Details

sample261.0ms

Algorithm

intervals

Results

97.0ms	747×	body	80	nan
25.0ms	37×	body	640	valid
23.0ms	182×	body	80	valid
14.0ms	10×	body	1280	valid
6.0ms	15×	body	320	valid
4.0ms	14×	body	160	valid

simplify15.0s

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

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: 8.0b

localize16.0ms

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)
0.1b	(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
5.6b	(log (- 1.0 y))

rewrite75.0ms

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:

54.0ms	(* (- z 1.0) (log (- 1.0 y)))
9.0ms	(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
0.0ms	(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
7.0ms	(log (- 1.0 y))

series603.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (- z 1.0) (log (- 1.0 y)))
259.0ms	(- (fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y)))) t)
188.0ms	(fma (- x 1.0) (log y) (* (- z 1.0) (log (- 1.0 y))))
71.0ms	(log (- 1.0 y))

simplify2.7s

Counts

104 → 104

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	214	1881
1	483	1718
2	1308	1515
3	4017	1384
done	5000	1382

prune546.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 3 expressions with local error:

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))))))

0.1b

(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)))))))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
33×	`prod-diff`
28×	`add-cube-cbrt`
17×	`distribute-rgt-in` `distribute-lft-in`
12×	`pow1`
7×	`flip3--` `associate--l+` `log-pow` `flip--`
6×	`log-prod` `associate-r`
5×	`add-exp-log` `associate-l` `add-cbrt-cube` `add-log-exp`
4×	`frac-times` `distribute-lft-out--`
3×	`expm1-log1p-u` `sub-neg` `fma-neg` `log1p-expm1-u` `difference-of-squares`
2×	`associate-r/` `associate-l/` `fma-udef`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 106

Calls

3 calls:

13.0ms

(- (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)

82.0ms

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

0.0ms

(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)))))))

series539.0ms

Counts

3 → 9

Calls

3 calls:

295.0ms

(- (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)

95.0ms

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

149.0ms

(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)))))))

simplify1.1s

Counts

115 → 115

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	237	5385
1	501	4186
2	1668	3509
done	5000	2853

prune525.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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:

1.0ms	(cbrt (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))))))))
1.0ms	(cbrt (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))))))))
1.0ms	(cbrt (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))))))))
31.0ms	(* (cbrt (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)))))))) (cbrt (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)))))))))

series10.5s

Counts

4 → 12

Calls

4 calls:

2.5s	(cbrt (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))))))))
2.5s	(cbrt (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))))))))
2.6s	(cbrt (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))))))))
2.9s	(* (cbrt (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)))))))) (cbrt (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)))))))))

simplify1.1s

Counts

93 → 93

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	219	5633
1	622	5242
2	2144	4767
done	5001	4105

prune909.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cbrt (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)))))))))
0.5b	(cbrt (cbrt (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)))))))))
0.5b	(cbrt (cbrt (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)))))))))
0.9b	(pow (cbrt (cbrt (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))))))))) (+ 3 1))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
16×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`unpow-prod-down`
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 → 76

Calls

4 calls:

11.0ms	(cbrt (cbrt (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)))))))))
1.0ms	(cbrt (cbrt (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)))))))))
1.0ms	(cbrt (cbrt (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)))))))))
9.0ms	(pow (cbrt (cbrt (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))))))))) (+ 3 1))

series13.8s

Counts

4 → 12

Calls

4 calls:

2.7s	(cbrt (cbrt (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)))))))))
2.8s	(cbrt (cbrt (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)))))))))
2.7s	(cbrt (cbrt (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)))))))))
5.5s	(pow (cbrt (cbrt (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))))))))) (+ 3 1))

simplify1.4s

Counts

88 → 88

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	239	4869
1	694	4431
2	2360	3996
done	5000	3956

prune971.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

regimes662.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample7.6s

Algorithm

intervals

Results

3.3s	24307×	body	80	nan
752.0ms	5855×	body	80	valid
636.0ms	668×	body	320	valid
447.0ms	793×	body	640	valid
310.0ms	235×	body	1280	valid
123.0ms	473×	body	160	valid