Details

sample55.0ms

Algorithm

intervals

Results

15.0ms	64×	body	1280	valid
12.0ms	73×	body	10240	exit
10.0ms	57×	body	640	valid
3.0ms	98×	body	80	valid
3.0ms	25×	body	320	valid
1.0ms	12×	body	160	valid

simplify17.0ms

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: 39.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
3.6b	(- (exp x) 1.0)

rewrite45.0ms

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:

25.0ms	(/ (exp x) (- (exp x) 1.0))
17.0ms	(- (exp x) 1.0)

series74.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(/ (exp x) (- (exp x) 1.0))
26.0ms	(- (exp x) 1.0)

simplify822.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	897
1	253
0	117

prune228.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (* x x) 1/2 x)
0.0b	(/ (exp x) (fma (* x (* x x)) 1/6 (fma (* x x) 1/2 x)))
0.1b	(* x (* x x))
10.3b	(fma (* x (* x x)) 1/6 (fma (* x x) 1/2 x))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
14×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube`
10×	`add-exp-log`
9×	`times-frac`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l`
2×	`fma-udef`
1×	`pow2` `cbrt-undiv` `clear-num` `frac-2neg` `pow-plus` `cube-unmult` `div-exp` `associate-r` `pow-sqr` `*-commutative` `div-inv` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

0.0ms	(fma (* x x) 1/2 x)
6.0ms	(/ (exp x) (fma (* x (* x x)) 1/6 (fma (* x x) 1/2 x)))
16.0ms	(* x (* x x))
1.0ms	(fma (* x (* x x)) 1/6 (fma (* x x) 1/2 x))

series199.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(fma (* x x) 1/2 x)
56.0ms	(/ (exp x) (fma (* x (* x x)) 1/6 (fma (* x x) 1/2 x)))
46.0ms	(* x (* x x))
37.0ms	(fma (* x (* x x)) 1/6 (fma (* x x) 1/2 x))

simplify1.3s

Counts

87 → 87

Iterations

Iter	Nodes
done	5001
2	1544
1	281
0	128

prune475.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite19.0ms

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` `log1p-expm1-u` `div-inv` `distribute-lft-out`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `fma-udef`

Counts

2 → 38

Calls

2 calls:

18.0ms	(+ (/ 1 x) 1/2)
1.0ms	(fma 1/12 x (+ (/ 1 x) 1/2))

series34.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(+ (/ 1 x) 1/2)
17.0ms	(fma 1/12 x (+ (/ 1 x) 1/2))

simplify1.9s

Counts

44 → 44

Iterations

Iter	Nodes
done	5000
3	2833
2	398
1	106
0	41

prune185.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (exp x))
0.2b	(/ (- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0)) (fma 1.0 (+ 1.0 (exp x)) (* (exp x) (exp x))))
0.3b	(/ (exp x) (/ (- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0)) (fma 1.0 (+ 1.0 (exp x)) (* (exp x) (exp x)))))
3.6b	(- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0))

rewrite87.0ms

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:

28.0ms	(* (exp x) (exp x))
26.0ms	(/ (- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0)) (fma 1.0 (+ 1.0 (exp x)) (* (exp x) (exp x))))
17.0ms	(/ (exp x) (/ (- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0)) (fma 1.0 (+ 1.0 (exp x)) (* (exp x) (exp x)))))
10.0ms	(- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0))

series341.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (exp x) (exp x))
134.0ms	(/ (- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0)) (fma 1.0 (+ 1.0 (exp x)) (* (exp x) (exp x))))
155.0ms	(/ (exp x) (/ (- (exp (fma 2 x x)) (* (* 1.0 1.0) 1.0)) (fma 1.0 (+ 1.0 (exp x)) (* (exp x) (exp x)))))
28.0ms	(- (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 (2 fresh and 2 done)

Merged error: 0.2b

regimes58.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 11.3b

bsearch55.0ms

Steps

Iters	Range		Point
10	-14746478108.679678	-0.00028809610572707044	-0.001088340742756658

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	26

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.0s	2532×	body	10240	exit
713.0ms	2220×	body	1280	valid
381.0ms	1665×	body	640	valid
144.0ms	820×	body	320	valid
98.0ms	2870×	body	80	valid
33.0ms	428×	body	160	valid