Details

sample175.0ms

Algorithm

intervals

Results

69.0ms	799×	body	80	nan
16.0ms	193×	body	80	valid
11.0ms	25×	body	640	valid
6.0ms	22×	body	320	valid
5.0ms	5×	body	1280	valid
2.0ms	14×	body	160	valid

simplify14.6s

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	14	17
1	27	16
2	57	16
3	130	16
4	281	16
5	649	16
6	1372	16
7	2484	16
8	3329	16
9	3557	16
10	3561	16
done	3561	16

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.8b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
0.1b	(* (- x 1.0) (log y))
4.5b	(log (- 1.0 y))

rewrite529.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`log-prod`
9×	`prod-diff`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log`
5×	`associate-l` `add-cbrt-cube`
4×	`associate-r`
3×	`distribute-rgt-in` `expm1-log1p-u` `flip3--` `distribute-lft-in` `fma-neg` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
2×	`log-div` `diff-log` `associate-*l/` `log-pow`
1×	`sub-neg` `rem-log-exp` `pow-prod-down` `prod-exp` `associate--l+` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 79

Calls

3 calls:

461.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
54.0ms	(* (- x 1.0) (log y))
11.0ms	(log (- 1.0 y))

series387.0ms

Counts

3 → 9

Calls

3 calls:

235.0ms	(- (+ (* (- x 1.0) (log y)) (* (- z 1.0) (log (- 1.0 y)))) t)
93.0ms	(* (- x 1.0) (log y))
59.0ms	(log (- 1.0 y))

simplify1.2s

Counts

88 → 88

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	209	1524
1	467	1352
2	1328	1173
done	5001	1063

prune411.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

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	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
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))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-sqr-sqrt`
85×	`*-un-lft-identity`
80×	`times-frac`
78×	`add-cube-cbrt` `associate-r`
56×	`unpow-prod-down`
48×	`prod-diff`
40×	`distribute-rgt-in` `distribute-lft-in`
34×	`associate-+r+`
31×	`add-exp-log`
27×	`flip3--` `flip--`
24×	`pow1` `log-prod` `associate-*l/` `unpow2` `sqr-pow`
19×	`unswap-sqr`
16×	`frac-add`
14×	`log-pow`
13×	`associate-l` `add-cbrt-cube`
12×	`frac-times` `prod-exp` `associate--l+`
9×	`div-exp`
7×	`associate-*r/`
6×	`pow-to-exp` `associate-+l+` `pow-exp` `add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--`
3×	`pow-prod-down` `*-commutative` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `fma-def` `flip3-+` `sum-log` `flip-+` `div-inv`

Counts

4 → 280

Calls

4 calls:

32.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
62.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
63.0ms	(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
24.0ms	(* (- x 1.0) (log y))

series458.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
61.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
118.0ms	(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
81.0ms	(* (- x 1.0) (log y))

simplify1.0s

Counts

292 → 292

Iterations

Useful iterations: done (997.0ms)

Iter	Nodes	Cost
0	570	9330
1	1451	7314
done	5000	6463

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
0.6b	(cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
0.6b	(cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
58.1b	(fma (- (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (* (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (* (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
1.0ms	(cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
1.0ms	(cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
1.0ms	(fma (- (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (* (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (* (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))

series697.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
146.0ms	(cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
182.0ms	(cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
229.0ms	(fma (- (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (* (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (* (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))

simplify1.4s

Counts

61 → 61

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	130	2579
1	313	1826
2	913	1670
3	3563	1459
done	5000	1446

prune650.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- x 1.0) (* 2 (log (cbrt y))))
0.3b	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (log (cbrt y)) (- x 1.0)))
0.6b	(cbrt y)
0.6b	(cbrt y)

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

59×	`distribute-rgt-in` `distribute-lft-in`
48×	`log-prod`
37×	`add-sqr-sqrt` `*-un-lft-identity`
35×	`add-cube-cbrt`
30×	`cbrt-prod`
24×	`associate-+l+`
22×	`associate-+r+`
18×	`prod-diff`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-*l/` `add-log-exp`
5×	`flip3--` `associate-l` `flip--`
4×	`expm1-log1p-u` `associate-*r/` `frac-add` `log1p-expm1-u`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sub-neg` `pow1/3`
1×	`+-commutative` `fma-def` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 138

Calls

4 calls:

41.0ms	(* (- x 1.0) (* 2 (log (cbrt y))))
48.0ms	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (log (cbrt y)) (- x 1.0)))
1.0ms	(cbrt y)
1.0ms	(cbrt y)

series986.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(* (- x 1.0) (* 2 (log (cbrt y))))
260.0ms	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (log (cbrt y)) (- x 1.0)))
314.0ms	(cbrt y)
237.0ms	(cbrt y)

simplify1.3s

Counts

150 → 150

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	274	2578
1	710	2248
2	2299	1746
done	5000	1699

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

regimes390.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	42
1	39	42
done	39	42

end0.0ms

sample6.2s

Algorithm

intervals

Results

3.0s	24209×	body	80	nan
648.0ms	5843×	body	80	valid
399.0ms	815×	body	640	valid
213.0ms	272×	body	1280	valid
203.0ms	683×	body	320	valid
93.0ms	421×	body	160	valid