Details

sample81.0ms

Algorithm

intervals

Results

27.0ms	78×	body	1280	valid
20.0ms	83×	body	10240	exit
11.0ms	47×	body	640	valid
4.0ms	95×	body	80	valid
3.0ms	24×	body	320	valid
1.0ms	12×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	8
2	8
1	7
0	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.7b	(/ (exp x) (- (exp x) 1.0))
3.6b	(- (exp x) 1.0)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 67

Calls

2 calls:

15.0ms	(/ (exp x) (- (exp x) 1.0))
26.0ms	(- (exp x) 1.0)

series46.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(/ (exp x) (- (exp x) 1.0))
16.0ms	(- (exp x) 1.0)

simplify794.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	897
1	253
0	117

prune268.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (fma 1/12 x 1/2) (/ 1 x))
0.1b	(fma 1/12 x 1/2)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `fma-def` `add-cube-cbrt`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `fma-udef` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `sum-log` `flip3-+` `flip-+` `div-inv`

Counts

2 → 29

Calls

2 calls:

9.0ms	(+ (fma 1/12 x 1/2) (/ 1 x))
0.0ms	(fma 1/12 x 1/2)

series69.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(+ (fma 1/12 x 1/2) (/ 1 x))
44.0ms	(fma 1/12 x 1/2)

simplify2.7s

Counts

35 → 35

Iterations

Iter	Nodes
done	5000
3	3869
2	503
1	115
0	42

prune201.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (/ 1 x) (fma 1/12 x 1/2))
0.1b	(fma 1/12 x 1/2)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

13×	`fma-def`
12×	`*-un-lft-identity`
9×	`add-sqr-sqrt` `times-frac` `add-cube-cbrt`
4×	`add-log-exp`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `fma-udef` `log1p-expm1-u` `div-inv` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `sum-log` `flip3-+` `flip-+`

Counts

2 → 39

Calls

2 calls:

18.0ms	(+ (/ 1 x) (fma 1/12 x 1/2))
0.0ms	(fma 1/12 x 1/2)

series74.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ (/ 1 x) (fma 1/12 x 1/2))
47.0ms	(fma 1/12 x 1/2)

simplify4.1s

Counts

45 → 45

Iterations

Iter	Nodes
done	5000
3	4920
2	504
1	116
0	42

prune208.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (exp x))
0.6b	(/ (- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0)) (fma 1.0 (+ 1.0 (exp x)) (* (exp x) (exp x))))
0.7b	(/ (exp x) (/ (- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0)) (fma 1.0 (+ 1.0 (exp x)) (* (exp x) (exp x)))))
3.8b	(- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
68×	`add-sqr-sqrt`
66×	`*-un-lft-identity` `add-cube-cbrt`
18×	`exp-prod`
16×	`associate-/r*`
13×	`add-cbrt-cube`
11×	`pow1`
9×	`add-exp-log`
6×	`div-inv` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `fma-neg` `div-exp` `prod-diff` `pow-prod-down` `pow-sqr` `pow-prod-up` `log1p-expm1-u`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`clear-num` `frac-2neg` `flip3--` `exp-sum` `fma-udef` `flip--` `associate-/l/`
1×	`pow2` `sub-neg` `pow-plus` `diff-log` `div-sub` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 162

Calls

4 calls:

24.0ms	(* (exp x) (exp x))
27.0ms	(/ (- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0)) (fma 1.0 (+ 1.0 (exp x)) (* (exp x) (exp x))))
29.0ms	(/ (exp x) (/ (- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0)) (fma 1.0 (+ 1.0 (exp x)) (* (exp x) (exp x)))))
20.0ms	(- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0))

series346.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (exp x) (exp x))
119.0ms	(/ (- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0)) (fma 1.0 (+ 1.0 (exp x)) (* (exp x) (exp x))))
165.0ms	(/ (exp x) (/ (- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0)) (fma 1.0 (+ 1.0 (exp x)) (* (exp x) (exp x)))))
38.0ms	(- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0))

simplify1.1s

Counts

174 → 174

Iterations

Iter	Nodes
done	5000
1	713
0	268

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

regimes72.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 20.6b

bsearch48.0ms

Steps

Iters	Range		Point
9	-0.042530208599811804	-3.2052418334402957e-07	-0.0014245372640456257

simplify11.0ms

Iterations

Iter	Nodes
done	32
1	32
0	26

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	2275×	body	1280	valid
697.0ms	2578×	body	10240	exit
348.0ms	1674×	body	640	valid
101.0ms	857×	body	320	valid
91.0ms	2759×	body	80	valid
33.0ms	435×	body	160	valid