Details

sample106.0ms

Algorithm

intervals

Results

34.0ms	702×	body	80	nan
10.0ms	188×	body	80	valid
10.0ms	15×	body	1280	valid
7.0ms	22×	body	640	valid
4.0ms	22×	body	320	valid
1.0ms	10×	body	160	valid

simplify69.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	9
1	57	8
2	136	8
3	312	8
4	709	8
5	1629	8
6	3564	8
7	5001	8
done	5001	8

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.1b	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
6.0b	(log (- 1.0 y))

rewrite38.0ms

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 (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
6.0ms	(log (- 1.0 y))

series293.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(* (- z 1.0) (log (- 1.0 y)))
205.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
43.0ms	(log (- 1.0 y))

simplify36.0ms

Counts

72 → 72

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	364	521
1	1204	461
2	5001	449
done	5001	449

prune223.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b

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

rewrite133.0ms

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:

82.0ms

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

37.0ms

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

0.0ms

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

series345.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms

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

51.0ms

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

223.0ms

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

simplify108.0ms

Counts

198 → 198

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	933	2711
1	4676	1841
2	5001	1841
done	5001	1841

prune626.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (log y) (- x 1.0)) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))
0.0b	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.2b	(* (log y) (- x 1.0))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

143×	`add-sqr-sqrt`
106×	`*-un-lft-identity`
99×	`add-cube-cbrt`
87×	`prod-diff`
80×	`times-frac`
79×	`associate-r`
56×	`distribute-rgt-in` `unpow-prod-down` `distribute-lft-in`
46×	`associate--l+`
39×	`associate-+r+`
31×	`add-exp-log`
24×	`pow1` `unpow2` `sqr-pow`
22×	`associate-+l+`
19×	`unswap-sqr`
14×	`log-pow`
13×	`add-cbrt-cube`
12×	`log-prod` `associate-l` `prod-exp`
11×	`flip3--` `flip--`
9×	`sub-neg` `associate-*r/` `div-exp` `add-log-exp`
6×	`pow-to-exp` `pow-exp`
4×	`expm1-log1p-u` `frac-times` `frac-add` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--`
3×	`pow-prod-down` `*-commutative` `difference-of-squares`
2×	`associate-*l/` `sum-log`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `fma-def` `flip3-+` `diff-log` `flip-+` `div-inv`

Counts

4 → 307

Calls

4 calls:

95.0ms	(+ (* (log y) (- x 1.0)) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))
83.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
35.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
25.0ms	(* (log y) (- x 1.0))

series505.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(+ (* (log y) (- x 1.0)) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))
72.0ms	(* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
52.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
97.0ms	(* (log y) (- x 1.0))

simplify71.0ms

Counts

319 → 319

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1492	4612
1	5002	3424
done	5002	3424

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

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:

10.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series816.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(* (cbrt x) (cbrt x))
184.0ms	(cbrt x)
214.0ms	(cbrt x)
174.0ms	(cbrt x)

simplify88.0ms

Counts

93 → 93

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	119	308
1	477	281
2	2972	258
3	5001	255
done	5001	255

prune547.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes368.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	27
1	42	27
done	42	27

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	24123×	body	80	nan
311.0ms	5877×	body	80	valid
227.0ms	765×	body	640	valid
156.0ms	261×	body	1280	valid
125.0ms	694×	body	320	valid
51.0ms	436×	body	160	valid