Details

sample220.0ms

Algorithm

intervals

Results

81.0ms	748×	body	80	nan
19.0ms	178×	body	80	valid
14.0ms	24×	body	640	valid
13.0ms	11×	body	1280	valid
9.0ms	28×	body	320	valid
4.0ms	19×	body	160	valid

simplify852.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.3b

localize16.0ms

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)
0.3b	(fma x (log y) (* z (log (- 1.0 y))))
4.6b	(log (- 1.0 y))

rewrite60.0ms

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:

31.0ms	(* z (log (- 1.0 y)))
14.0ms	(- (fma x (log y) (* z (log (- 1.0 y)))) t)
1.0ms	(fma x (log y) (* z (log (- 1.0 y))))
10.0ms	(log (- 1.0 y))

series427.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* z (log (- 1.0 y)))
143.0ms	(- (fma x (log y) (* z (log (- 1.0 y)))) t)
134.0ms	(fma x (log y) (* z (log (- 1.0 y))))
66.0ms	(log (- 1.0 y))

simplify1.4s

Counts

100 → 100

Iterations

Useful iterations: done (1.4s)

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

prune510.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.0b

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

0.2b

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt` `times-frac`
68×	`associate-r`
56×	`unpow-prod-down`
46×	`*-un-lft-identity`
44×	`add-cube-cbrt`
26×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`prod-exp`
9×	`div-exp` `prod-diff`
8×	`add-cbrt-cube`
6×	`pow-to-exp` `pow-exp`
5×	`pow1` `add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-l` `log1p-expm1-u`
2×	`cbrt-unprod` `fma-udef`
1×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `associate-r/` `pow-prod-down` `associate--l+` `-commutative` `flip--` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 151

Calls

3 calls:

48.0ms

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

7.0ms

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

0.0ms

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

series534.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms

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

259.0ms

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

199.0ms

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

simplify2.0s

Counts

160 → 160

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	302	3017
1	799	2688
2	3469	2263
done	5001	2126

prune971.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

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:

23.0ms	(* (cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))
2.0ms	(cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
2.0ms	(cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
2.0ms	(cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))

series5.0s

Counts

4 → 12

Calls

4 calls:

1.3s	(* (cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))) (cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))
1.2s	(cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
1.3s	(cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
1.3s	(cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))

simplify848.0ms

Counts

93 → 93

Iterations

Useful iterations: done (842.0ms)

Iter	Nodes	Cost
0	139	3815
1	337	3580
2	1188	3247
done	5000	2766

prune746.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
0.6b	(cbrt (cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))
0.6b	(cbrt (cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))
0.6b	(cbrt (cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

30×	`cbrt-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 61

Calls

4 calls:

1.0ms	(cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
1.0ms	(cbrt (cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))
1.0ms	(cbrt (cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))
2.0ms	(cbrt (cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))

series4.5s

Counts

4 → 12

Calls

4 calls:

1.2s	(cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2))))))))
1.1s	(cbrt (cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))
937.0ms	(cbrt (cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))
1.3s	(cbrt (cbrt (fma x (log y) (* z (- (log 1.0) (fma 1.0 y (* 1/2 (/ (pow y 2) (pow 1.0 2)))))))))

simplify1.4s

Counts

73 → 73

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	113	2469
1	243	2442
2	682	2241
3	2548	2213
done	5001	2089

prune582.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.1b

regimes366.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.5s	24313×	body	80	nan
863.0ms	5569×	body	80	valid
425.0ms	845×	body	640	valid
332.0ms	414×	body	1280	valid
307.0ms	744×	body	320	valid
73.0ms	462×	body	160	valid