Details

sample117.0ms

Algorithm

intervals

Results

34.0ms	96×	body	10240	exit
25.0ms	64×	body	1280	valid
17.0ms	61×	body	640	valid
6.0ms	104×	body	80	valid
4.0ms	16×	body	320	valid
1.0ms	11×	body	160	valid

simplify94.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
2	8
1	7
0	5

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize21.0ms

Local error

Found 2 expressions with local error:

0.7b	(/ (exp x) (- (exp x) 1.0))
3.2b	(- (exp x) 1.0)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 51

Calls

2 calls:

35.0ms	(/ (exp x) (- (exp x) 1.0))
33.0ms	(- (exp x) 1.0)

series304.0ms

Counts

2 → 6

Calls

2 calls:

263.0ms	(/ (exp x) (- (exp x) 1.0))
39.0ms	(- (exp x) 1.0)

simplify5.3s

Counts

57 → 57

Iterations

Iter	Nodes
done	5005
3	1509
2	540
1	191
0	91

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize72.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 1/12 x) (/ 1 x))
0.3b	(* 1/12 x)

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`+-commutative` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 29

Calls

2 calls:

35.0ms	(+ (* 1/12 x) (/ 1 x))
54.0ms	(* 1/12 x)

series561.0ms

Counts

2 → 6

Calls

2 calls:

425.0ms	(+ (* 1/12 x) (/ 1 x))
119.0ms	(* 1/12 x)

simplify11.4s

Counts

35 → 35

Iterations

Iter	Nodes
done	5000
3	1330
2	382
1	135
0	51

prune313.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize51.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

29.0ms	(* (cbrt x) (cbrt x))
2.0ms	(cbrt x)
2.0ms	(cbrt x)
2.0ms	(cbrt x)

series2.9s

Counts

4 → 12

Calls

4 calls:

866.0ms	(* (cbrt x) (cbrt x))
770.0ms	(cbrt x)
479.0ms	(cbrt x)
799.0ms	(cbrt x)

simplify19.3s

Counts

85 → 85

Iterations

Iter	Nodes
done	5002
4	3625
3	1001
2	372
1	137
0	61

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 1/12 (pow (* x x) 1/3)) (cbrt x))
0.4b	(* 1/12 (pow (* x x) 1/3))
0.6b	(cbrt x)
30.8b	(pow (* x x) 1/3)

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log`
16×	`prod-exp`
14×	`pow1` `add-sqr-sqrt`
11×	`associate-r` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-unprod`
6×	`cbrt-prod` `pow-pow` `pow-exp`
4×	`associate-l` `add-log-exp`
3×	`pow-to-exp` `unpow-prod-down` `pow-unpow` `unpow1/3` `unswap-sqr` `sqr-pow`
2×	`pow-prod-down` `*-commutative`
1×	`pow2` `pow-plus` `pow1/3` `pow-sqr` `pow-prod-up`

Counts

4 → 82

Calls

4 calls:

195.0ms	(* (* 1/12 (pow (* x x) 1/3)) (cbrt x))
36.0ms	(* 1/12 (pow (* x x) 1/3))
2.0ms	(cbrt x)
26.0ms	(pow (* x x) 1/3)

series2.8s

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (* 1/12 (pow (* x x) 1/3)) (cbrt x))
839.0ms	(* 1/12 (pow (* x x) 1/3))
1.0s	(cbrt x)
875.0ms	(pow (* x x) 1/3)

simplify9.5s

Counts

94 → 94

Iterations

Iter	Nodes
done	5002
3	2367
2	840
1	291
0	117

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

regimes68.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 21.5b

bsearch221.0ms

Steps

Iters	Range		Point
9	-1.440408271564231	-1.963203309137196e-05	-0.0015746675324234964

simplify95.0ms

Iterations

Iter	Nodes
done	45
1	45
0	33

end0.0ms

sample15.3s

Algorithm

intervals

Results

6.3s	2605×	body	10240	exit
2.8s	2844×	body	80	valid
2.4s	2280×	body	1280	valid
2.0s	840×	body	320	valid
1.2s	1590×	body	640	valid
90.0ms	447×	body	160	valid