Details

sample38.0ms

Algorithm

intervals

Results

13.0ms	65×	body	1280	valid
8.0ms	62×	body	640	valid
4.0ms	182×	body	80	valid
3.0ms	33×	body	320	valid
1.0ms	12×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.8b	(- (exp x) 1.0)

rewrite35.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`associate-/r*` `fma-neg`
2×	`expm1-log1p-u` `pow1` `flip3--` `log1p-expm1-u` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

2 → 68

Calls

2 calls:

23.0ms	(/ (- (exp x) 1.0) x)
10.0ms	(- (exp x) 1.0)

series94.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(/ (- (exp x) 1.0) x)
20.0ms	(- (exp x) 1.0)

simplify733.0ms

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
2	1006
1	296
0	127

prune307.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

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

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

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

series116.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(fma x 1/2 (fma 1/6 (* x x) 1))
86.0ms	(fma 1/6 (* x x) 1)

simplify1.1s

Counts

26 → 26

Iterations

Iter	Nodes
done	5000
3	1360
2	200
1	54
0	33

prune189.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `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)

series88.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(fma x (fma 1/6 x 1/2) 1)
41.0ms	(fma 1/6 x 1/2)

simplify506.0ms

Counts

26 → 26

Iterations

Iter	Nodes
done	5001
3	764
2	170
1	57
0	33

prune486.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 3)
0.0b	(/ (- (pow (exp x) 3) (pow 1.0 3)) (* x (fma 1.0 (+ 1.0 (exp x)) (exp (+ x x)))))
0.0b	(* x (fma 1.0 (+ 1.0 (exp x)) (exp (+ x x))))
3.7b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite227.0ms

Algorithm

rewrite-expression-head

Rules

161×	`add-sqr-sqrt`
144×	`prod-diff`
117×	`*-un-lft-identity`
114×	`unpow-prod-down` `cube-prod`
87×	`add-cube-cbrt`
50×	`sqr-pow`
48×	`difference-of-squares`
26×	`cube-mult` `unpow3`
25×	`times-frac` `associate-/l*`
15×	`distribute-lft-out--`
12×	`add-cbrt-cube` `fma-neg`
11×	`add-exp-log`
7×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u`
3×	`difference-cubes` `pow-unpow` `exp-prod` `associate-r` `associate-l`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `cbrt-unprod` `fma-udef` `flip--` `associate-/l/`
1×	`distribute-rgt-in` `pow-to-exp` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `div-sub` `pow-prod-down` `pow-exp` `-commutative` `div-inv` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 312

Calls

4 calls:

4.0ms	(pow (exp x) 3)
130.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (* x (fma 1.0 (+ 1.0 (exp x)) (exp (+ x x)))))
10.0ms	(* x (fma 1.0 (+ 1.0 (exp x)) (exp (+ x x))))
59.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series418.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(pow (exp x) 3)
224.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (* x (fma 1.0 (+ 1.0 (exp x)) (exp (+ x x)))))
92.0ms	(* x (fma 1.0 (+ 1.0 (exp x)) (exp (+ x x))))
65.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify2.5s

Counts

324 → 324

Iterations

Iter	Nodes
done	5000
2	4203
1	869
0	341

prune960.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes55.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.2b

bsearch59.0ms

Steps

Iters	Range		Point
8	-0.00181011214377754	-1.6902992745682556e-06	-0.00016704963527402913

simplify4.0ms

Iterations

Iter	Nodes
done	33
1	33
0	28

end0.0ms

sample1.8s

Algorithm

intervals

Results

796.0ms	2317×	body	1280	valid
386.0ms	1622×	body	640	valid
223.0ms	5413×	body	80	valid
102.0ms	833×	body	320	valid
35.0ms	402×	body	160	valid