Details

sample224.0ms

Algorithm

intervals

Results

69.0ms	49×	body	640	valid
43.0ms	60×	body	1280	valid
43.0ms	58×	body	10240	exit
33.0ms	323×	body	80	valid
5.0ms	19×	body	320	valid
2.0ms	11×	body	160	valid

simplify29.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (+ 1.0 eps) x))
0.0b	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
0.0b	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
2.2b	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

rewrite498.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity`
106×	`times-frac`
90×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
26×	`distribute-lft-out--`
17×	`difference-of-squares`
10×	`distribute-lft-out` `associate-/l*` `add-log-exp`
8×	`add-cbrt-cube`
6×	`add-exp-log` `associate-/r*`
4×	`pow1` `div-inv` `associate-/l/`
3×	`div-sub`
2×	`cbrt-undiv` `flip3--` `exp-to-pow` `frac-2neg` `div-exp` `clear-num` `flip--`
1×	`sub-neg` `exp-prod` `distribute-rgt-out--` `flip3-+` `diff-log` `sum-log` `frac-sub` `flip-+` `rem-exp-log` `sub-div` `associate--r-`

Counts

4 → 127

Calls

4 calls:

7.0ms	(exp (* (+ 1.0 eps) x))
48.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
42.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
395.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

series450.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(exp (* (+ 1.0 eps) x))
88.0ms	(/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x)))
60.0ms	(/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x)))
278.0ms	(- (/ (/ (+ 1.0 (/ 1.0 eps)) (exp (* (- 1.0 eps) x))) 2.0) (/ (/ (- (/ 1.0 eps) 1.0) (exp (* (+ 1.0 eps) x))) 2.0))

simplify69.0ms

Counts: 139 → 139

prune548.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize8.0ms

Local error

Found 1 expressions with local error:

0.1b	(* (pow x 2) (- (* x 0.33333333333333337) 0.5))

rewrite69.0ms

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:

68.0ms

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

series103.0ms

Counts

1 → 3

Calls

1 calls:

103.0ms

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

simplify87.0ms

Counts: 36 → 36

prune90.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (cbrt x) 2)
0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt x)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `unpow2` `sqr-pow`

Counts

4 → 55

Calls

4 calls:

3.0ms	(pow (cbrt x) 2)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series999.0ms

Counts

4 → 12

Calls

4 calls:

311.0ms	(pow (cbrt x) 2)
247.0ms	(cbrt x)
196.0ms	(cbrt x)
245.0ms	(cbrt x)

simplify33.0ms

Counts: 67 → 67

prune296.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt x)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

2.0ms	(cbrt x)
2.0ms	(cbrt x)
2.0ms	(cbrt x)
2.0ms	(cbrt x)

series1.2s

Counts

4 → 12

Calls

4 calls:

269.0ms	(cbrt x)
274.0ms	(cbrt x)
323.0ms	(cbrt x)
287.0ms	(cbrt x)

simplify60.0ms

Counts: 56 → 56

prune358.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

regimes90.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.9b

bsearch253.0ms

Steps

Iters	Range		Point
10	0.020866843422312147	2505339872.7713137	13.353249535540975

simplify31.0ms

end0.0ms

sample8.7s

Algorithm

intervals

Results

2.6s	1972×	body	10240	exit
2.4s	1744×	body	1280	valid
1.9s	10189×	body	80	valid
738.0ms	1273×	body	640	valid
279.0ms	603×	body	320	valid
67.0ms	316×	body	160	valid