Details

sample196.0ms

Algorithm

intervals

Results

65.0ms	776×	body	80	nan
24.0ms	11×	body	1280	valid
17.0ms	186×	body	80	valid
10.0ms	22×	body	640	valid
8.0ms	24×	body	320	valid
3.0ms	15×	body	160	valid

simplify14.5s

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.1b	(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
4.7b	(log (- 1.0 y))

rewrite60.0ms

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:

7.0ms	(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
43.0ms	(* (- z 1.0) (log (- 1.0 y)))
0.0ms	(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
7.0ms	(log (- 1.0 y))

series469.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
62.0ms	(* (- z 1.0) (log (- 1.0 y)))
159.0ms	(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
45.0ms	(log (- 1.0 y))

simplify2.1s

Counts

104 → 104

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	214	1881
1	483	1718
2	1305	1515
3	4009	1384
done	5000	1382

prune448.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
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)))))))

rewrite131.0ms

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:

44.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
13.0ms	(- (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)
61.0ms	(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
1.0ms	(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)))))))

series582.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
270.0ms	(- (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)
82.0ms	(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
154.0ms	(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)))))))

simplify1.8s

Counts

230 → 230

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	445	6887
1	964	5493
2	2717	4541
done	5000	3896

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize59.0ms

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)))))))) (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)))))))))
0.6b	(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))))))))
0.6b	(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))))))))
0.6b	(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))))))))

rewrite19.0ms

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:

13.0ms	(* (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)))))))))
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))))))))
2.0ms	(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))))))))

series11.2s

Counts

4 → 12

Calls

4 calls:

3.1s	(* (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)))))))))
2.5s	(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))))))))
2.9s	(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))))))))
2.7s	(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))))))))

simplify1.3s

Counts

93 → 93

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	219	5633
1	622	5242
2	2144	4767
done	5000	4105

prune910.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.6b	(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))))))))
0.6b	(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))))))))
0.6b	(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))))))))
0.6b	(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))))))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

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))))))))
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))))))))

series10.7s

Counts

4 → 12

Calls

4 calls:

2.7s	(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))))))))
2.7s	(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))))))))
2.5s	(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))))))))
2.8s	(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))))))))

simplify2.5s

Counts

64 → 64

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	119	3396
1	329	3256
2	1052	2976
3	4761	2612
done	5000	2608

prune822.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes873.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample8.0s

Algorithm

intervals

Results

3.9s	24665×	body	80	nan
771.0ms	5964×	body	80	valid
497.0ms	761×	body	640	valid
361.0ms	632×	body	320	valid
269.0ms	265×	body	1280	valid
127.0ms	412×	body	160	valid