Details

sample32.0ms

Algorithm

intervals

Results

14.0ms	84×	body	1280	valid
4.0ms	198×	body	80	valid
4.0ms	37×	body	640	valid
1.0ms	24×	body	320	valid
1.0ms	14×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	6
1	11	6
2	18	6
3	27	6
4	51	6
5	109	6
6	270	6
7	751	6
8	2509	6
done	5000	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.4b	(- (exp (* a x)) 1.0)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
6×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

1.0ms	(exp (* a x))
5.0ms	(- (exp (* a x)) 1.0)

series52.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
40.0ms	(- (exp (* a x)) 1.0)

simplify1.2s

Counts

46 → 46

Iterations

Useful iterations: 3 (228.0ms)

Iter	Nodes	Cost
0	79	557
1	175	457
2	436	386
3	1572	346
done	5001	346

prune313.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(exp (* 2 (* x a)))
0.0b	(/ (- (exp (* 2 (* x a))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
3.4b	(- (exp (* 2 (* x a))) (* 1.0 1.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `times-frac`
10×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
3×	`fma-neg` `prod-diff`
2×	`exp-prod` `flip3--` `exp-to-pow` `associate-/r/` `flip--` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 88

Calls

4 calls:

1.0ms	(exp (* a x))
2.0ms	(exp (* 2 (* x a)))
17.0ms	(/ (- (exp (* 2 (* x a))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
6.0ms	(- (exp (* 2 (* x a))) (* 1.0 1.0))

series140.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(exp (* a x))
17.0ms	(exp (* 2 (* x a)))
64.0ms	(/ (- (exp (* 2 (* x a))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
46.0ms	(- (exp (* 2 (* x a))) (* 1.0 1.0))

simplify1.9s

Counts

100 → 100

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	149	1798
1	371	1730
2	1039	1598
3	4002	1545
done	5001	1541

prune293.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (fma 1.0 1.0 (exp (* x (* 2 a)))))
0.0b	(/ (/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (fma 1.0 1.0 (exp (* x (* 2 a))))) (+ (exp (* a x)) 1.0))
0.0b	(exp (* (* a x) 4))
3.4b	(- (exp (* (* a x) 4)) (pow 1.0 4))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

226×	`times-frac`
211×	`add-sqr-sqrt`
203×	`*-un-lft-identity`
111×	`add-cube-cbrt`
60×	`difference-of-squares`
32×	`associate-/l*`
29×	`unpow-prod-down`
26×	`distribute-lft-out`
23×	`sqr-pow`
21×	`prod-diff`
20×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`associate-/r*` `div-inv`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-neg` `div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `associate-/r/` `flip--`
1×	`sub-neg` `exp-prod` `exp-to-pow` `flip3-+` `diff-log` `flip-+` `rem-exp-log`

Counts

4 → 251

Calls

4 calls:

19.0ms	(/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (fma 1.0 1.0 (exp (* x (* 2 a)))))
26.0ms	(/ (/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (fma 1.0 1.0 (exp (* x (* 2 a))))) (+ (exp (* a x)) 1.0))
2.0ms	(exp (* (* a x) 4))
8.0ms	(- (exp (* (* a x) 4)) (pow 1.0 4))

series257.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (fma 1.0 1.0 (exp (* x (* 2 a)))))
113.0ms	(/ (/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (fma 1.0 1.0 (exp (* x (* 2 a))))) (+ (exp (* a x)) 1.0))
18.0ms	(exp (* (* a x) 4))
46.0ms	(- (exp (* (* a x) 4)) (pow 1.0 4))

simplify1.2s

Counts

263 → 263

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	398	10507
1	964	9937
2	2912	9520
done	5001	9502

prune979.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (* a x) 4))
0.0b	(exp (* (* a x) 4))
0.0b	(exp (* (* a x) 4))
3.3b	(- (* (exp (* (* a x) 4)) (exp (* (* a x) 4))) (* (pow 1.0 4) (pow 1.0 4)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u`
3×	`exp-prod` `exp-to-pow` `rem-exp-log`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--` `difference-of-squares`

Counts

4 → 53

Calls

4 calls:

2.0ms	(exp (* (* a x) 4))
2.0ms	(exp (* (* a x) 4))
2.0ms	(exp (* (* a x) 4))
7.0ms	(- (* (exp (* (* a x) 4)) (exp (* (* a x) 4))) (* (pow 1.0 4) (pow 1.0 4)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(exp (* (* a x) 4))
19.0ms	(exp (* (* a x) 4))
18.0ms	(exp (* (* a x) 4))
62.0ms	(- (* (exp (* (* a x) 4)) (exp (* (* a x) 4))) (* (pow 1.0 4) (pow 1.0 4)))

simplify1.6s

Counts

65 → 65

Iterations

Useful iterations: 3 (446.0ms)

Iter	Nodes	Cost
0	72	917
1	191	674
2	658	573
3	3057	561
done	5001	561

prune259.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.4b

regimes124.0ms

Accuracy

47.8% (12.1b remaining)

Error of 18.5b against oracle of 6.5b and baseline of 29.6b

bsearch249.0ms

Steps

Iters	Range		Point
11	1.2907170496906384e+102	4.530903372306731e+124	5.462278384153823e+102
5	2.2246589479599322e-154	7.158499548377816e-154	2.3441106150668665e-154
9	6.620541548345641e-269	6.927856295162215e-263	6.803818232128274e-263
8	-2.2623457567027846e+42	-3.641950481783047e+38	-1.1958856342471646e+42

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	71	194
1	88	194
done	88	194

end0.0ms

sample912.0ms

Algorithm

intervals

Results

426.0ms	2674×	body	1280	valid
134.0ms	1331×	body	640	valid
106.0ms	5485×	body	80	valid
51.0ms	717×	body	320	valid
19.0ms	431×	body	160	valid