Details

sample179.0ms

Algorithm

intervals

Results

72.0ms	799×	body	80	nan
17.0ms	193×	body	80	valid
12.0ms	25×	body	640	valid
6.0ms	22×	body	320	valid
5.0ms	5×	body	1280	valid
3.0ms	14×	body	160	valid

simplify15.6s

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.8b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
5×	`log-prod` `add-log-exp`
4×	`pow1` `add-exp-log`
3×	`expm1-log1p-u` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `flip3--` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `diff-log` `rem-log-exp` `associate--l+` `log-pow`

Counts

3 → 57

Calls

3 calls:

15.0ms	(- (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))

series395.0ms

Counts

3 → 9

Calls

3 calls:

179.0ms	(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
134.0ms	(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
81.0ms	(log (- 1.0 y))

simplify2.6s

Counts

66 → 66

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	159	1368
1	361	1221
2	835	1077
3	2469	953
done	5002	921

prune307.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 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	(* 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	(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)))))))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

105×	`add-sqr-sqrt`
80×	`times-frac`
74×	`associate-r`
70×	`*-un-lft-identity`
63×	`add-cube-cbrt`
56×	`unpow-prod-down`
33×	`prod-diff`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
18×	`unswap-sqr`
17×	`distribute-rgt-in` `distribute-lft-in`
15×	`pow1`
11×	`prod-exp` `add-cbrt-cube`
9×	`div-exp`
8×	`associate-l`
7×	`flip3--` `associate--l+` `log-pow` `flip--`
6×	`pow-to-exp` `log-prod` `pow-exp` `add-log-exp`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `distribute-lft-out--`
3×	`sub-neg` `fma-neg` `associate-*r/` `cbrt-unprod` `difference-of-squares`
2×	`pow-prod-down` `associate-l/` `-commutative` `fma-udef`
1×	`cbrt-undiv` `diff-log` `div-inv`

Counts

4 → 218

Calls

4 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)
66.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
68.0ms	(* (- 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)))))))

series625.0ms

Counts

4 → 12

Calls

4 calls:

277.0ms	(- (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)
79.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
80.0ms	(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
190.0ms	(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)))))))

simplify2.0s

Counts

230 → 230

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	445	6887
1	964	5493
2	2714	4541
done	5000	3896

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (- z 1.0)) (cbrt (- z 1.0)))
0.3b	(cbrt (- z 1.0))
0.3b	(cbrt (- z 1.0))
0.3b	(cbrt (- z 1.0))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

43×	`cbrt-prod`
37×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
9×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
8×	`associate-r` `associate-l`
7×	`difference-of-squares`
6×	`add-exp-log`
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 → 109

Calls

4 calls:

56.0ms	(* (cbrt (- z 1.0)) (cbrt (- z 1.0)))
6.0ms	(cbrt (- z 1.0))
5.0ms	(cbrt (- z 1.0))
5.0ms	(cbrt (- z 1.0))

series498.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (cbrt (- z 1.0)) (cbrt (- z 1.0)))
119.0ms	(cbrt (- z 1.0))
124.0ms	(cbrt (- z 1.0))
127.0ms	(cbrt (- z 1.0))

simplify1.7s

Counts

121 → 121

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	171	1613
1	386	1452
2	1024	1384
3	2780	1286
done	5000	1278

prune920.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- z 1.0))
0.3b	(cbrt (cbrt (- z 1.0)))
0.3b	(cbrt (cbrt (- z 1.0)))
0.6b	(pow (cbrt (cbrt (- z 1.0))) (+ 4 1))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

44×	`cbrt-prod`
23×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
11×	`unpow-prod-down`
10×	`cbrt-div`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-unpow` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`flip3--` `flip--`
2×	`pow-pow`
1×	`unpow-prod-up` `pow-to-exp` `pow-exp` `distribute-lft-out` `sqr-pow`

Counts

4 → 87

Calls

4 calls:

12.0ms	(cbrt (- z 1.0))
5.0ms	(cbrt (cbrt (- z 1.0)))
5.0ms	(cbrt (cbrt (- z 1.0)))
16.0ms	(pow (cbrt (cbrt (- z 1.0))) (+ 4 1))

series662.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(cbrt (- z 1.0))
118.0ms	(cbrt (cbrt (- z 1.0)))
116.0ms	(cbrt (cbrt (- z 1.0)))
316.0ms	(pow (cbrt (cbrt (- z 1.0))) (+ 4 1))

simplify2.1s

Counts

99 → 99

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	234	1406
1	576	1229
2	1444	1160
3	4131	1118
done	5000	1114

prune890.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

regimes462.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.1s	24209×	body	80	nan
657.0ms	5843×	body	80	valid
366.0ms	815×	body	640	valid
231.0ms	272×	body	1280	valid
216.0ms	683×	body	320	valid
71.0ms	421×	body	160	valid