Details

sample187.0ms

Algorithm

intervals

Results

70.0ms	95×	body	1280	valid
58.0ms	88×	body	640	valid
23.0ms	274×	body	80	valid
16.0ms	48×	body	320	valid
3.0ms	17×	body	160	valid

simplify41.0ms

Counts

1 → 1

Iterations

Iter	Nodes
7	36
6	36
5	35
4	33
3	29
2	22
1	14
0	7

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.3b

localize18.0ms

Local error

Found 1 expressions with local error:

5.2b	(- (exp x) (exp (- x)))

rewrite22.0ms

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:

22.0ms

(- (exp x) (exp (- x)))

series52.0ms

Counts

1 → 3

Calls

1 calls:

52.0ms

(- (exp x) (exp (- x)))

simplify3.4s

Counts

31 → 31

Iterations

Iter	Nodes
4	3810
3	1113
2	405
1	168
0	73

prune271.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/3 (* x x) 2)
0.0b	(fma x (fma 1/3 (* x x) 2) (* (pow x 5) 1/60))
0.1b	(* (pow x 5) 1/60)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`add-exp-log`
7×	`associate-l`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`add-cbrt-cube`
4×	`unpow-prod-down`
3×	`expm1-log1p-u` `pow1` `associate-r` `prod-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 47

Calls

3 calls:

0.0ms	(fma 1/3 (* x x) 2)
0.0ms	(fma x (fma 1/3 (* x x) 2) (* (pow x 5) 1/60))
7.0ms	(* (pow x 5) 1/60)

series272.0ms

Counts

3 → 9

Calls

3 calls:

101.0ms	(fma 1/3 (* x x) 2)
84.0ms	(fma x (fma 1/3 (* x x) 2) (* (pow x 5) 1/60))
87.0ms	(* (pow x 5) 1/60)

simplify3.3s

Counts

56 → 56

Iterations

Iter	Nodes
4	6032
3	1392
2	417
1	169
0	83

prune609.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (fma x (fma 1/3 (* x x) 2) (* (pow x 5) 1/60))) (cbrt (fma x (fma 1/3 (* x x) 2) (* (pow x 5) 1/60))))
0.7b	(cbrt (fma x (fma 1/3 (* x x) 2) (* (pow x 5) 1/60)))
0.7b	(cbrt (fma x (fma 1/3 (* x x) 2) (* (pow x 5) 1/60)))
0.7b	(cbrt (fma x (fma 1/3 (* x x) 2) (* (pow x 5) 1/60)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
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:

6.0ms	(* (cbrt (fma x (fma 1/3 (* x x) 2) (* (pow x 5) 1/60))) (cbrt (fma x (fma 1/3 (* x x) 2) (* (pow x 5) 1/60))))
1.0ms	(cbrt (fma x (fma 1/3 (* x x) 2) (* (pow x 5) 1/60)))
1.0ms	(cbrt (fma x (fma 1/3 (* x x) 2) (* (pow x 5) 1/60)))
1.0ms	(cbrt (fma x (fma 1/3 (* x x) 2) (* (pow x 5) 1/60)))

series831.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(* (cbrt (fma x (fma 1/3 (* x x) 2) (* (pow x 5) 1/60))) (cbrt (fma x (fma 1/3 (* x x) 2) (* (pow x 5) 1/60))))
189.0ms	(cbrt (fma x (fma 1/3 (* x x) 2) (* (pow x 5) 1/60)))
214.0ms	(cbrt (fma x (fma 1/3 (* x x) 2) (* (pow x 5) 1/60)))
217.0ms	(cbrt (fma x (fma 1/3 (* x x) 2) (* (pow x 5) 1/60)))

simplify1.1s

Counts

93 → 93

Iterations

Iter	Nodes
3	2660
2	824
1	310
0	139

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (exp x))
0.0b	(sqrt (exp x))
5.2b	(fma (sqrt (exp x)) (sqrt (exp x)) (- (exp (- x))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`sqrt-pow1`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`exp-prod` `sqrt-prod`
5×	`pow1`
3×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `pow1/2`
1×	`fma-udef`

Counts

3 → 46

Calls

3 calls:

4.0ms	(sqrt (exp x))
5.0ms	(sqrt (exp x))
0.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) (- (exp (- x))))

series162.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(sqrt (exp x))
23.0ms	(sqrt (exp x))
124.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) (- (exp (- x))))

simplify1.4s

Counts

55 → 55

Iterations

Iter	Nodes
5	3512
4	988
3	439
2	198
1	103
0	61

prune506.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes44.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	12
1	12
0	11

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.6s	3370×	body	1280	valid
1.1s	2441×	body	640	valid
627.0ms	8370×	body	80	valid
408.0ms	1264×	body	320	valid
142.0ms	625×	body	160	valid