.0ms	(* (* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
4.0ms	(* x (log y))

series849.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(+ (* x (log y)) (* (* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
199.0ms	(* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
476.0ms	(* (* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (- (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
38.0ms	(* x (log y))

simplify926.0ms

Counts

120 → 120

Iterations

Useful iterations: 2 (260.0ms)

Iter	Nodes	Cost
0	240	4404
1	650	3232
2	2703	2863
done	5000	2863

prune487.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

regimes217.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	35
1	33	35
done	33	35

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.1s	24277×	body	80	nan
283.0ms	5613×	body	80	valid
251.0ms	860×	body	640	valid
236.0ms	398×	body	1280	valid
118.0ms	697×	body	320	valid
49.0ms	466×	body	160	valid