Details

sample111.0ms

Algorithm

intervals

Results

35.0ms	706×	body	80	nan
9.0ms	179×	body	80	valid
9.0ms	26×	body	640	valid
7.0ms	11×	body	1280	valid
5.0ms	25×	body	320	valid
2.0ms	17×	body	160	valid

simplify10.2s

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.0b	(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
0.2b	(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
6.2b	(log (- 1.0 y))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

29.0ms	(* (- z 1.0) (log (- 1.0 y)))
7.0ms	(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
0.0ms	(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
6.0ms	(log (- 1.0 y))

series362.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (- z 1.0) (log (- 1.0 y)))
156.0ms	(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
118.0ms	(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
46.0ms	(log (- 1.0 y))

simplify1.7s

Counts

104 → 104

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	214	1881
1	483	1718
2	1308	1515
3	4017	1384
done	5000	1382

prune332.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b

(- (fma (- 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

(fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
33×	`prod-diff`
28×	`add-cube-cbrt`
17×	`distribute-rgt-in` `distribute-lft-in`
12×	`pow1`
7×	`flip3--` `associate--l+` `log-pow` `flip--`
6×	`log-prod` `associate-r`
5×	`add-exp-log` `associate-l` `add-cbrt-cube` `add-log-exp`
4×	`frac-times` `distribute-lft-out--`
3×	`expm1-log1p-u` `sub-neg` `fma-neg` `log1p-expm1-u` `difference-of-squares`
2×	`associate-r/` `associate-l/` `fma-udef`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 106

Calls

3 calls:

7.0ms

(- (fma (- 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)

46.0ms

(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

0.0ms

(fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series381.0ms

Counts

3 → 9

Calls

3 calls:

198.0ms

(- (fma (- 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)

66.0ms

(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))

117.0ms

(fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify830.0ms

Counts

115 → 115

Iterations

Useful iterations: done (825.0ms)

Iter	Nodes	Cost
0	237	5385
1	501	4186
2	1668	3509
done	5000	2853

prune411.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.1b	(fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.5b	(cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.7b	(pow (cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) 3)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
28×	`add-cube-cbrt`
24×	`prod-diff`
17×	`distribute-rgt-in` `distribute-lft-in`
14×	`pow1`
9×	`cbrt-prod`
7×	`add-exp-log` `log-pow`
6×	`unpow-prod-down` `log-prod` `flip3--` `cube-prod` `associate-r` `associate--l+` `add-cbrt-cube` `flip--`
5×	`associate-l`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `distribute-lft-out--`
2×	`sub-neg` `pow-pow` `pow1/3` `associate-r/` `associate-l/` `difference-of-squares`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`

Counts

4 → 122

Calls

4 calls:

46.0ms	(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0ms	(fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
1.0ms	(cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
3.0ms	(pow (cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) 3)

series3.3s

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
116.0ms	(fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
1.9s	(cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
1.2s	(pow (cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) 3)

simplify1.4s

Counts

134 → 134

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	326	6385
1	816	5062
2	2913	4203
done	5000	4144

prune564.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.5b	(cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.5b	(cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.5b	(* (cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))

rewrite15.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 81

Calls

4 calls:

1.0ms	(cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
1.0ms	(cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
1.0ms	(cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
11.0ms	(* (cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))

series8.1s

Counts

4 → 12

Calls

4 calls:

2.0s	(cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
2.0s	(cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
1.9s	(cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
2.2s	(* (cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (cbrt (fma (- x 1.0) (log y) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))

simplify813.0ms

Counts

93 → 93

Iterations

Useful iterations: done (808.0ms)

Iter	Nodes	Cost
0	219	5633
1	622	5242
2	2144	4767
done	5001	4105

prune597.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 0.1b

regimes631.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	27
1	22	27
done	22	27

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.2s	24249×	body	80	nan
318.0ms	5840×	body	80	valid
239.0ms	780×	body	640	valid
182.0ms	291×	body	1280	valid
121.0ms	667×	body	320	valid
52.0ms	459×	body	160	valid