Details

sample276.0ms

Algorithm

intervals

Results

87.0ms	336×	body	80	valid
58.0ms	61×	body	1280	valid
54.0ms	59×	body	10240	exit
30.0ms	41×	body	640	valid
8.0ms	21×	body	320	valid
3.0ms	11×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	19	29
1	46	29
2	122	29
3	335	27
4	933	27
5	4084	27
done	5000	27

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b	(exp (* (+ 1.0 eps) x))
0.0b	(exp (* (- 1.0 eps) x))
2.9b	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

rewrite336.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
34×	`times-frac`
15×	`add-cube-cbrt`
14×	`add-log-exp`
12×	`difference-of-squares`
11×	`distribute-lft-out--`
6×	`add-cbrt-cube` `associate-/l*`
5×	`add-exp-log`
4×	`pow1` `exp-to-pow`
3×	`associate-/r*`
2×	`exp-prod` `flip3--` `diff-log` `div-sub` `flip--` `rem-exp-log` `associate-/l/` `distribute-lft-out`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `div-exp` `clear-num` `sum-log` `frac-sub` `div-inv` `associate--r-`

Counts

4 → 87

Calls

4 calls:

48.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
6.0ms	(exp (* (+ 1.0 eps) x))
9.0ms	(exp (* (- 1.0 eps) x))
269.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

series367.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
27.0ms	(exp (* (+ 1.0 eps) x))
22.0ms	(exp (* (- 1.0 eps) x))
269.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

simplify1.9s

Counts

99 → 99

Iterations

Useful iterations: 3 (711.0ms)

Iter	Nodes	Cost
0	182	2161
1	424	2075
2	1007	1949
3	3401	1913
done	5001	1913

prune418.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 1 expressions with local error:

0.0b	(* (pow x 2) (- (* x 0.6666666666666667) 1.0))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`associate-l`
6×	`add-exp-log`
4×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `unswap-sqr`
3×	`associate-r` `prod-exp` `add-cbrt-cube`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/` `unpow2` `sqr-pow`
1×	`pow1` `pow-to-exp` `flip3--` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

66.0ms

(* (pow x 2) (- (* x 0.6666666666666667) 1.0))

series119.0ms

Counts

1 → 3

Calls

1 calls:

119.0ms

(* (pow x 2) (- (* x 0.6666666666666667) 1.0))

simplify1.7s

Counts

36 → 36

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	69	467
1	161	440
2	543	385
3	2157	385
done	5001	385

prune74.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (+ 1.0 eps) x))
0.0b	(exp (* (+ 1.0 eps) x))
0.0b	(exp (* (- 1.0 eps) x))
2.9b	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x))))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
18×	`add-log-exp`
15×	`*-un-lft-identity`
13×	`times-frac`
6×	`exp-to-pow` `difference-of-squares`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`exp-prod` `rem-exp-log` `distribute-lft-out--`
2×	`diff-log` `sum-log`
1×	`sub-neg` `flip3--` `frac-sub` `flip--` `distribute-lft-out`

Counts

4 → 55

Calls

4 calls:

7.0ms	(exp (* (+ 1.0 eps) x))
6.0ms	(exp (* (+ 1.0 eps) x))
12.0ms	(exp (* (- 1.0 eps) x))
203.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x))))

series245.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(exp (* (+ 1.0 eps) x))
35.0ms	(exp (* (+ 1.0 eps) x))
39.0ms	(exp (* (- 1.0 eps) x))
149.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (/ 1.0 eps) (exp (* (+ 1.0 eps) x))))

simplify1.5s

Counts

67 → 67

Iterations

Useful iterations: 3 (539.0ms)

Iter	Nodes	Cost
0	107	1246
1	247	1212
2	584	1121
3	2284	1094
done	5000	1094

prune322.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (- 1.0 eps) x))
0.0b	(exp (* (- 1.0 eps) x))
0.0b	(exp (* (- 1.0 eps) x))
4.6b	(- (/ (+ (/ 1.0 eps) 1.0) (* (* (cbrt (exp (* (- 1.0 eps) x))) (cbrt (exp (* (- 1.0 eps) x)))) (cbrt (exp (* (- 1.0 eps) x))))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

rewrite536.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-log-exp`
9×	`add-sqr-sqrt`
6×	`exp-to-pow` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `diff-log` `add-cbrt-cube`
3×	`exp-prod` `rem-exp-log`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `times-frac` `div-sub` `frac-sub` `flip--` `distribute-lft-out--` `associate--r-`

Counts

4 → 50

Calls

4 calls:

9.0ms	(exp (* (- 1.0 eps) x))
9.0ms	(exp (* (- 1.0 eps) x))
9.0ms	(exp (* (- 1.0 eps) x))
508.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (* (* (cbrt (exp (* (- 1.0 eps) x))) (cbrt (exp (* (- 1.0 eps) x)))) (cbrt (exp (* (- 1.0 eps) x))))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

series348.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(exp (* (- 1.0 eps) x))
40.0ms	(exp (* (- 1.0 eps) x))
26.0ms	(exp (* (- 1.0 eps) x))
247.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (* (* (cbrt (exp (* (- 1.0 eps) x))) (cbrt (exp (* (- 1.0 eps) x)))) (cbrt (exp (* (- 1.0 eps) x))))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

simplify1.5s

Counts

62 → 62

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	98	1525
1	243	1490
2	662	1025
3	2386	914
done	5002	913

prune382.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.2b

regimes69.0ms

Accuracy

96.7% (0.5b remaining)

Error of 0.9b against oracle of 0.3b and baseline of 16.4b

bsearch237.0ms

Steps

Iters	Range		Point
8	0.16004325332292868	3739.899882177282	31.670085078716635

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	61
1	39	61
done	39	61

end0.0ms

sample9.2s

Algorithm

intervals

Results

2.3s	1923×	body	10240	exit
2.1s	1291×	body	640	valid
2.0s	10075×	body	80	valid
1.9s	1764×	body	1280	valid
284.0ms	650×	body	320	valid
77.0ms	324×	body	160	valid