Details

sample196.0ms

Algorithm

intervals

Results

95.0ms	843×	body	80	nan
15.0ms	191×	body	80	valid
11.0ms	28×	body	640	valid
6.0ms	7×	body	1280	valid
5.0ms	22×	body	320	valid
1.0ms	8×	body	160	valid

simplify15.2s

Counts

1 → 1

Iterations

Useful iterations: 1 (11.0ms)

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.9b

localize18.0ms

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))))
6.3b	(log (- 1.0 y))

rewrite45.0ms

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))))
13.0ms	(log (- 1.0 y))

series270.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(* (- z 1.0) (log (- 1.0 y)))
159.0ms	(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
49.0ms	(log (- 1.0 y))

simplify2.6s

Counts

72 → 72

Iterations

Useful iterations: done (2.6s)

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

prune361.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 3 expressions with local error:

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)))))))

rewrite145.0ms

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:

58.0ms

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

65.0ms

(* (- 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)))))))

series329.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms

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

99.0ms

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

147.0ms

(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

198 → 198

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	396	5512
1	863	4258
2	2517	3429
done	5000	2943

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize59.0ms

Local error

Found 3 expressions with local error:

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))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

103×	`add-sqr-sqrt`
80×	`times-frac`
78×	`associate-r`
66×	`*-un-lft-identity`
59×	`add-cube-cbrt`
56×	`unpow-prod-down`
30×	`add-exp-log`
24×	`prod-diff` `unpow2` `sqr-pow`
20×	`distribute-rgt-in` `distribute-lft-in`
19×	`unswap-sqr`
17×	`pow1`
13×	`associate-l`
12×	`log-prod` `prod-exp` `add-cbrt-cube`
9×	`div-exp`
8×	`log-pow`
7×	`flip3--` `flip--`
6×	`pow-to-exp` `pow-exp` `associate--l+`
4×	`frac-times` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
3×	`expm1-log1p-u` `associate-r/` `pow-prod-down` `-commutative` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
2×	`sub-neg`
1×	`cbrt-undiv` `div-inv`

Counts

3 → 210

Calls

3 calls:

48.0ms	(* 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))))))
24.0ms	(* (- x 1.0) (log y))

series285.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
96.0ms	(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
108.0ms	(* (- x 1.0) (log y))

simplify2.4s

Counts

219 → 219

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	449	5485
1	968	4214
2	2851	3405
done	5001	2918

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

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)

rewrite135.0ms

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:

47.0ms	(* (- x 1.0) (* 2 (log (cbrt y))))
78.0ms	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (log (cbrt y)) (- x 1.0)))
1.0ms	(cbrt y)
2.0ms	(cbrt y)

series873.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (- x 1.0) (* 2 (log (cbrt y))))
180.0ms	(+ (* (- x 1.0) (* 2 (log (cbrt y)))) (* (log (cbrt y)) (- x 1.0)))
260.0ms	(cbrt y)
292.0ms	(cbrt y)

simplify1.2s

Counts

150 → 150

Iterations

Useful iterations: done (1.2s)

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: 0.0b

regimes282.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	49
1	38	49
done	38	49

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.7s	24189×	body	80	nan
1.3s	5875×	body	80	valid
416.0ms	794×	body	640	valid
278.0ms	238×	body	1280	valid
211.0ms	686×	body	320	valid
111.0ms	438×	body	160	valid