Details

sample273.0ms

Algorithm

intervals

Results

70.0ms	40×	body	10240	exit
57.0ms	56×	body	1280	valid
35.0ms	51×	body	640	valid
16.0ms	100×	body	80	valid
13.0ms	4×	body	2560	valid
12.0ms	26×	body	320	valid
8.0ms	78×	body	80	nan
6.0ms	19×	body	160	valid
4.0ms	11×	body	320	nan
3.0ms	6×	body	640	nan
1.0ms	3×	body	160	nan
1.0ms	1×	body	1280	nan

simplify6.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
12	4180
11	2096
10	1513
9	971
8	550
7	350
6	232
5	144
4	77
3	53
2	35
1	20
0	12

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.8b

localize32.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (log (fma (expm1 z) y 1.0)) t)
5.0b	(log (fma (expm1 z) y 1.0))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac` `add-cube-cbrt`
7×	`pow1`
5×	`add-exp-log` `log-pow`
4×	`add-cbrt-cube` `associate-/l*`
3×	`log-prod` `associate-/r*`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `rem-log-exp` `div-inv`

Counts

2 → 49

Calls

2 calls:

12.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
3.0ms	(log (fma (expm1 z) y 1.0))

series306.0ms

Counts

2 → 6

Calls

2 calls:

192.0ms	(/ (log (fma (expm1 z) y 1.0)) t)
114.0ms	(log (fma (expm1 z) y 1.0))

simplify2.5s

Counts

55 → 55

Iterations

Iter	Nodes
done	5002
3	2821
2	790
1	283
0	130

prune396.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b	(sqrt (fma (expm1 z) y 1.0))
0.5b	(sqrt (fma (expm1 z) y 1.0))
4.5b	(log (sqrt (fma (expm1 z) y 1.0)))
4.5b	(log (sqrt (fma (expm1 z) y 1.0)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `log-prod` `sqrt-prod`
10×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp`

Counts

4 → 72

Calls

4 calls:

2.0ms	(sqrt (fma (expm1 z) y 1.0))
2.0ms	(sqrt (fma (expm1 z) y 1.0))
3.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
4.0ms	(log (sqrt (fma (expm1 z) y 1.0)))

series833.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(sqrt (fma (expm1 z) y 1.0))
309.0ms	(sqrt (fma (expm1 z) y 1.0))
156.0ms	(log (sqrt (fma (expm1 z) y 1.0)))
224.0ms	(log (sqrt (fma (expm1 z) y 1.0)))

simplify2.9s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	2293
1	594
0	210

prune740.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

localize32.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
5.0b	(log (fma (expm1 z) y 1.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
13×	`associate-r`
12×	`*-un-lft-identity` `add-exp-log`
11×	`times-frac` `add-cube-cbrt`
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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `rec-exp` `1-exp` `rem-log-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

2 → 55

Calls

2 calls:

17.0ms	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
2.0ms	(log (fma (expm1 z) y 1.0))

series297.0ms

Counts

2 → 6

Calls

2 calls:

209.0ms	(* (log (fma (expm1 z) y 1.0)) (/ 1 t))
88.0ms	(log (fma (expm1 z) y 1.0))

simplify2.0s

Counts

61 → 61

Iterations

Iter	Nodes
done	5003
3	3331
2	1096
1	377
0	153

prune380.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize47.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fma (expm1 z) y 1.0))
0.6b	(cbrt (fma (expm1 z) y 1.0))
4.5b	(log (cbrt (fma (expm1 z) y 1.0)))
4.8b	(log (* (cbrt (fma (expm1 z) y 1.0)) (cbrt (fma (expm1 z) y 1.0))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1`
11×	`log-pow`
9×	`cbrt-prod` `pow1/3`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
7×	`log-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp`

Counts

4 → 69

Calls

4 calls:

1.0ms	(cbrt (fma (expm1 z) y 1.0))
1.0ms	(cbrt (fma (expm1 z) y 1.0))
2.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
8.0ms	(log (* (cbrt (fma (expm1 z) y 1.0)) (cbrt (fma (expm1 z) y 1.0))))

series713.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt (fma (expm1 z) y 1.0))
166.0ms	(cbrt (fma (expm1 z) y 1.0))
154.0ms	(log (cbrt (fma (expm1 z) y 1.0)))
207.0ms	(log (* (cbrt (fma (expm1 z) y 1.0)) (cbrt (fma (expm1 z) y 1.0))))

simplify2.7s

Counts

81 → 81

Iterations

Iter	Nodes
done	5010
2	1596
1	470
0	182

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

regimes608.0ms

Accuracy

48% (4.0b remaining)

Error of 7.5b against oracle of 3.5b and baseline of 11.2b

bsearch479.0ms

Steps

Iters	Range	Point
8	1.420916407840857e-121	1.7173713759258274e-118	1.5179641018211793e-121
5	9.841725025012944e-139	2.5397497498267892e-138	2.2704556920605612e-138
8	-3.0472952012619954e-45	-2.4918485500733093e-48	-8.129712844584067e-48

Iters

Range

Point

1.420916407840857e-121

1.7173713759258274e-118

1.5179641018211793e-121

9.841725025012944e-139

2.5397497498267892e-138

2.2704556920605612e-138

-3.0472952012619954e-45

-2.4918485500733093e-48

-8.129712844584067e-48

simplify25.0ms

Iterations

Iter	Nodes
done	49
3	49
2	46
1	43
0	34

end0.0ms

sample8.9s

Algorithm

intervals

Results

2.1s	1521×	body	10240	exit
1.8s	1496×	body	1280	valid
1.5s	1546×	body	640	valid
720.0ms	2568×	body	80	nan
610.0ms	3566×	body	80	valid
548.0ms	288×	body	640	nan
537.0ms	857×	body	320	valid
229.0ms	95×	body	2560	valid
143.0ms	465×	body	160	valid
82.0ms	203×	body	320	nan
76.0ms	98×	body	1280	nan
27.0ms	110×	body	160	nan