Details

sample200.0ms

Algorithm

intervals

Results

82.0ms	747×	body	80	nan
18.0ms	37×	body	640	valid
17.0ms	182×	body	80	valid
12.0ms	10×	body	1280	valid
5.0ms	15×	body	320	valid
3.0ms	14×	body	160	valid

simplify6.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.0b

localize35.0ms

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))

rewrite296.0ms

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:

56.0ms	(* (- z 1.0) (log (- 1.0 y)))
166.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
61.0ms	(* (- x 1.0) (log y))
10.0ms	(log (- 1.0 y))

series383.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (- z 1.0) (log (- 1.0 y)))
200.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
69.0ms	(* (- x 1.0) (log y))
50.0ms	(log (- 1.0 y))

simplify1.1s

Counts

106 → 106

Iterations

Useful iterations: done (1.1s)

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

prune499.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

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

rewrite300.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

39.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
97.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
123.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
35.0ms	(* (- x 1.0) (log y))

series629.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
298.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
74.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
65.0ms	(* (- x 1.0) (log y))

simplify2.1s

Counts

141 → 141

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	319	5151
1	888	4731
2	4333	4577
done	5001	4572

prune896.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize58.0ms

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)

rewrite18.0ms

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:

13.0ms	(* (cbrt y) (cbrt y))
1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series905.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(* (cbrt y) (cbrt y))
194.0ms	(cbrt y)
255.0ms	(cbrt y)
230.0ms	(cbrt y)

simplify4.3s

Counts

85 → 85

Iterations

Useful iterations: done (4.3s)

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

prune660.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (log (* (cbrt 1) (pow y 2/3))) (- x 1.0))
0.2b	(+ (* (log (* (cbrt 1) (pow y 2/3))) (- x 1.0)) (+ (* (log (cbrt y)) (- x 1.0)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.6b	(cbrt y)
6.0b	(pow y 2/3)

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

78×	`associate-*r/`
68×	`frac-add`
59×	`flip3--` `flip--`
16×	`frac-times`
13×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`add-cube-cbrt` `add-log-exp`
8×	`pow1` `associate-*l/`
7×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`associate-r`
4×	`distribute-rgt-in` `sub-neg` `associate-+l+` `distribute-lft-in` `associate-l`
3×	`cbrt-prod` `unpow-prod-down` `pow-unpow` `flip3-+` `sum-log` `flip-+`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 108

Calls

4 calls:

47.0ms	(* (log (* (cbrt 1) (pow y 2/3))) (- x 1.0))
90.0ms	(+ (* (log (* (cbrt 1) (pow y 2/3))) (- x 1.0)) (+ (* (log (cbrt y)) (- x 1.0)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
2.0ms	(cbrt y)
5.0ms	(pow y 2/3)

series1.4s

Counts

4 → 12

Calls

4 calls:

188.0ms	(* (log (* (cbrt 1) (pow y 2/3))) (- x 1.0))
675.0ms	(+ (* (log (* (cbrt 1) (pow y 2/3))) (- x 1.0)) (+ (* (log (cbrt y)) (- x 1.0)) (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
267.0ms	(cbrt y)
226.0ms	(pow y 2/3)

simplify947.0ms

Counts

120 → 120

Iterations

Useful iterations: done (940.0ms)

Iter	Nodes	Cost
0	430	8600
1	1571	7512
done	5001	7228

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

regimes396.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	35	48
1	52	47
2	54	45
done	54	45

end0.0ms

sample7.3s

Algorithm

intervals

Results

3.6s	24307×	body	80	nan
776.0ms	5855×	body	80	valid
443.0ms	793×	body	640	valid
245.0ms	668×	body	320	valid
242.0ms	235×	body	1280	valid
99.0ms	473×	body	160	valid