Details

sample51.0ms

Algorithm

intervals

Results

20.0ms	86×	body	1280	valid
8.0ms	190×	body	80	valid
5.0ms	36×	body	640	valid
2.0ms	20×	body	320	valid
1.0ms	10×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	11	6
2	18	6
3	27	6
4	51	6
5	116	6
6	273	6
7	807	6
8	2954	6
done	5000	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.0b

localize6.0ms

Local error

Found 1 expressions with local error:

2.8b	(- (exp (* a x)) 1.0)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 28

Calls

1 calls:

30.0ms

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

series56.0ms

Counts

1 → 3

Calls

1 calls:

56.0ms

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

simplify4.0s

Counts

31 → 31

Iterations

Useful iterations: 4 (2.1s)

Iter	Nodes	Cost
0	72	472
1	164	384
2	369	313
3	1232	255
4	4654	245
done	5000	245

prune104.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (* a x)) 1.0)
0.0b	(/ (- (exp (* 2 (* a x))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
0.0b	(* 2 (* a x))
2.8b	(- (exp (* 2 (* a x))) (* 1.0 1.0))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
18×	`add-cube-cbrt`
16×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`add-log-exp`
6×	`distribute-lft-out` `difference-of-squares`
4×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
3×	`fma-def` `fma-neg` `associate-l` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-r` `clear-num` `sum-log` `*-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

23.0ms	(+ (exp (* a x)) 1.0)
91.0ms	(/ (- (exp (* 2 (* a x))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
17.0ms	(* 2 (* a x))
60.0ms	(- (exp (* 2 (* a x))) (* 1.0 1.0))

series209.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ (exp (* a x)) 1.0)
70.0ms	(/ (- (exp (* 2 (* a x))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
33.0ms	(* 2 (* a x))
84.0ms	(- (exp (* 2 (* a x))) (* 1.0 1.0))

simplify1.3s

Counts

113 → 113

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	172	1938
1	436	1878
2	1326	1705
done	5001	1643

prune461.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* a x) 0.5)
0.1b	(* (* a x) (+ 1.0 (* (* a x) 0.5)))
0.2b	(pow (* a x) 3)
14.8b	(fma (pow (* a x) 3) 0.16666666666666663 (* (* a x) (+ 1.0 (* (* a x) 0.5))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`pow-pow` `associate-r/` `associate-l` `pow-exp` `-commutative` `rem-cube-cbrt`
1×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `unpow-prod-down` `distribute-lft-in` `flip3-+` `unpow3` `cube-prod` `flip-+` `fma-udef` `sqr-pow`

Counts

4 → 78

Calls

4 calls:

20.0ms	(* (* a x) 0.5)
32.0ms	(* (* a x) (+ 1.0 (* (* a x) 0.5)))
6.0ms	(pow (* a x) 3)
0.0ms	(fma (pow (* a x) 3) 0.16666666666666663 (* (* a x) (+ 1.0 (* (* a x) 0.5))))

series349.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (* a x) 0.5)
85.0ms	(* (* a x) (+ 1.0 (* (* a x) 0.5)))
81.0ms	(pow (* a x) 3)
161.0ms	(fma (pow (* a x) 3) 0.16666666666666663 (* (* a x) (+ 1.0 (* (* a x) 0.5))))

simplify1.4s

Counts

90 → 90

Iterations

Useful iterations: 2 (369.0ms)

Iter	Nodes	Cost
0	123	1054
1	306	954
2	1581	803
done	5000	803

prune344.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* a x) 3)
0.2b	(pow (* x a) 2)
3.4b	(+ (* 1.0 (* a x)) (* 0.5 (pow (* x a) 2)))
14.8b	(fma (pow (* a x) 3) 0.16666666666666663 (+ (* 1.0 (* a x)) (* 0.5 (pow (* x a) 2))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log`
7×	`add-cbrt-cube`
6×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity` `add-log-exp`
4×	`expm1-log1p-u` `pow-pow` `pow-exp` `log1p-expm1-u`
2×	`pow-to-exp` `unpow-prod-down` `pow-prod-down` `prod-exp` `rem-cube-cbrt` `sqr-pow`
1×	`+-commutative` `cube-mult` `fma-def` `flip3-+` `unpow3` `cube-prod` `sum-log` `cbrt-unprod` `flip-+` `fma-udef` `unpow2`

Counts

4 → 68

Calls

4 calls:

7.0ms	(pow (* a x) 3)
13.0ms	(pow (* x a) 2)
36.0ms	(+ (* 1.0 (* a x)) (* 0.5 (pow (* x a) 2)))
1.0ms	(fma (pow (* a x) 3) 0.16666666666666663 (+ (* 1.0 (* a x)) (* 0.5 (pow (* x a) 2))))

series340.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow (* a x) 3)
44.0ms	(pow (* x a) 2)
95.0ms	(+ (* 1.0 (* a x)) (* 0.5 (pow (* x a) 2)))
139.0ms	(fma (pow (* a x) 3) 0.16666666666666663 (+ (* 1.0 (* a x)) (* 0.5 (pow (* x a) 2))))

simplify1.2s

Counts

80 → 80

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	106	976
1	250	846
2	1027	766
done	5000	733

prune260.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

regimes186.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.6b

bsearch1.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	51
1	36	51
done	36	51

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.2s	2727×	body	1280	valid
315.0ms	1276×	body	640	valid
260.0ms	5596×	body	80	valid
174.0ms	744×	body	320	valid
34.0ms	390×	body	160	valid