Details

sample162.0ms

Algorithm

intervals

Results

36.0ms	45×	body	1280	valid
31.0ms	41×	body	10240	exit
26.0ms	43×	body	640	valid
11.0ms	121×	body	80	valid
9.0ms	32×	body	320	valid
5.0ms	83×	body	80	nan
4.0ms	2×	body	2560	valid
4.0ms	14×	body	640	nan
2.0ms	14×	body	160	valid
1.0ms	7×	body	320	nan
0.0ms	1×	body	1280	nan
0.0ms	1×	body	160	nan

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 10 (513.0ms)

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: 8.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- x (/ (log (fma (expm1 z) y 1.0)) t))
0.1b	(/ (log (fma (expm1 z) y 1.0)) t)
3.3b	(log (fma (expm1 z) y 1.0))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 115

Calls

3 calls:

15.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
11.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
3.0ms	(log (fma (expm1 z) y 1.0))

series399.0ms

Counts

3 → 9

Calls

3 calls:

141.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
160.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
97.0ms	(log (fma (expm1 z) y 1.0))

simplify1.5s

Counts

124 → 124

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	252	4198
1	580	3760
2	1528	2551
done	5001	2111

prune424.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(- x (* (log (fma (expm1 z) y 1.0)) (/ 1 t)))
0.1b	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
3.3b	(log (fma (expm1 z) y 1.0))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`add-exp-log` `associate-r`
11×	`times-frac`
8×	`add-cbrt-cube`
7×	`pow1`
5×	`add-log-exp`
4×	`associate-l` `prod-exp`
3×	`expm1-log1p-u` `log-prod` `fma-neg` `prod-diff` `log1p-expm1-u` `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--` `div-inv`

Counts

3 → 73

Calls

3 calls:

12.0ms	(- 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))

series434.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(- x (* (log (fma (expm1 z) y 1.0)) (/ 1 t)))
192.0ms	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
125.0ms	(log (fma (expm1 z) y 1.0))

simplify3.1s

Counts

82 → 82

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	189	1282
1	442	1075
2	1147	955
3	3218	936
done	5000	902

prune340.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (- (/ (log (fma (expm1 z) y 1.0)) t)))
0.1b	(/ (log (fma (expm1 z) y 1.0)) t)
3.3b	(log (fma (expm1 z) y 1.0))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`times-frac`
8×	`pow1`
7×	`add-log-exp`
6×	`add-exp-log`
5×	`log-pow` `add-cbrt-cube`
4×	`associate-/l*`
3×	`expm1-log1p-u` `log-prod` `fma-def` `associate-/r*` `log1p-expm1-u`
2×	`sum-log` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+r-` `distribute-rgt-neg-in` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `unsub-neg` `neg-log` `clear-num` `flip-+` `div-inv`

Counts

3 → 69

Calls

3 calls:

25.0ms	(+ x (- (/ (log (fma (expm1 z) y 1.0)) t)))
15.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
12.0ms	(log (fma (expm1 z) y 1.0))

series405.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(+ x (- (/ (log (fma (expm1 z) y 1.0)) t)))
190.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
100.0ms	(log (fma (expm1 z) y 1.0))

simplify2.2s

Counts

78 → 78

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	162	1046
1	365	979
2	977	895
3	2662	890
done	5001	885

prune450.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (log (fma (expm1 z) y 1.0)) t))
3.3b	(log (fma (expm1 z) y 1.0))
3.3b	(log (fma (expm1 z) y 1.0))
3.3b	(log (fma (expm1 z) y 1.0))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

16×	`cbrt-prod`
15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`pow1`
9×	`log-prod`
7×	`add-exp-log`
6×	`log-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 69

Calls

4 calls:

3.0ms	(cbrt (/ (log (fma (expm1 z) y 1.0)) 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))

series732.0ms

Counts

4 → 12

Calls

4 calls:

462.0ms	(cbrt (/ (log (fma (expm1 z) y 1.0)) t))
105.0ms	(log (fma (expm1 z) y 1.0))
74.0ms	(log (fma (expm1 z) y 1.0))
91.0ms	(log (fma (expm1 z) y 1.0))

simplify992.0ms

Counts

81 → 81

Iterations

Useful iterations: done (989.0ms)

Iter	Nodes	Cost
0	197	1445
1	458	1353
2	1337	1229
done	5000	1180

prune569.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.4b

regimes347.0ms

Accuracy

43.9% (3.8b remaining)

Error of 8.4b against oracle of 4.6b and baseline of 11.3b

bsearch159.0ms

Steps

Iters	Range		Point
8	-8.638556380710241e-134	-2.110475534095123e-136	-6.310119903545574e-134

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	38
1	33	38
done	33	38

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.3s	1557×	body	10240	exit
1.2s	1443×	body	1280	valid
806.0ms	1545×	body	640	valid
448.0ms	3558×	body	80	valid
302.0ms	915×	body	320	valid
182.0ms	2431×	body	80	nan
178.0ms	84×	body	2560	valid
84.0ms	263×	body	640	nan
83.0ms	478×	body	160	valid
52.0ms	110×	body	1280	nan
45.0ms	195×	body	320	nan
14.0ms	100×	body	160	nan