Details

sample190.0ms

Algorithm

intervals

Results

38.0ms	46×	body	10240	exit
36.0ms	42×	body	1280	valid
23.0ms	46×	body	640	valid
21.0ms	77×	body	80	nan
11.0ms	39×	body	320	valid
11.0ms	114×	body	80	valid
8.0ms	4×	body	2560	valid
4.0ms	13×	body	640	nan
2.0ms	12×	body	160	valid
2.0ms	8×	body	320	nan
0.0ms	1×	body	1280	nan
0.0ms	1×	body	160	nan

simplify940.0ms

Counts

1 → 1

Iterations

Useful iterations: 10 (475.0ms)

Iter	Nodes	Cost
0	12	13
1	20	13
2	35	12
3	53	12
4	77	12
5	106	12
6	138	12
7	176	12
8	232	12
9	295	12
10	459	10
11	498	10
12	500	10
done	500	10

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.3b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (expm1 z) y 1.0)
0.1b	(/ (log (fma (expm1 z) y 1.0)) t)
2.4b	(log (fma (expm1 z) y 1.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
8×	`pow1`
6×	`add-exp-log`
5×	`log-pow` `add-cbrt-cube`
4×	`associate-/l*`
3×	`expm1-log1p-u` `log-prod` `associate-/r*` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `fma-udef` `div-inv`

Counts

3 → 57

Calls

3 calls:

1.0ms	(fma (expm1 z) y 1.0)
15.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
3.0ms	(log (fma (expm1 z) y 1.0))

series372.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(fma (expm1 z) y 1.0)
218.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
92.0ms	(log (fma (expm1 z) y 1.0))

simplify2.1s

Counts

66 → 66

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	146	855
1	310	819
2	802	747
3	2138	738
done	5000	733

prune275.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (expm1 z) y 1.0)
0.1b	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
2.4b	(log (fma (expm1 z) y 1.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
13×	`add-exp-log` `-un-lft-identity` `associate-r*`
12×	`add-cube-cbrt`
11×	`times-frac`
8×	`add-cbrt-cube`
7×	`pow1`
4×	`associate-l` `prod-exp`
3×	`expm1-log1p-u` `log-prod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`div-exp` `log-pow` `cbrt-unprod`
1×	`cbrt-undiv` `rec-exp` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `un-div-inv` `-commutative` `fma-udef` `div-inv`

Counts

3 → 63

Calls

3 calls:

1.0ms	(fma (expm1 z) y 1.0)
17.0ms	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
2.0ms	(log (fma (expm1 z) y 1.0))

series761.0ms

Counts

3 → 9

Calls

3 calls:

498.0ms	(fma (expm1 z) y 1.0)
170.0ms	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
93.0ms	(log (fma (expm1 z) y 1.0))

simplify2.2s

Counts

72 → 72

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	169	943
1	394	825
2	1005	717
3	2558	708
done	5000	703

prune323.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cbrt (pow (log (fma (expm1 z) y 1.0)) 3)) t)
0.2b	(pow (log (fma (expm1 z) y 1.0)) 3)
0.2b	(cbrt (pow (log (fma (expm1 z) y 1.0)) 3))
2.4b	(log (fma (expm1 z) y 1.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

70×	`cbrt-prod`
51×	`times-frac`
45×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down` `cube-prod`
18×	`pow1`
17×	`associate-/l*`
13×	`log-pow`
8×	`add-exp-log`
6×	`cube-mult` `unpow3` `add-cbrt-cube` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `log-prod` `associate-/r*`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `div-exp` `rem-log-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 151

Calls

4 calls:

14.0ms	(/ (cbrt (pow (log (fma (expm1 z) y 1.0)) 3)) t)
4.0ms	(pow (log (fma (expm1 z) y 1.0)) 3)
3.0ms	(cbrt (pow (log (fma (expm1 z) y 1.0)) 3))
2.0ms	(log (fma (expm1 z) y 1.0))

series613.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (cbrt (pow (log (fma (expm1 z) y 1.0)) 3)) t)
256.0ms	(pow (log (fma (expm1 z) y 1.0)) 3)
87.0ms	(cbrt (pow (log (fma (expm1 z) y 1.0)) 3))
76.0ms	(log (fma (expm1 z) y 1.0))

simplify1.5s

Counts

163 → 163

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	304	3300
1	733	2641
2	2496	2424
done	5000	2415

prune636.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (expm1 z) y 1.0)
0.1b	(/ t (log (fma (expm1 z) y 1.0)))
0.1b	(/ (cbrt (pow 1 3)) (/ t (log (fma (expm1 z) y 1.0))))
2.4b	(log (fma (expm1 z) y 1.0))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

444×	`times-frac`
210×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
204×	`cbrt-prod`
57×	`pow1`
53×	`log-pow`
51×	`unpow-prod-down` `cube-prod`
20×	`associate-/r*`
18×	`div-inv` `associate-/l*`
17×	`cube-mult` `unpow3` `sqr-pow`
12×	`add-exp-log`
9×	`add-cbrt-cube`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`log-prod`
2×	`frac-2neg` `clear-num`
1×	`rem-log-exp` `associate-/r/` `fma-udef`

Counts

4 → 345

Calls

4 calls:

0.0ms	(fma (expm1 z) y 1.0)
5.0ms	(/ t (log (fma (expm1 z) y 1.0)))
32.0ms	(/ (cbrt (pow 1 3)) (/ t (log (fma (expm1 z) y 1.0))))
3.0ms	(log (fma (expm1 z) y 1.0))

series531.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(fma (expm1 z) y 1.0)
256.0ms	(/ t (log (fma (expm1 z) y 1.0)))
130.0ms	(/ (cbrt (pow 1 3)) (/ t (log (fma (expm1 z) y 1.0))))
86.0ms	(log (fma (expm1 z) y 1.0))

simplify1.2s

Counts

357 → 357

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	470	8967
1	827	6411
2	1843	5759
done	5000	5642

prune681.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.1b

regimes451.0ms

Accuracy

41.5% (4.1b remaining)

Error of 8.9b against oracle of 4.7b and baseline of 11.8b

bsearch3.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	33
1	29	33
done	29	33

end0.0ms

sample7.3s

Algorithm

intervals

Results

1.7s	1500×	body	10240	exit
1.4s	1413×	body	1280	valid
1.1s	2509×	body	80	nan
889.0ms	1545×	body	640	valid
453.0ms	1011×	body	320	valid
418.0ms	3475×	body	80	valid
205.0ms	99×	body	2560	valid
113.0ms	125×	body	1280	nan
108.0ms	289×	body	640	nan
98.0ms	485×	body	160	valid
49.0ms	192×	body	320	nan
21.0ms	126×	body	160	nan