Details

sample292.0ms

Algorithm

intervals

Results

93.0ms	821×	body	80	nan
39.0ms	20×	body	320	valid
25.0ms	191×	body	80	valid
24.0ms	15×	body	1280	valid
17.0ms	25×	body	640	valid
2.0ms	7×	body	160	valid

simplify6.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	26	17
2	49	17
3	116	17
4	241	17
5	506	17
6	1039	17
7	1619	17
8	2053	17
9	2158	17
done	2158	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.0b	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
0.1b	(* (- x 1.0) (log y))
5.6b	(log (- 1.0 y))

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

61.0ms	(* (- z 1.0) (log (- 1.0 y)))
138.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
42.0ms	(* (- x 1.0) (log y))
5.0ms	(log (- 1.0 y))

series507.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (- z 1.0) (log (- 1.0 y)))
255.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
89.0ms	(* (- x 1.0) (log y))
83.0ms	(log (- 1.0 y))

simplify966.0ms

Counts

106 → 106

Iterations

Useful iterations: done (961.0ms)

Iter	Nodes	Cost
0	231	1491
1	498	1443
2	1556	1279
done	5000	1253

prune544.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
0.0b	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (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)))
0.1b	(* (- x 1.0) (log y))

rewrite280.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-sqr-sqrt`
80×	`times-frac`
72×	`associate-r`
56×	`unpow-prod-down`
50×	`*-un-lft-identity`
46×	`add-cube-cbrt`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
22×	`flip3--` `associate-*l/` `flip--`
18×	`log-prod` `unswap-sqr`
16×	`frac-add`
11×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `add-cbrt-cube` `add-log-exp`
10×	`associate-+r+`
9×	`pow1` `div-exp`
8×	`frac-times` `associate-l`
7×	`associate--l+`
6×	`pow-to-exp` `associate-+l+` `pow-exp`
5×	`associate-*r/`
3×	`sub-neg` `cbrt-unprod`
2×	`diff-log` `pow-prod-down` `sum-log` `*-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `flip3-+` `log-pow` `flip-+` `div-inv`

Counts

4 → 198

Calls

4 calls:

130.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
38.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
72.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
28.0ms	(* (- x 1.0) (log y))

series723.0ms

Counts

4 → 12

Calls

4 calls:

368.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
198.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
80.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
77.0ms	(* (- x 1.0) (log y))

simplify2.7s

Counts

210 → 210

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	477	5346
1	1258	4812
2	4983	4447
done	5000	4447

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize62.0ms

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)

rewrite39.0ms

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:

31.0ms	(* (cbrt y) (cbrt y))
1.0ms	(cbrt y)
2.0ms	(cbrt y)
2.0ms	(cbrt y)

series1.1s

Counts

4 → 12

Calls

4 calls:

238.0ms	(* (cbrt y) (cbrt y))
230.0ms	(cbrt y)
300.0ms	(cbrt y)
343.0ms	(cbrt y)

simplify4.6s

Counts

85 → 85

Iterations

Useful iterations: done (4.6s)

Iter	Nodes	Cost
0	61	524
1	115	417
2	319	397
3	1092	379
4	4427	374
done	5001	364

prune672.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 1.0) (log y))
9.5b	(+ (* (- z 1.0) (log (+ (sqrt 1.0) (sqrt y)))) (* (log (- (sqrt 1.0) (sqrt y))) (- z 1.0)))
11.6b	(log (+ (sqrt 1.0) (sqrt y)))
12.0b	(log (- (sqrt 1.0) (sqrt y)))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

30×	`log-prod` `*-un-lft-identity`
24×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `sqrt-prod`
10×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
9×	`pow1`
8×	`add-exp-log`
6×	`flip3--` `associate-*l/` `add-cbrt-cube` `flip--` `distribute-lft-out` `add-log-exp`
5×	`associate-l` `difference-of-squares`
4×	`log-div` `associate-+r+` `associate-r/` `associate-r*` `frac-add`
3×	`log-pow` `distribute-lft-out--`
2×	`sub-neg` `flip3-+` `rem-log-exp` `flip-+`
1×	`+-commutative` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 94

Calls

4 calls:

33.0ms	(* (- x 1.0) (log y))
69.0ms	(+ (* (- z 1.0) (log (+ (sqrt 1.0) (sqrt y)))) (* (log (- (sqrt 1.0) (sqrt y))) (- z 1.0)))
16.0ms	(log (+ (sqrt 1.0) (sqrt y)))
18.0ms	(log (- (sqrt 1.0) (sqrt y)))

series796.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (- x 1.0) (log y))
381.0ms	(+ (* (- z 1.0) (log (+ (sqrt 1.0) (sqrt y)))) (* (log (- (sqrt 1.0) (sqrt y))) (- z 1.0)))
146.0ms	(log (+ (sqrt 1.0) (sqrt y)))
174.0ms	(log (- (sqrt 1.0) (sqrt y)))

simplify1.2s

Counts

106 → 106

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	251	2015
1	623	1818
2	1952	1520
done	5000	1511

prune489.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes377.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	41
1	35	41
done	35	41

end0.0ms

sample6.8s

Algorithm

intervals

Results

3.4s	23761×	body	80	nan
623.0ms	5871×	body	80	valid
396.0ms	774×	body	640	valid
261.0ms	301×	body	1280	valid
238.0ms	676×	body	320	valid
77.0ms	421×	body	160	valid