Details

sample164.0ms

Algorithm

intervals

Results

63.0ms	61×	body	10240	exit
33.0ms	55×	body	1280	valid
25.0ms	325×	body	80	valid
13.0ms	38×	body	640	valid
5.0ms	21×	body	320	valid
2.0ms	12×	body	160	valid

simplify31.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b	(exp (* (- 1.0 eps) x))
0.0b	(exp (* (+ 1.0 eps) x))
3.9b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite389.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
94×	`times-frac`
81×	`add-sqr-sqrt`
26×	`distribute-lft-out--`
25×	`add-cube-cbrt`
17×	`difference-of-squares`
14×	`add-log-exp`
6×	`add-cbrt-cube` `distribute-lft-out` `associate-/l*`
5×	`add-exp-log`
4×	`pow1` `exp-to-pow`
3×	`div-sub` `associate-/r*` `div-inv`
2×	`exp-prod` `flip3--` `diff-log` `flip--` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `distribute-rgt-out--` `frac-2neg` `div-exp` `clear-num` `sum-log` `frac-sub` `sub-div` `associate--r-`

Counts

4 → 105

Calls

4 calls:

47.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
9.0ms	(exp (* (- 1.0 eps) x))
6.0ms	(exp (* (+ 1.0 eps) x))
321.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series293.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
23.0ms	(exp (* (- 1.0 eps) x))
21.0ms	(exp (* (+ 1.0 eps) x))
196.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify43.0ms

Counts: 117 → 117

prune372.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`associate-l`
6×	`add-exp-log`
4×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `unswap-sqr`
3×	`associate-r` `prod-exp` `add-cbrt-cube`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/` `unpow2` `sqr-pow`
1×	`pow1` `pow-to-exp` `flip3--` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `add-log-exp`

Counts

1 → 33

Calls

1 calls:

38.0ms

(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

series85.0ms

Counts

1 → 3

Calls

1 calls:

85.0ms

(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

simplify157.0ms

Counts: 36 → 36

prune72.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5))) (cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5))))
37.6b	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
37.6b	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
37.6b	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*r/`
18×	`cbrt-div`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`flip3--` `pow1/3` `flip--`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`frac-times` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `associate-*l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

57.0ms	(* (cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5))) (cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5))))
12.0ms	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
12.0ms	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
17.0ms	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))

series593.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(* (cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5))) (cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5))))
138.0ms	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
135.0ms	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
140.0ms	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))

simplify46.0ms

Counts: 84 → 84

prune314.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize23.0ms

Local error

Found 4 expressions with local error:

37.6b	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
37.6b	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
37.6b	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
37.6b	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

8×	`cbrt-div` `associate-*r/`
4×	`pow1` `add-exp-log` `cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `flip3--` `*-un-lft-identity` `pow1/3` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

13.0ms	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
12.0ms	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
18.0ms	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
13.0ms	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))

series573.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
145.0ms	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
140.0ms	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))
144.0ms	(cbrt (* (pow x 2) (- (* x 0.33333333333333337) 0.5)))

simplify86.0ms

Counts: 56 → 56

prune306.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

regimes85.0ms

Accuracy

90.7% (1.6b remaining)

Error of 2.0b against oracle of 0.4b and baseline of 17.2b

bsearch153.0ms

Steps

Iters	Range		Point
8	2.1318049287245128e-27	3.447572751372202e-23	3.375282683015706e-23

simplify1.0ms

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.6s	2007×	body	10240	exit
1.4s	10148×	body	80	valid
1.2s	1653×	body	1280	valid
662.0ms	1247×	body	640	valid
148.0ms	618×	body	320	valid
57.0ms	347×	body	160	valid