Details

sample158.0ms

Algorithm

intervals

Results

66.0ms	663×	body	80	nan
12.0ms	168×	body	80	valid
10.0ms	14×	body	1280	valid
10.0ms	28×	body	640	valid
6.0ms	28×	body	320	valid
3.0ms	19×	body	160	valid

simplify944.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	12	13
1	22	12
2	38	12
3	53	12
4	61	12
5	78	12
6	113	12
7	238	12
8	767	12
done	5000	12

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-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`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`fma-neg` `associate-l`
2×	`log-div` `flip3--` `log-pow` `flip--` `fma-udef`
1×	`sub-neg` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

30.0ms	(* z (log (- 1.0 y)))
23.0ms	(- (fma x (log y) (* z (log (- 1.0 y)))) t)
1.0ms	(fma x (log y) (* z (log (- 1.0 y))))
12.0ms	(log (- 1.0 y))

series398.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* z (log (- 1.0 y)))
118.0ms	(- (fma x (log y) (* z (log (- 1.0 y)))) t)
105.0ms	(fma x (log y) (* z (log (- 1.0 y))))
71.0ms	(log (- 1.0 y))

simplify920.0ms

Counts

100 → 100

Iterations

Useful iterations: done (915.0ms)

Iter	Nodes	Cost
0	204	1528
1	488	1381
2	1555	1220
done	5000	1128

prune631.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

103×	`add-sqr-sqrt`
80×	`times-frac`
74×	`associate-r`
68×	`*-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`
7×	`associate--l+` `log-pow`
6×	`pow-to-exp` `log-prod` `associate-l` `pow-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `associate-*r/` `cbrt-unprod` `distribute-lft-out--`
2×	`flip3--` `pow-prod-down` `*-commutative` `flip--` `fma-udef` `difference-of-squares`
1×	`cbrt-undiv` `diff-log` `div-inv`

Counts

4 → 210

Calls

4 calls:

7.0ms	(- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
58.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
69.0ms	(* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
0.0ms	(fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series733.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(- (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) t)
82.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
165.0ms	(* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))
196.0ms	(fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify2.5s

Counts

222 → 222

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	411	6086
1	1034	4745
2	4532	3826
done	5000	3824

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (cbrt (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
12.5b	(cbrt (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
12.5b	(cbrt (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
12.5b	(cbrt (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

rewrite456.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

405.0ms	(* (cbrt (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (cbrt (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
17.0ms	(cbrt (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
17.0ms	(cbrt (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
15.0ms	(cbrt (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

series2.0s

Counts

4 → 12

Calls

4 calls:

566.0ms	(* (cbrt (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))) (cbrt (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
504.0ms	(cbrt (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
485.0ms	(cbrt (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))
466.0ms	(cbrt (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))

simplify1.5s

Counts

92 → 92

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	223	4372
1	612	4011
2	2573	3713
done	5001	3426

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fma x (log y) (* z (- (log (- (pow 1.0 3) (pow y 3))) (log (fma 1.0 1.0 (* y (+ 1.0 y))))))) t)
0.2b	(fma x (log y) (* z (- (log (- (pow 1.0 3) (pow y 3))) (log (fma 1.0 1.0 (* y (+ 1.0 y)))))))
2.3b	(log (- (pow 1.0 3) (pow y 3)))
6.3b	(log (fma 1.0 1.0 (* y (+ 1.0 y))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
28×	`log-prod`
25×	`*-un-lft-identity`
17×	`difference-of-squares`
13×	`add-cube-cbrt`
12×	`unpow-prod-down` `cube-prod`
9×	`prod-diff`
8×	`sqr-pow`
6×	`pow1` `add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg`
2×	`log-div` `flip3--` `rem-log-exp` `log-pow` `flip--` `fma-udef`
1×	`difference-cubes` `sub-neg` `diff-log` `associate--l+`

Counts

4 → 91

Calls

4 calls:

12.0ms	(- (fma x (log y) (* z (- (log (- (pow 1.0 3) (pow y 3))) (log (fma 1.0 1.0 (* y (+ 1.0 y))))))) t)
0.0ms	(fma x (log y) (* z (- (log (- (pow 1.0 3) (pow y 3))) (log (fma 1.0 1.0 (* y (+ 1.0 y)))))))
38.0ms	(log (- (pow 1.0 3) (pow y 3)))
2.0ms	(log (fma 1.0 1.0 (* y (+ 1.0 y))))

series931.0ms

Counts

4 → 12

Calls

4 calls:

238.0ms	(- (fma x (log y) (* z (- (log (- (pow 1.0 3) (pow y 3))) (log (fma 1.0 1.0 (* y (+ 1.0 y))))))) t)
198.0ms	(fma x (log y) (* z (- (log (- (pow 1.0 3) (pow y 3))) (log (fma 1.0 1.0 (* y (+ 1.0 y)))))))
396.0ms	(log (- (pow 1.0 3) (pow y 3)))
98.0ms	(log (fma 1.0 1.0 (* y (+ 1.0 y))))

simplify1.3s

Counts

103 → 103

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	243	2636
1	545	2410
2	1672	2158
done	5000	1975

prune738.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes334.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	23
1	20	23
done	20	23

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.1s	23684×	body	80	nan
574.0ms	5503×	body	80	valid
411.0ms	882×	body	640	valid
340.0ms	416×	body	1280	valid
236.0ms	739×	body	320	valid
80.0ms	482×	body	160	valid