Details

sample207.0ms

Algorithm

intervals

Results

59.0ms	58×	body	10240	exit
34.0ms	39×	body	1280	valid
29.0ms	50×	body	640	valid
13.0ms	120×	body	80	valid
10.0ms	30×	body	320	valid
7.0ms	91×	body	80	nan
5.0ms	12×	body	640	nan
4.0ms	2×	body	2560	valid
4.0ms	17×	body	160	valid
3.0ms	6×	body	1280	nan
1.0ms	4×	body	320	nan
0.0ms	2×	body	160	nan

simplify955.0ms

Counts

1 → 1

Iterations

Useful iterations: 10 (474.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.8b

localize26.0ms

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)
3.6b	(log (fma (expm1 z) y 1.0))

rewrite21.0ms

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))

series345.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(fma (expm1 z) y 1.0)
163.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
94.0ms	(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

prune392.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize21.0ms

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)))
0.2b	(/ 1 (/ t (log (fma (expm1 z) y 1.0))))
3.6b	(log (fma (expm1 z) y 1.0))

rewrite38.0ms

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

series579.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(fma (expm1 z) y 1.0)
256.0ms	(/ t (log (fma (expm1 z) y 1.0)))
144.0ms	(/ 1 (/ t (log (fma (expm1 z) y 1.0))))
114.0ms	(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

prune566.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fma (expm1 z) y 1.0))
0.2b	(/ 1 (/ t (+ (* 2 (log (cbrt (fma (expm1 z) y 1.0)))) (log (cbrt (fma (expm1 z) y 1.0))))))
3.6b	(log (cbrt (fma (expm1 z) y 1.0)))
3.6b	(log (cbrt (fma (expm1 z) y 1.0)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
86×	`*-un-lft-identity`
74×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`distribute-rgt-out` `associate-/r*`
19×	`pow1`
17×	`add-exp-log`
16×	`log-pow`
12×	`log-prod` `distribute-lft1-in`
9×	`cbrt-prod` `associate-/r/` `add-cbrt-cube`
7×	`div-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow1/3` `associate-/l*`
2×	`rec-exp` `1-exp` `rem-log-exp`
1×	`pow-flip` `frac-2neg` `clear-num` `inv-pow`

Counts

4 → 171

Calls

4 calls:

1.0ms	(cbrt (fma (expm1 z) y 1.0))
46.0ms	(/ 1 (/ t (+ (* 2 (log (cbrt (fma (expm1 z) y 1.0)))) (log (cbrt (fma (expm1 z) y 1.0))))))
2.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
2.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

series785.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(cbrt (fma (expm1 z) y 1.0))
229.0ms	(/ 1 (/ t (+ (* 2 (log (cbrt (fma (expm1 z) y 1.0)))) (log (cbrt (fma (expm1 z) y 1.0))))))
189.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
171.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

simplify1.5s

Counts

183 → 183

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	333	4931
1	763	3450
2	1911	3040
done	5000	2891

prune787.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fma (expm1 z) y 1.0))
0.2b	(/ 1 (/ t (+ (* 2 (* 1/3 (log (fma (expm1 z) y 1.0)))) (log (cbrt (fma (expm1 z) y 1.0))))))
3.6b	(log (fma (expm1 z) y 1.0))
3.6b	(log (cbrt (fma (expm1 z) y 1.0)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

81×	`times-frac`
52×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
17×	`add-exp-log`
15×	`associate-/r*`
9×	`log-prod` `associate-/r/` `add-cbrt-cube`
7×	`pow1` `div-exp`
6×	`cbrt-prod`
5×	`div-inv`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `log-pow` `associate-/l*`
2×	`rec-exp` `pow1/3` `1-exp` `rem-log-exp`
1×	`pow-flip` `frac-2neg` `clear-num` `inv-pow`

Counts

4 → 131

Calls

4 calls:

1.0ms	(cbrt (fma (expm1 z) y 1.0))
57.0ms	(/ 1 (/ t (+ (* 2 (* 1/3 (log (fma (expm1 z) y 1.0)))) (log (cbrt (fma (expm1 z) y 1.0))))))
3.0ms	(log (fma (expm1 z) y 1.0))
4.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

series722.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(cbrt (fma (expm1 z) y 1.0))
322.0ms	(/ 1 (/ t (+ (* 2 (* 1/3 (log (fma (expm1 z) y 1.0)))) (log (cbrt (fma (expm1 z) y 1.0))))))
80.0ms	(log (fma (expm1 z) y 1.0))
191.0ms	(log (cbrt (fma (expm1 z) y 1.0)))

simplify1.7s

Counts

143 → 143

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	320	4277
1	746	3675
2	1969	3252
done	5000	3202

prune712.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

regimes327.0ms

Accuracy

38.5% (4.1b remaining)

Error of 8.5b against oracle of 4.4b and baseline of 11.1b

bsearch87.0ms

Steps

Iters	Range		Point
5	-7.653706237395124e-160	-3.5877351750007996e-160	-7.557323451675197e-160

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	39
1	30	39
done	30	39

end0.0ms

sample7.1s

Algorithm

intervals

Results

1.8s	1386×	body	1280	valid
1.6s	1461×	body	10240	exit
905.0ms	1593×	body	640	valid
713.0ms	910×	body	320	valid
521.0ms	3570×	body	80	valid
244.0ms	2526×	body	80	nan
150.0ms	79×	body	2560	valid
102.0ms	490×	body	160	valid
98.0ms	261×	body	640	nan
66.0ms	116×	body	1280	nan
45.0ms	186×	body	320	nan
17.0ms	104×	body	160	nan