Details

sample178.0ms

Algorithm

intervals

Results

54.0ms	59×	body	10240	exit
38.0ms	61×	body	1280	valid
31.0ms	336×	body	80	valid
18.0ms	41×	body	640	valid
6.0ms	21×	body	320	valid
2.0ms	11×	body	160	valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 3 (70.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize32.0ms

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))))

rewrite416.0ms

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:

68.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
9.0ms	(exp (* (+ 1.0 eps) x))
19.0ms	(exp (* (- 1.0 eps) x))
315.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

series384.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
25.0ms	(exp (* (+ 1.0 eps) x))
24.0ms	(exp (* (- 1.0 eps) x))
271.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* (- 1.0 eps) x))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

simplify2.1s

Counts

99 → 99

Iterations

Useful iterations: 3 (850.0ms)

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

prune464.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 1 expressions with local error:

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

rewrite55.0ms

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:

54.0ms

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

series112.0ms

Counts

1 → 3

Calls

1 calls:

112.0ms

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

simplify2.2s

Counts

36 → 36

Iterations

Useful iterations: 2 (118.0ms)

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

prune117.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize27.0ms

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

rewrite426.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

58.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
13.0ms	(exp (* (+ 1.0 eps) x))
15.0ms	(exp (* x (- 1.0 eps)))
333.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* x (- 1.0 eps)))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

series457.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
33.0ms	(exp (* (+ 1.0 eps) x))
27.0ms	(exp (* x (- 1.0 eps)))
325.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (exp (* x (- 1.0 eps)))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

simplify2.1s

Counts

102 → 102

Iterations

Useful iterations: 3 (911.0ms)

Iter	Nodes	Cost
0	190	2197
1	435	2111
2	1025	1987
3	3338	1949
done	5002	1949

prune438.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite586.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

7.0ms	(exp (* x (- 1.0 eps)))
7.0ms	(exp (* x (- 1.0 eps)))
8.0ms	(exp (* x (- 1.0 eps)))
560.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (* (* (cbrt (exp (* x (- 1.0 eps)))) (cbrt (exp (* x (- 1.0 eps))))) (cbrt (exp (* x (- 1.0 eps)))))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

series341.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(exp (* x (- 1.0 eps)))
25.0ms	(exp (* x (- 1.0 eps)))
26.0ms	(exp (* x (- 1.0 eps)))
263.0ms	(- (/ (+ (/ 1.0 eps) 1.0) (* (* (cbrt (exp (* x (- 1.0 eps)))) (cbrt (exp (* x (- 1.0 eps))))) (cbrt (exp (* x (- 1.0 eps)))))) (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))))

simplify1.6s

Counts

71 → 71

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	105	1633
1	253	1598
2	686	1139
3	2385	1022
done	5001	1021

prune293.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.2b

regimes99.0ms

Accuracy

96.7% (0.5b remaining)

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

bsearch204.0ms

Steps

Iters	Range		Point
8	0.16004325332292868	3739.899882177282	31.670085078716635

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	44
1	35	44
done	35	44

end0.0ms

sample8.9s

Algorithm

intervals

Results

2.9s	1923×	body	10240	exit
1.9s	10075×	body	80	valid
1.8s	1764×	body	1280	valid
752.0ms	1291×	body	640	valid
516.0ms	324×	body	160	valid
310.0ms	650×	body	320	valid