Details

sample99.0ms

Algorithm

intervals

Results

37.0ms	809×	body	80	nan
9.0ms	183×	body	80	valid
8.0ms	13×	body	1280	valid
6.0ms	18×	body	640	valid
3.0ms	21×	body	320	valid
2.0ms	23×	body	160	valid

simplify147.0ms

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	173	13
done	173	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(* z (log (- 1.0 y)))
0.3b	(* x (log y))
5.7b	(log (- 1.0 y))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 70

Calls

3 calls:

7.0ms	(* z (log (- 1.0 y)))
4.0ms	(* x (log y))
3.0ms	(log (- 1.0 y))

series152.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(* z (log (- 1.0 y)))
36.0ms	(* x (log y))
46.0ms	(log (- 1.0 y))

simplify1.0s

Counts

79 → 79

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	168	766
1	333	740
2	775	654
3	1839	638
done	5001	636

prune230.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `log-prod`
21×	`*-un-lft-identity`
16×	`distribute-rgt-in` `add-cube-cbrt` `distribute-lft-in`
13×	`associate--l+`
11×	`add-log-exp`
10×	`pow1` `associate-+r+` `associate-r`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-+l+` `associate-l`
5×	`sub-neg`
3×	`distribute-lft-out--`
2×	`flip3--` `diff-log` `associate-r/` `pow-prod-down` `prod-exp` `sum-log` `log-pow` `-commutative` `flip--` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `flip3-+` `flip-+`

Counts

4 → 101

Calls

4 calls:

17.0ms	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
7.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
31.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
4.0ms	(* x (log y))

series453.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(- (+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
125.0ms	(+ (* x (log y)) (* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
106.0ms	(* z (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
37.0ms	(* x (log y))

simplify1.7s

Counts

113 → 113

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	201	2374
1	429	2239
2	1109	2120
3	3978	2069
done	5001	2067

prune426.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

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)

series737.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(* (cbrt y) (cbrt y))
175.0ms	(cbrt y)
186.0ms	(cbrt y)
172.0ms	(cbrt y)

simplify3.6s

Counts

85 → 85

Iterations

Useful iterations: 4 (1.8s)

Iter	Nodes	Cost
0	61	524
1	115	465
2	319	397
3	1162	379
4	3669	374
done	5000	374

prune399.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize21.0ms

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)))))))
0.3b	(* x (log y))
0.3b	(* (* 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)))))))

rewrite124.0ms

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))))))))
37.0ms	(* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
4.0ms	(* x (log y))
72.0ms	(* (* 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)))))))

series804.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(+ (* 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))))))))
192.0ms	(* z (+ (sqrt (log 1.0)) (sqrt (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
36.0ms	(* x (log y))
454.0ms	(* (* 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)))))))

simplify1.0s

Counts

120 → 120

Iterations

Useful iterations: 2 (330.0ms)

Iter	Nodes	Cost
0	240	4404
1	650	3240
2	2436	2863
done	5001	2863

prune474.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

regimes193.0ms

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 (1.0ms)

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

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.1s	24450×	body	80	nan
284.0ms	5594×	body	80	valid
268.0ms	891×	body	640	valid
249.0ms	412×	body	1280	valid
119.0ms	686×	body	320	valid
46.0ms	436×	body	160	valid