Details

sample109.0ms

Algorithm

intervals

Results

28.0ms	46×	body	10240	exit
23.0ms	44×	body	1280	valid
15.0ms	53×	body	640	valid
7.0ms	110×	body	80	valid
5.0ms	25×	body	320	valid
3.0ms	81×	body	80	nan
2.0ms	23×	body	160	valid
2.0ms	10×	body	640	nan
2.0ms	1×	body	2560	valid
1.0ms	5×	body	1280	nan
1.0ms	4×	body	320	nan
0.0ms	2×	body	160	nan

simplify559.0ms

Counts

1 → 1

Iterations

Useful iterations: 10 (262.0ms)

Iter	Nodes	Cost
0	12	13
1	20	13
2	35	12
3	51	12
4	77	12
5	105	12
6	137	12
7	176	12
8	217	12
9	280	12
10	470	10
11	533	10
12	535	10
done	535	10

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (log (fma (expm1 z) y 1.0)) t)
4.7b	(log (fma (expm1 z) y 1.0))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
7×	`pow1`
5×	`add-exp-log` `log-pow`
4×	`add-cbrt-cube` `associate-/l*`
3×	`log-prod` `associate-/r*`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `div-inv`

Counts

2 → 47

Calls

2 calls:

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

series242.0ms

Counts

2 → 6

Calls

2 calls:

165.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
77.0ms	(log (fma (expm1 z) y 1.0))

simplify1.5s

Counts

53 → 53

Iterations

Useful iterations: 3 (483.0ms)

Iter	Nodes	Cost
0	130	750
1	275	718
2	757	656
3	2180	652
done	5000	652

prune210.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.5b

localize13.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
4.7b	(log (fma (expm1 z) y 1.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`associate-r`
12×	`add-exp-log` `*-un-lft-identity`
11×	`add-cube-cbrt` `times-frac`
7×	`add-cbrt-cube`
6×	`pow1`
4×	`associate-l` `prod-exp`
3×	`log-prod` `unswap-sqr`
2×	`expm1-log1p-u` `div-exp` `log-pow` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `rec-exp` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

2 → 53

Calls

2 calls:

8.0ms	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
1.0ms	(log (fma (expm1 z) y 1.0))

series240.0ms

Counts

2 → 6

Calls

2 calls:

157.0ms	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
82.0ms	(log (fma (expm1 z) y 1.0))

simplify1.8s

Counts

59 → 59

Iterations

Useful iterations: 3 (864.0ms)

Iter	Nodes	Cost
0	153	838
1	365	724
2	964	626
3	2678	622
done	5000	622

prune213.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (pow (log (fma (expm1 z) y 1.0)) 3)) (/ 1 t))
0.2b	(pow (log (fma (expm1 z) y 1.0)) 3)
0.2b	(cbrt (pow (log (fma (expm1 z) y 1.0)) 3))
4.7b	(log (fma (expm1 z) y 1.0))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`cbrt-prod`
27×	`*-un-lft-identity`
22×	`add-cube-cbrt`
19×	`times-frac`
17×	`associate-l`
15×	`add-exp-log` `unpow-prod-down` `cube-prod` `unswap-sqr`
14×	`pow1`
13×	`associate-r`
8×	`add-cbrt-cube`
7×	`log-pow`
6×	`sqr-pow`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`cube-mult` `pow-unpow` `log-prod` `unpow3`
2×	`div-exp` `cbrt-unprod`
1×	`cbrt-undiv` `pow-to-exp` `rec-exp` `pow-pow` `pow1/3` `1-exp` `associate-r/` `rem-log-exp` `pow-prod-down` `pow-exp` `un-div-inv` `-commutative` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 130

Calls

4 calls:

18.0ms	(* (cbrt (pow (log (fma (expm1 z) y 1.0)) 3)) (/ 1 t))
2.0ms	(pow (log (fma (expm1 z) y 1.0)) 3)
2.0ms	(cbrt (pow (log (fma (expm1 z) y 1.0)) 3))
1.0ms	(log (fma (expm1 z) y 1.0))

series511.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(* (cbrt (pow (log (fma (expm1 z) y 1.0)) 3)) (/ 1 t))
189.0ms	(pow (log (fma (expm1 z) y 1.0)) 3)
83.0ms	(cbrt (pow (log (fma (expm1 z) y 1.0)) 3))
77.0ms	(log (fma (expm1 z) y 1.0))

simplify1.1s

Counts

142 → 142

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	295	2734
1	823	2156
2	3007	1955
done	5000	1954

prune482.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (log (fma (expm1 z) y 1.0)) t))
4.7b	(log (fma (expm1 z) y 1.0))
4.7b	(log (fma (expm1 z) y 1.0))
4.7b	(log (fma (expm1 z) y 1.0))

rewrite6.0ms

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:

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

series612.0ms

Counts

4 → 12

Calls

4 calls:

369.0ms	(cbrt (/ (log (fma (expm1 z) y 1.0)) t))
82.0ms	(log (fma (expm1 z) y 1.0))
85.0ms	(log (fma (expm1 z) y 1.0))
75.0ms	(log (fma (expm1 z) y 1.0))

simplify795.0ms

Counts

81 → 81

Iterations

Useful iterations: done (791.0ms)

Iter	Nodes	Cost
0	197	1445
1	459	1353
2	1427	1229
done	5000	1195

prune359.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.5b

regimes355.0ms

Accuracy

38.8% (4.3b remaining)

Error of 8.8b against oracle of 4.5b and baseline of 11.5b

bsearch218.0ms

Steps

Iters	Range		Point
10	5.595112303613655e-18	3.1829129060004216e-05	3.22238127471037e-17
6	8.075171960992006e-125	4.005351970408988e-124	1.8330086343134758e-124
6	-5.585633506564931e-38	-5.158362140144754e-39	-5.207348419951887e-38

simplify9.0ms

Iterations

Useful iterations: 2 (3.0ms)

Iter	Nodes	Cost
0	31	76
1	40	57
2	43	46
3	46	46
done	46	46

end0.0ms

sample3.3s

Algorithm

intervals

Results

822.0ms	1619×	body	10240	exit
786.0ms	1457×	body	1280	valid
448.0ms	1531×	body	640	valid
224.0ms	3529×	body	80	valid
167.0ms	928×	body	320	valid
106.0ms	83×	body	2560	valid
91.0ms	2516×	body	80	nan
61.0ms	298×	body	640	nan
58.0ms	504×	body	160	valid
38.0ms	129×	body	1280	nan
27.0ms	181×	body	320	nan
10.0ms	96×	body	160	nan