Details

sample32.0ms

Algorithm

intervals

Results

13.0ms	79×	body	1280	valid
6.0ms	57×	body	640	valid
3.0ms	181×	body	80	valid
1.0ms	20×	body	320	valid
1.0ms	14×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.8b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
4.1b	(- (exp x) 1.0)

rewrite42.0ms

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:

25.0ms	(/ (- (exp x) 1.0) x)
14.0ms	(- (exp x) 1.0)

series58.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (- (exp x) 1.0) x)
16.0ms	(- (exp x) 1.0)

simplify35.0ms

Counts

74 → 74

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	282	468
1	919	380
2	5001	377
done	5001	377

prune142.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.2b	(fma 1/6 (pow x 2) (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 (pow x 2) (fma 1/2 x 1))

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

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

simplify25.0ms

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	36	59
1	104	52
2	535	52
3	5002	52
done	5002	52

prune37.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

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)))) 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))))
4.1b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite272.0ms

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:

86.0ms	(/ (/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x)))) x)
5.0ms	(pow (exp x) 3)
92.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x))))
38.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series297.0ms

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)))) x)
23.0ms	(pow (exp x) 3)
93.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (fma 1.0 (+ (exp x) 1.0) (exp (+ x x))))
45.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify133.0ms

Counts

689 → 689

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1570	12187
1	5002	11358
done	5002	11358

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 3)
0.0b	(pow (exp x) 3)
0.0b	(* (pow (exp x) 3) (pow (exp x) 3))
4.0b	(- (* (pow (exp x) 3) (pow (exp x) 3)) (* (pow 1.0 3) (pow 1.0 3)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
32×	`unpow-prod-down` `cube-prod`
28×	`add-cube-cbrt` `*-un-lft-identity`
18×	`swap-sqr`
16×	`unswap-sqr`
14×	`sqr-pow`
12×	`associate-r` `associate-l`
10×	`add-exp-log`
9×	`prod-exp`
8×	`pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube`
6×	`pow1` `cube-mult` `pow-unpow` `exp-prod` `unpow3` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down`
2×	`rem-cube-cbrt`
1×	`difference-cubes` `pow2` `sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `difference-of-squares`

Counts

4 → 156

Calls

4 calls:

4.0ms	(pow (exp x) 3)
4.0ms	(pow (exp x) 3)
26.0ms	(* (pow (exp x) 3) (pow (exp x) 3))
22.0ms	(- (* (pow (exp x) 3) (pow (exp x) 3)) (* (pow 1.0 3) (pow 1.0 3)))

series134.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow (exp x) 3)
22.0ms	(pow (exp x) 3)
33.0ms	(* (pow (exp x) 3) (pow (exp x) 3))
53.0ms	(- (* (pow (exp x) 3) (pow (exp x) 3)) (* (pow 1.0 3) (pow 1.0 3)))

simplify72.0ms

Counts

168 → 168

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	348	827
1	1669	695
2	5002	621
done	5002	621

prune362.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes27.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 21.2b

bsearch37.0ms

Steps

Iters	Range		Point
10	-0.001391736753177052	-4.1211929036737376e-16	-9.202491378555593e-05

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample876.0ms

Algorithm

intervals

Results

366.0ms	2262×	body	1280	valid
172.0ms	1661×	body	640	valid
95.0ms	5474×	body	80	valid
56.0ms	888×	body	320	valid
16.0ms	395×	body	160	valid