Details

sample105.0ms

Algorithm

intervals

Results

38.0ms	741×	body	80	nan
11.0ms	32×	body	640	valid
10.0ms	181×	body	80	valid
5.0ms	6×	body	1280	valid
4.0ms	21×	body	320	valid
2.0ms	17×	body	160	valid

simplify10.7s

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	14	17
1	27	16
2	56	16
3	102	16
4	240	16
5	580	16
6	1338	16
7	3078	16
8	4495	16
9	4752	16
10	4827	16
done	4827	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.0b

localize14.0ms

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))))
0.1b	(* (- x 1.0) (log y))
5.7b	(log (- 1.0 y))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

37×	`log-prod`
35×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-*l/`
11×	`pow1`
10×	`associate-+r+` `associate-l`
9×	`add-exp-log`
8×	`associate-r` `add-cbrt-cube`
7×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`
6×	`associate-+l+` `add-log-exp`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u`
3×	`log-pow`
2×	`log-div` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `rem-log-exp` `sum-log` `flip-+`

Counts

4 → 118

Calls

4 calls:

17.0ms	(* (- z 1.0) (log (- 1.0 y)))
13.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
11.0ms	(* (- x 1.0) (log y))
3.0ms	(log (- 1.0 y))

series264.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (- z 1.0) (log (- 1.0 y)))
120.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y))))
58.0ms	(* (- x 1.0) (log y))
42.0ms	(log (- 1.0 y))

simplify761.0ms

Counts

130 → 130

Iterations

Useful iterations: done (757.0ms)

Iter	Nodes	Cost
0	261	1918
1	688	1761
2	2582	1619
done	5000	1618

prune425.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
57×	`prod-diff`
51×	`add-cube-cbrt`
40×	`distribute-rgt-in` `distribute-lft-in`
34×	`associate-+r+`
28×	`flip3--` `flip--`
24×	`log-prod` `associate-*l/`
22×	`pow1`
16×	`frac-add`
14×	`log-pow`
13×	`associate--l+`
12×	`frac-times`
11×	`add-log-exp`
10×	`associate-r` `associate-l`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-+l+` `associate-*r/`
5×	`sub-neg` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`fma-neg`
2×	`diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `flip-+`

Counts

4 → 198

Calls

4 calls:

15.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
47.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
26.0ms	(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
11.0ms	(* (- x 1.0) (log y))

series510.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
235.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
68.0ms	(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
59.0ms	(* (- x 1.0) (log y))

simplify388.0ms

Counts

210 → 210

Iterations

Useful iterations: done (377.0ms)

Iter	Nodes	Cost
0	415	9275
1	1100	7274
done	5000	6573

prune807.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- x 1.0) (log (cbrt y)))
0.3b	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (- x 1.0) (log (cbrt y))))
0.7b	(cbrt y)
0.7b	(cbrt y)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

48×	`log-prod`
36×	`distribute-rgt-in` `distribute-lft-in`
30×	`cbrt-prod`
28×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt` `associate-+l+`
12×	`associate-+r+`
10×	`associate-*l/`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`flip3--` `associate-r` `associate-l` `flip--`
4×	`expm1-log1p-u` `frac-add` `log1p-expm1-u`
3×	`pow1/3`
2×	`log-pow`
1×	`+-commutative` `fma-def` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

12.0ms	(* (- x 1.0) (log (cbrt y)))
18.0ms	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (- x 1.0) (log (cbrt y))))
0.0ms	(cbrt y)
1.0ms	(cbrt y)

series619.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (- x 1.0) (log (cbrt y)))
159.0ms	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (- x 1.0) (log (cbrt y))))
169.0ms	(cbrt y)
173.0ms	(cbrt y)

simplify918.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (189.0ms)

Iter	Nodes	Cost
0	212	1942
1	541	1538
2	2447	1351
done	5001	1351

prune690.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- x 1.0) 1/3)
0.3b	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (* (- x 1.0) 1/3) (log y)))
0.3b	(* (* (- x 1.0) 1/3) (log y))
0.7b	(cbrt y)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod`
30×	`distribute-rgt-in` `distribute-lft-in`
24×	`add-sqr-sqrt` `associate-+l+`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`associate-*l/`
15×	`cbrt-prod`
12×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
7×	`associate-r`
6×	`associate-+r+` `flip3--` `associate-l` `flip--` `add-log-exp`
4×	`expm1-log1p-u` `pow-prod-down` `frac-add` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
2×	`*-commutative`
1×	`+-commutative` `fma-def` `flip3-+` `pow1/3` `sum-log` `log-pow` `flip-+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 114

Calls

4 calls:

12.0ms	(* (- x 1.0) 1/3)
19.0ms	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (* (- x 1.0) 1/3) (log y)))
17.0ms	(* (* (- x 1.0) 1/3) (log y))
1.0ms	(cbrt y)

series545.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (- x 1.0) 1/3)
269.0ms	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (* (- x 1.0) 1/3) (log y)))
63.0ms	(* (* (- x 1.0) 1/3) (log y))
171.0ms	(cbrt y)

simplify1.0s

Counts

126 → 126

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	250	1982
1	668	1757
2	2847	1458
done	5000	1456

prune696.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes278.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	40
1	36	40
done	36	40

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	24144×	body	80	nan
333.0ms	5858×	body	80	valid
244.0ms	784×	body	640	valid
168.0ms	268×	body	1280	valid
131.0ms	698×	body	320	valid
49.0ms	416×	body	160	valid