Details

sample213.0ms

Algorithm

intervals

Results

55.0ms	62×	body	10240	exit
55.0ms	61×	body	1280	valid
23.0ms	47×	body	640	valid
11.0ms	110×	body	80	valid
9.0ms	3×	body	2560	valid
8.0ms	23×	body	320	valid
6.0ms	91×	body	80	nan
3.0ms	10×	body	640	nan
3.0ms	12×	body	160	valid
2.0ms	8×	body	320	nan
2.0ms	3×	body	1280	nan
0.0ms	2×	body	160	nan

simplify975.0ms

Counts

1 → 1

Iterations

Useful iterations: 10 (450.0ms)

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

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.5b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(- x (/ (log (fma (expm1 z) y 1.0)) t))
0.0b	(/ (log (fma (expm1 z) y 1.0)) t)
3.5b	(log (fma (expm1 z) y 1.0))

rewrite49.0ms

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:

24.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
14.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
3.0ms	(log (fma (expm1 z) y 1.0))

series423.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms	(- x (/ (log (fma (expm1 z) y 1.0)) t))
206.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
114.0ms	(log (fma (expm1 z) y 1.0))

simplify1.7s

Counts

124 → 124

Iterations

Useful iterations: done (1.7s)

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

prune487.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fma (expm1 z) y 1.0))
0.1b	(cbrt (fma (expm1 z) y 1.0))
3.3b	(log (cbrt (fma (expm1 z) y 1.0)))
3.3b	(log (cbrt (fma (expm1 z) y 1.0)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `log-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow1/3` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-log-exp`

Counts

4 → 62

Calls

4 calls:

2.0ms	(cbrt (fma (expm1 z) y 1.0))
2.0ms	(cbrt (fma (expm1 z) y 1.0))
4.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
4.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

series832.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(cbrt (fma (expm1 z) y 1.0))
198.0ms	(cbrt (fma (expm1 z) y 1.0))
220.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
225.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

simplify2.0s

Counts

74 → 74

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	110	1166
1	261	1088
2	696	994
3	2292	950
done	5000	896

prune524.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (log (fma (expm1 z) y 1.0)))
3.5b	(log (fma (expm1 z) y 1.0))
3.5b	(log (fma (expm1 z) y 1.0))
3.5b	(log (fma (expm1 z) y 1.0))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

2.0ms	(cbrt (log (fma (expm1 z) y 1.0)))
3.0ms	(log (fma (expm1 z) y 1.0))
3.0ms	(log (fma (expm1 z) y 1.0))
3.0ms	(log (fma (expm1 z) y 1.0))

series598.0ms

Counts

4 → 12

Calls

4 calls:

305.0ms	(cbrt (log (fma (expm1 z) y 1.0)))
111.0ms	(log (fma (expm1 z) y 1.0))
85.0ms	(log (fma (expm1 z) y 1.0))
97.0ms	(log (fma (expm1 z) y 1.0))

simplify2.9s

Counts

68 → 68

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	124	1061
1	321	983
2	967	858
3	4169	831
done	5000	829

prune485.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (log (fma (expm1 z) y 1.0)))
3.5b	(log (fma (expm1 z) y 1.0))
3.5b	(log (fma (expm1 z) y 1.0))
3.5b	(log (fma (expm1 z) y 1.0))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

2.0ms	(cbrt (log (fma (expm1 z) y 1.0)))
3.0ms	(log (fma (expm1 z) y 1.0))
3.0ms	(log (fma (expm1 z) y 1.0))
3.0ms	(log (fma (expm1 z) y 1.0))

series602.0ms

Counts

4 → 12

Calls

4 calls:

292.0ms	(cbrt (log (fma (expm1 z) y 1.0)))
118.0ms	(log (fma (expm1 z) y 1.0))
105.0ms	(log (fma (expm1 z) y 1.0))
87.0ms	(log (fma (expm1 z) y 1.0))

simplify2.7s

Counts

68 → 68

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	124	1061
1	321	983
2	967	858
3	4169	831
done	5000	829

prune501.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.4b

regimes497.0ms

Accuracy

41.9% (4.1b remaining)

Error of 8.9b against oracle of 4.9b and baseline of 11.9b

bsearch78.0ms

Steps

Iters	Range		Point
5	-1.9392852685458433e-69	-9.529910149440609e-70	-1.1486240881917044e-69

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	58
1	34	58
done	34	58

end0.0ms

sample6.8s

Algorithm

intervals

Results

1.6s	1588×	body	10240	exit
1.3s	1411×	body	1280	valid
831.0ms	3534×	body	80	valid
815.0ms	1578×	body	640	valid
612.0ms	2562×	body	80	nan
280.0ms	946×	body	320	valid
132.0ms	71×	body	2560	valid
95.0ms	485×	body	160	valid
87.0ms	263×	body	640	nan
78.0ms	111×	body	160	nan
78.0ms	191×	body	320	nan
58.0ms	118×	body	1280	nan