Details

sample222.0ms

Algorithm

intervals

Results

51.0ms	46×	body	10240	exit
44.0ms	42×	body	1280	valid
38.0ms	46×	body	640	valid
15.0ms	39×	body	320	valid
15.0ms	114×	body	80	valid
11.0ms	4×	body	2560	valid
7.0ms	77×	body	80	nan
6.0ms	13×	body	640	nan
3.0ms	12×	body	160	valid
2.0ms	8×	body	320	nan
1.0ms	1×	body	1280	nan
0.0ms	1×	body	160	nan

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 10 (565.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.3b

localize21.0ms

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)
14.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
3.0ms	(log (fma (expm1 z) y 1.0))

series367.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(fma (expm1 z) y 1.0)
187.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
106.0ms	(log (fma (expm1 z) y 1.0))

simplify2.0s

Counts

66 → 66

Iterations

Useful iterations: done (2.0s)

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

prune254.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.1b

localize11.0ms

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))

rewrite32.0ms

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)
26.0ms	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
1.0ms	(log (fma (expm1 z) y 1.0))

series394.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(fma (expm1 z) y 1.0)
212.0ms	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
120.0ms	(log (fma (expm1 z) y 1.0))

simplify2.1s

Counts

72 → 72

Iterations

Useful iterations: done (2.1s)

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

prune372.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.1b

localize23.0ms

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))

rewrite33.0ms

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:

13.0ms	(/ (cbrt (pow (log (fma (expm1 z) y 1.0)) 3)) t)
6.0ms	(pow (log (fma (expm1 z) y 1.0)) 3)
5.0ms	(cbrt (pow (log (fma (expm1 z) y 1.0)) 3))
3.0ms	(log (fma (expm1 z) y 1.0))

series563.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(/ (cbrt (pow (log (fma (expm1 z) y 1.0)) 3)) t)
206.0ms	(pow (log (fma (expm1 z) y 1.0)) 3)
83.0ms	(cbrt (pow (log (fma (expm1 z) y 1.0)) 3))
91.0ms	(log (fma (expm1 z) y 1.0))

simplify1.6s

Counts

163 → 163

Iterations

Useful iterations: done (1.6s)

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

prune744.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.1b

localize20.0ms

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
63×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
22×	`pow1`
20×	`associate-/r*`
18×	`add-exp-log`
17×	`log-pow`
11×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`log-prod`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`pow-flip` `rem-log-exp` `associate-/r/` `fma-udef` `inv-pow`

Counts

4 → 147

Calls

4 calls:

0.0ms	(fma (expm1 z) y 1.0)
5.0ms	(/ t (log (fma (expm1 z) y 1.0)))
11.0ms	(/ 1 (/ t (log (fma (expm1 z) y 1.0))))
1.0ms	(log (fma (expm1 z) y 1.0))

series527.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(fma (expm1 z) y 1.0)
252.0ms	(/ t (log (fma (expm1 z) y 1.0)))
97.0ms	(/ 1 (/ t (log (fma (expm1 z) y 1.0))))
105.0ms	(log (fma (expm1 z) y 1.0))

simplify1.2s

Counts

159 → 159

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	283	2723
1	643	2403
2	1718	2148
done	5000	2103

prune525.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.1b

regimes421.0ms

Accuracy

41.6% (4.1b remaining)

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

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	40
1	31	40
done	31	40

end0.0ms

sample6.7s

Algorithm

intervals

Results

1.9s	1413×	body	1280	valid
1.4s	1500×	body	10240	exit
851.0ms	1545×	body	640	valid
814.0ms	3475×	body	80	valid
314.0ms	1011×	body	320	valid
213.0ms	2509×	body	80	nan
192.0ms	99×	body	2560	valid
146.0ms	289×	body	640	nan
124.0ms	485×	body	160	valid
60.0ms	125×	body	1280	nan
44.0ms	192×	body	320	nan
18.0ms	126×	body	160	nan