Details

sample147.0ms

Algorithm

intervals

Results

44.0ms	691×	body	80	nan
37.0ms	204×	body	80	valid
8.0ms	21×	body	640	valid
5.0ms	7×	body	1280	valid
3.0ms	14×	body	320	valid
1.0ms	10×	body	160	valid

simplify14.2s

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

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: 6.6b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.1b	(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
5.2b	(log (- 1.0 y))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

30.0ms	(* (- 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))

series223.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(* (- z 1.0) (log (- 1.0 y)))
125.0ms	(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
49.0ms	(log (- 1.0 y))

simplify2.1s

Counts

72 → 72

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	159	966
1	354	928
2	1026	820
3	2896	806
done	5002	802

prune292.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 3 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))))))

0.0b

(* 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)))))))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 189

Calls

3 calls:

71.0ms

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

51.0ms

(* 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)))))))

series322.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms

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

74.0ms

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

158.0ms

(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)))))))

simplify1.7s

Counts

198 → 198

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	396	5512
1	864	4254
2	2507	3429
done	5000	2943

prune911.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.6b	(cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.6b	(cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
0.6b	(cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

168×	`cbrt-div`
148×	`frac-times`
126×	`flip3--` `flip--`
50×	`associate-r/` `associate-l/`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 170

Calls

4 calls:

71.0ms	(* (cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
22.0ms	(cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
23.0ms	(cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
23.0ms	(cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series1.7s

Counts

4 → 12

Calls

4 calls:

550.0ms	(* (cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
371.0ms	(cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
376.0ms	(cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
356.0ms	(cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify948.0ms

Counts

182 → 182

Iterations

Useful iterations: done (930.0ms)

Iter	Nodes	Cost
0	340	13030
1	630	11757
2	1711	11392
done	5000	10986

prune1.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.6b	(cbrt (cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.6b	(cbrt (cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.9b	(pow (cbrt (cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (+ 3 1))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

48×	`cbrt-div`
20×	`cbrt-prod`
18×	`flip3--` `flip--`
12×	`frac-times` `*-un-lft-identity`
10×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`unpow-prod-down`
6×	`associate-r/` `associate-l/`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-unpow` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-pow`
1×	`unpow-prod-up` `pow-to-exp` `pow-exp` `distribute-lft-out` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

11.0ms	(cbrt (cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
6.0ms	(cbrt (cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
6.0ms	(cbrt (cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
13.0ms	(pow (cbrt (cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (+ 3 1))

series1.8s

Counts

4 → 12

Calls

4 calls:

342.0ms	(cbrt (cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
460.0ms	(cbrt (cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
390.0ms	(cbrt (cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
628.0ms	(pow (cbrt (cbrt (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (+ 3 1))

simplify998.0ms

Counts

104 → 104

Iterations

Useful iterations: done (988.0ms)

Iter	Nodes	Cost
0	224	4392
1	538	3854
2	1533	3698
done	5001	3648

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes838.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.6s	24276×	body	80	nan
694.0ms	5904×	body	80	valid
404.0ms	770×	body	640	valid
291.0ms	664×	body	320	valid
260.0ms	273×	body	1280	valid
87.0ms	422×	body	160	valid