Details

sample36.0ms

Algorithm

intervals

Results

13.0ms	68×	body	1280	valid
6.0ms	47×	body	640	valid
4.0ms	178×	body	80	valid
2.0ms	29×	body	320	valid
1.0ms	10×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
2.6b	(- (exp x) 1.0)

rewrite58.0ms

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:

43.0ms	(/ (- (exp x) 1.0) x)
13.0ms	(- (exp x) 1.0)

series71.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ (- (exp x) 1.0) x)
16.0ms	(- (exp x) 1.0)

simplify2.1s

Counts

74 → 74

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	127	854
1	281	745
2	612	665
3	1785	619
done	5001	605

prune216.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite3.0ms

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:

1.0ms	(fma x (fma 1/6 x 1/2) 1)
1.0ms	(fma 1/6 x 1/2)

series80.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(fma x (fma 1/6 x 1/2) 1)
57.0ms	(fma 1/6 x 1/2)

simplify2.6s

Counts

26 → 26

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	33	213
1	53	204
2	114	176
3	381	175
4	1753	175
done	5001	175

prune71.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (fma x (fma 1/6 x 1/2) 1)) (cbrt (fma x (fma 1/6 x 1/2) 1)))
11.6b	(cbrt (fma x (fma 1/6 x 1/2) 1))
11.6b	(cbrt (fma x (fma 1/6 x 1/2) 1))
11.6b	(cbrt (fma x (fma 1/6 x 1/2) 1))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

11.0ms	(* (cbrt (fma x (fma 1/6 x 1/2) 1)) (cbrt (fma x (fma 1/6 x 1/2) 1)))
1.0ms	(cbrt (fma x (fma 1/6 x 1/2) 1))
1.0ms	(cbrt (fma x (fma 1/6 x 1/2) 1))
1.0ms	(cbrt (fma x (fma 1/6 x 1/2) 1))

series330.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (cbrt (fma x (fma 1/6 x 1/2) 1)) (cbrt (fma x (fma 1/6 x 1/2) 1)))
76.0ms	(cbrt (fma x (fma 1/6 x 1/2) 1))
84.0ms	(cbrt (fma x (fma 1/6 x 1/2) 1))
94.0ms	(cbrt (fma x (fma 1/6 x 1/2) 1))

simplify3.0s

Counts

93 → 93

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	108	1792
1	214	1668
2	502	1553
3	1149	1312
4	3065	1248
done	5000	1179

prune396.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x))))
0.0b	(pow (exp x) 3)
0.0b	(/ (/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x)))) x)
2.6b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite388.0ms

Algorithm

rewrite-expression-head

Rules

717×	`add-sqr-sqrt`
612×	`times-frac`
479×	`*-un-lft-identity`
309×	`add-cube-cbrt`
282×	`unpow-prod-down` `cube-prod`
272×	`difference-of-squares`
162×	`sqr-pow`
144×	`prod-diff`
104×	`associate-/l*`
85×	`distribute-lft-out--`
26×	`cube-mult` `unpow3`
17×	`difference-cubes`
12×	`fma-neg` `add-cbrt-cube`
11×	`add-exp-log`
6×	`associate-/r*` `div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `pow-pow` `div-exp` `log1p-expm1-u`
3×	`pow-unpow` `exp-prod` `div-sub` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`pow-to-exp` `sub-neg` `diff-log` `pow-exp` `rem-cube-cbrt`

Counts

4 → 677

Calls

4 calls:

141.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x))))
8.0ms	(pow (exp x) 3)
120.0ms	(/ (/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x)))) x)
43.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series403.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x))))
34.0ms	(pow (exp x) 3)
169.0ms	(/ (/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x)))) x)
64.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify3.0s

Counts

689 → 689

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	691	24819
1	1541	20801
2	4434	19635
done	5000	19634

prune1.8s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes43.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.3b

bsearch48.0ms

Steps

Iters	Range		Point
8	-0.1517943218839364	-1.6640733670284383e-05	-0.00013926054794957644

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	32
1	24	32
done	24	32

end0.0ms

sample1.3s

Algorithm

intervals

Results

541.0ms	2218×	body	1280	valid
262.0ms	1716×	body	640	valid
145.0ms	5418×	body	80	valid
81.0ms	823×	body	320	valid
25.0ms	397×	body	160	valid