Details

sample103.0ms

Algorithm

intervals

Results

56.0ms	75×	body	1280	valid
21.0ms	56×	body	640	valid
4.0ms	21×	body	320	valid
4.0ms	88×	body	80	valid
2.0ms	85×	body	80	nan
2.0ms	16×	body	160	valid

simplify2.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	5	4
done	5	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize4.0ms

Local error

Found 1 expressions with local error:

4.6b	(log (+ 1.0 x))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log-prod` `*-un-lft-identity`
2×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `log-div`
1×	`expm1-log1p-u` `flip3-+` `rem-log-exp` `log-pow` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`

Counts

1 → 17

Calls

1 calls:

5.0ms

(log (+ 1.0 x))

series50.0ms

Counts

1 → 3

Calls

1 calls:

50.0ms

(log (+ 1.0 x))

simplify1.4s

Counts

20 → 20

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	60	188
1	257	174
done	5000	159

prune108.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

80×	`times-frac`
72×	`add-sqr-sqrt`
68×	`associate-r`
56×	`unpow-prod-down`
38×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow-to-exp` `pow-exp`
4×	`pow1` `add-log-exp`
3×	`fma-neg` `associate-l` `prod-diff`
2×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `associate-r/` `pow-prod-down` `associate--l+` `-commutative` `flip--` `fma-udef` `div-inv`

Counts

2 → 133

Calls

2 calls:

6.0ms	(- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
57.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))

series153.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
79.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))

simplify816.0ms

Counts

139 → 139

Iterations

Useful iterations: done (810.0ms)

Iter	Nodes	Cost
0	262	2048
done	5000	1657

prune514.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (cbrt (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
10.8b	(cbrt (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
10.8b	(cbrt (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
10.8b	(cbrt (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3--` `pow1/3` `flip--`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

69.0ms	(* (cbrt (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (cbrt (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
7.0ms	(cbrt (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
6.0ms	(cbrt (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
6.0ms	(cbrt (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

350.0ms	(* (cbrt (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (cbrt (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
287.0ms	(cbrt (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
350.0ms	(cbrt (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
276.0ms	(cbrt (- (fma 1.0 x (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify1.6s

Counts

107 → 107

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	207	4540
1	1725	4229
done	5000	3520

prune599.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b	(cbrt (pow (log (+ 1.0 x)) 3))
0.2b	(pow (log (+ 1.0 x)) 3)
4.6b	(log (+ 1.0 x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
12×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`pow1`
8×	`unpow-prod-down` `cube-prod`
5×	`add-exp-log` `log-pow`
4×	`log-prod` `add-cbrt-cube`
3×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
2×	`cube-mult` `log-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `flip3-+` `pow1/3` `rem-log-exp` `pow-exp` `rem-cbrt-cube` `flip-+` `distribute-lft-out` `rem-cube-cbrt`

Counts

3 → 69

Calls

3 calls:

3.0ms	(cbrt (pow (log (+ 1.0 x)) 3))
3.0ms	(pow (log (+ 1.0 x)) 3)
8.0ms	(log (+ 1.0 x))

series276.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(cbrt (pow (log (+ 1.0 x)) 3))
143.0ms	(pow (log (+ 1.0 x)) 3)
55.0ms	(log (+ 1.0 x))

simplify1.8s

Counts

78 → 78

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	164	1021
1	1350	808
done	5001	742

prune212.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

regimes252.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.7b

bsearch3.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	25
1	18	25
done	18	25

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.7s	2266×	body	1280	valid
605.0ms	1667×	body	640	valid
187.0ms	822×	body	320	valid
153.0ms	2827×	body	80	valid
71.0ms	2731×	body	80	nan
50.0ms	418×	body	160	valid