Details

sample192.0ms

Algorithm

intervals

Results

40.0ms	51×	body	10240	exit
36.0ms	40×	body	1280	valid
24.0ms	28×	body	320	valid
22.0ms	45×	body	640	valid
12.0ms	118×	body	80	valid
6.0ms	94×	body	80	nan
5.0ms	23×	body	160	valid
4.0ms	11×	body	640	nan
3.0ms	2×	body	2560	valid
2.0ms	9×	body	320	nan
2.0ms	4×	body	1280	nan
1.0ms	7×	body	160	nan

simplify956.0ms

Counts

1 → 1

Iterations

Useful iterations: 10 (492.0ms)

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: 13.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (expm1 z) y 1.0)
0.0b	(- x (/ (log (fma (expm1 z) y 1.0)) t))
0.1b	(/ (log (fma (expm1 z) y 1.0)) t)
3.7b	(log (fma (expm1 z) y 1.0))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
55×	`add-cube-cbrt`
49×	`times-frac`
48×	`prod-diff`
18×	`pow1`
14×	`log-pow`
7×	`add-exp-log`
6×	`add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*`
3×	`log-prod` `fma-neg` `associate-/r*`
2×	`difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `flip--` `fma-udef` `distribute-lft-out--`

Counts

4 → 125

Calls

4 calls:

1.0ms	(fma (expm1 z) y 1.0)
31.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
15.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
3.0ms	(log (fma (expm1 z) y 1.0))

series422.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(fma (expm1 z) y 1.0)
97.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
171.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
83.0ms	(log (fma (expm1 z) y 1.0))

simplify1.5s

Counts

137 → 137

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	268	4303
1	616	3861
2	1612	2642
done	5000	2196

prune477.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (expm1 z) y 1.0)
0.0b	(- x (* (log (fma (expm1 z) y 1.0)) (/ 1 t)))
0.1b	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
3.7b	(log (fma (expm1 z) y 1.0))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`add-cube-cbrt`
14×	`add-exp-log`
13×	`associate-r`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u`
3×	`log-prod` `fma-neg` `prod-diff` `unswap-sqr`
2×	`div-exp` `log-pow` `cbrt-unprod`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `flip3--` `diff-log` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `un-div-inv` `-commutative` `flip--` `fma-udef` `div-inv`

Counts

4 → 83

Calls

4 calls:

0.0ms	(fma (expm1 z) y 1.0)
17.0ms	(- x (* (log (fma (expm1 z) y 1.0)) (/ 1 t)))
32.0ms	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
3.0ms	(log (fma (expm1 z) y 1.0))

series451.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(fma (expm1 z) y 1.0)
107.0ms	(- x (* (log (fma (expm1 z) y 1.0)) (/ 1 t)))
199.0ms	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
92.0ms	(log (fma (expm1 z) y 1.0))

simplify2.5s

Counts

95 → 95

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	205	1387
1	478	1176
2	1230	1046
3	3470	1021
done	5000	1018

prune543.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.8b

localize56.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
3.7b	(log (fma (expm1 z) y 1.0))
3.7b	(log (fma (expm1 z) y 1.0))
3.7b	(log (fma (expm1 z) y 1.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`log-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `rem-log-exp` `log-pow`
1×	`pow1/3`

Counts

4 → 55

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(log (fma (expm1 z) y 1.0))
1.0ms	(log (fma (expm1 z) y 1.0))
2.0ms	(log (fma (expm1 z) y 1.0))

series627.0ms

Counts

4 → 12

Calls

4 calls:

325.0ms	(cbrt t)
80.0ms	(log (fma (expm1 z) y 1.0))
110.0ms	(log (fma (expm1 z) y 1.0))
113.0ms	(log (fma (expm1 z) y 1.0))

simplify3.4s

Counts

67 → 67

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	88	734
1	184	688
2	456	607
3	1266	598
4	4140	586
done	5000	583

prune514.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.7b

localize41.0ms

Local error

Found 4 expressions with local error:

3.7b	(log (fma (expm1 z) y 1.0))
3.7b	(log (fma (expm1 z) y 1.0))
3.8b	(log (sqrt (fma (expm1 z) y 1.0)))
3.8b	(log (sqrt (fma (expm1 z) y 1.0)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

18×	`log-prod`
10×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `log-pow`
6×	`sqrt-prod`
4×	`expm1-log1p-u` `rem-log-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow1/2`

Counts

4 → 66

Calls

4 calls:

3.0ms	(log (fma (expm1 z) y 1.0))
3.0ms	(log (fma (expm1 z) y 1.0))
5.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
10.0ms	(log (sqrt (fma (expm1 z) y 1.0)))

series682.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(log (fma (expm1 z) y 1.0))
121.0ms	(log (fma (expm1 z) y 1.0))
258.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
217.0ms	(log (sqrt (fma (expm1 z) y 1.0)))

simplify1.5s

Counts

78 → 78

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	198	1718
1	546	1568
2	1823	1434
done	5000	1322

prune646.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.7b

regimes670.0ms

Accuracy

40.5% (4.3b remaining)

Error of 8.6b against oracle of 4.3b and baseline of 11.5b

bsearch110.0ms

Steps

Iters	Range		Point
8	-9.437501128818057e-35	-1.6769430254240637e-39	-1.483213486755814e-38

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	38
1	32	38
done	32	38

end0.0ms

sample6.2s

Algorithm

intervals

Results

1.5s	1469×	body	1280	valid
1.4s	1531×	body	10240	exit
739.0ms	1505×	body	640	valid
538.0ms	2675×	body	80	nan
459.0ms	3559×	body	80	valid
304.0ms	897×	body	320	valid
191.0ms	90×	body	2560	valid
116.0ms	500×	body	160	valid
89.0ms	129×	body	1280	nan
88.0ms	284×	body	640	nan
36.0ms	178×	body	320	nan
15.0ms	120×	body	160	nan