Details

sample60.0ms

Algorithm

intervals

Results

22.0ms	69×	body	1280	valid
13.0ms	59×	body	640	valid
6.0ms	163×	body	80	valid
4.0ms	29×	body	320	valid
2.0ms	20×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.3b

localize10.0ms

Local error

Found 1 expressions with local error:

5.1b	(- (exp x) 1.0)

rewrite19.0ms

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×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 28

Calls

1 calls:

18.0ms

(- (exp x) 1.0)

series29.0ms

Counts

1 → 3

Calls

1 calls:

29.0ms

(- (exp x) 1.0)

simplify1.9s

Counts

31 → 31

Iterations

Iter	Nodes
done	5000
3	2110
2	428
1	149
0	66

prune112.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* x x) (fma 1/6 x 1/2) x)
0.1b	(fma 1/6 x 1/2)
2.3b	(/ (fma (* x x) (fma 1/6 x 1/2) x) x)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma (* x x) (fma 1/6 x 1/2) x)
0.0ms	(fma 1/6 x 1/2)
8.0ms	(/ (fma (* x x) (fma 1/6 x 1/2) x) x)

series159.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(fma (* x x) (fma 1/6 x 1/2) x)
42.0ms	(fma 1/6 x 1/2)
71.0ms	(/ (fma (* x x) (fma 1/6 x 1/2) x) x)

simplify2.2s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
3	3143
2	513
1	148
0	81

prune301.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (exp x) 3) (pow 1.0 3)) (fma (exp x) (+ 1.0 (exp x)) (* 1.0 1.0)))
0.0b	(+ 1.0 (exp x))
0.0b	(pow (exp x) 3)
5.0b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

234×	`add-sqr-sqrt`
166×	`*-un-lft-identity`
144×	`prod-diff`
138×	`unpow-prod-down` `cube-prod`
114×	`add-cube-cbrt`
80×	`difference-of-squares`
75×	`times-frac`
66×	`sqr-pow`
26×	`cube-mult` `unpow3`
25×	`associate-/l*` `distribute-lft-out--`
12×	`fma-neg`
8×	`add-log-exp`
7×	`add-cbrt-cube`
6×	`add-exp-log`
5×	`pow1` `difference-cubes`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u`
3×	`pow-unpow` `exp-prod` `associate-/r*` `fma-def`
2×	`flip3--` `flip--` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `pow-exp` `flip-+` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 357

Calls

4 calls:

130.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (fma (exp x) (+ 1.0 (exp x)) (* 1.0 1.0)))
7.0ms	(+ 1.0 (exp x))
4.0ms	(pow (exp x) 3)
48.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series235.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (fma (exp x) (+ 1.0 (exp x)) (* 1.0 1.0)))
9.0ms	(+ 1.0 (exp x))
38.0ms	(pow (exp x) 3)
72.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify2.3s

Counts

369 → 369

Iterations

Iter	Nodes
done	5000
2	3997
1	926
0	378

prune904.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes36.0ms

Accuracy

99.1% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.2b

bsearch61.0ms

Steps

Iters	Range		Point
10	-938.9819325385033	-1.6260248627107784e-07	-0.00015927208545311257

simplify5.0ms

Iterations

Iter	Nodes
done	22
1	22
0	21

end0.0ms

sample2.1s

Algorithm

intervals

Results

780.0ms	2291×	body	1280	valid
652.0ms	1661×	body	640	valid
224.0ms	5426×	body	80	valid
150.0ms	827×	body	320	valid
33.0ms	419×	body	160	valid