Details

sample36.0ms

Algorithm

intervals

Results

15.0ms	62×	body	1280	valid
7.0ms	62×	body	640	valid
4.0ms	183×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	12×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	5	6
1	10	6
2	13	6
3	15	6
done	15	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.6b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.0b	(- (exp x) 1.0)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

13.0ms	(/ (- (exp x) 1.0) x)
6.0ms	(- (exp x) 1.0)

series58.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- (exp x) 1.0) x)
14.0ms	(- (exp x) 1.0)

simplify1.5s

Counts

74 → 74

Iterations

Useful iterations: 3 (528.0ms)

Iter	Nodes	Cost
0	127	854
1	281	745
2	620	665
3	1996	637
done	5001	637

prune146.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 1/6 (* x x) (fma 1/2 x 1))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma 1/6 (* x x) (fma 1/2 x 1))

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

(fma 1/6 (* x x) (fma 1/2 x 1))

simplify2.5s

Counts

13 → 13

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	23	158
1	39	152
2	101	134
3	413	107
4	2831	107
done	5000	107

prune36.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma x (fma x 1/6 1/2) 1)
0.1b	(fma x 1/6 1/2)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma x (fma x 1/6 1/2) 1)
0.0ms	(fma x 1/6 1/2)

series52.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(fma x (fma x 1/6 1/2) 1)
31.0ms	(fma x 1/6 1/2)

simplify1.7s

Counts

26 → 26

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	34	213
1	54	204
2	115	176
3	353	175
4	1645	175
done	5001	175

prune59.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ (exp x) 1.0))
0.0b	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
0.0b	(* (exp x) (exp x))
3.9b	(- (* (exp x) (exp x)) (* 1.0 1.0))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
18×	`add-cube-cbrt` `exp-prod`
13×	`pow1` `add-cbrt-cube`
11×	`add-exp-log`
7×	`associate-r`
6×	`associate-l` `add-log-exp`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `times-frac` `associate-r/` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `associate-/l`
3×	`swap-sqr` `prod-exp` `cbrt-unprod` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `flip3-+` `div-exp` `associate-/r/` `*-commutative` `flip--` `flip-+` `associate-/l/` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `pow-plus` `fma-neg` `diff-log` `div-sub` `prod-diff` `clear-num` `associate-/r*` `div-inv` `distribute-lft-out`

Counts

4 → 108

Calls

4 calls:

14.0ms	(* x (+ (exp x) 1.0))
24.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
8.0ms	(* (exp x) (exp x))
7.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

series162.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* x (+ (exp x) 1.0))
83.0ms	(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
14.0ms	(* (exp x) (exp x))
29.0ms	(- (* (exp x) (exp x)) (* 1.0 1.0))

simplify813.0ms

Counts

120 → 120

Iterations

Useful iterations: 2 (278.0ms)

Iter	Nodes	Cost
0	171	1476
1	441	1302
2	1683	1139
done	5000	1139

prune248.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes16.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 22.0b

bsearch41.0ms

Steps

Iters	Range		Point
10	-3752817.331716861	-5.670122129476186e-07	-0.0001664903813288805

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	34
1	28	34
done	28	34

end0.0ms

sample928.0ms

Algorithm

intervals

Results

392.0ms	2216×	body	1280	valid
194.0ms	1666×	body	640	valid
114.0ms	5558×	body	80	valid
63.0ms	814×	body	320	valid
19.0ms	398×	body	160	valid