Details

sample169.0ms

Algorithm

intervals

Results

62.0ms	781×	body	80	nan
15.0ms	183×	body	80	valid
12.0ms	27×	body	640	valid
11.0ms	11×	body	1280	valid
5.0ms	21×	body	320	valid
3.0ms	16×	body	160	valid

simplify4.5s

Counts

1 → 1

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	14	17
1	27	16
2	57	16
3	135	16
4	388	16
5	1306	16
6	3670	16
done	5000	16

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.0b	(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
0.2b	(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
6.3b	(log (- 1.0 y))

rewrite85.0ms

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:

56.0ms	(* (- z 1.0) (log (- 1.0 y)))
13.0ms	(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
1.0ms	(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
12.0ms	(log (- 1.0 y))

series530.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (- z 1.0) (log (- 1.0 y)))
221.0ms	(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
171.0ms	(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
73.0ms	(log (- 1.0 y))

simplify1.4s

Counts

104 → 104

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	214	1881
1	512	1721
2	1835	1517
done	5002	1413

prune375.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

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))))))
0.2b	(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)))))))

rewrite150.0ms

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:

57.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
18.0ms	(- (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)
62.0ms	(* (- 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)))))))

series605.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
250.0ms	(- (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)
111.0ms	(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
151.0ms	(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)))))))

simplify745.0ms

Counts

230 → 230

Iterations

Useful iterations: done (733.0ms)

Iter	Nodes	Cost
0	445	6887
1	1145	5504
done	5001	4761

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
60×	`*-un-lft-identity`
57×	`prod-diff`
51×	`add-cube-cbrt`
40×	`distribute-rgt-in` `distribute-lft-in`
34×	`associate-+r+`
28×	`flip3--` `flip--`
24×	`log-prod` `associate-*l/`
22×	`pow1`
16×	`frac-add`
14×	`log-pow`
13×	`associate--l+`
12×	`frac-times`
11×	`add-log-exp`
10×	`associate-r` `associate-l`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-+l+` `associate-*r/`
5×	`sub-neg` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`fma-neg`
2×	`diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `flip-+`

Counts

4 → 198

Calls

4 calls:

137.0ms	(- (+ (* (- 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)
67.0ms	(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
44.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
31.0ms	(* (- x 1.0) (log y))

series679.0ms

Counts

4 → 12

Calls

4 calls:

326.0ms	(- (+ (* (- 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)
75.0ms	(* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
196.0ms	(+ (* (- x 1.0) (log y)) (* (- z 1.0) (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
81.0ms	(* (- x 1.0) (log y))

simplify566.0ms

Counts

210 → 210

Iterations

Useful iterations: done (554.0ms)

Iter	Nodes	Cost
0	415	9275
1	1172	7277
done	5001	6576

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
0.7b	(cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
0.7b	(cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
58.0b	(fma (- (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (* (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (* (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
1.0ms	(cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
1.0ms	(cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
0.0ms	(fma (- (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (* (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (* (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))

series708.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
155.0ms	(cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
167.0ms	(cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))
238.0ms	(fma (- (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (* (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) (* (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (* (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (cbrt (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))

simplify645.0ms

Counts

61 → 61

Iterations

Useful iterations: done (641.0ms)

Iter	Nodes	Cost
0	130	2579
1	313	1826
2	1033	1670
done	5000	1469

prune644.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes567.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	115
1	32	115
done	32	115

end0.0ms

sample7.7s

Algorithm

intervals

Results

3.4s	25084×	body	80	nan
706.0ms	274×	body	1280	valid
638.0ms	5849×	body	80	valid
598.0ms	752×	body	640	valid
225.0ms	696×	body	320	valid
98.0ms	467×	body	160	valid