Details

sample327.0ms

Algorithm

intervals

Results

103.0ms	94×	body	2560	valid
73.0ms	107×	body	1280	valid
68.0ms	68×	body	10240	exit
51.0ms	29×	body	640	valid
6.0ms	324×	pre	80	true
2.0ms	10×	body	320	valid
1.0ms	5×	body	160	valid
1.0ms	11×	body	80	valid

simplify90.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
2.6b	(- (exp (* a eps)) 1.0)
2.7b	(- (exp (* b eps)) 1.0)
4.3b	(- (exp (* (+ a b) eps)) 1.0)

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `flip3--` `*-un-lft-identity` `flip--` `add-log-exp`
8×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `frac-times` `add-cube-cbrt` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod`
3×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/` `associate-/l/`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 73

Calls

4 calls:

54.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
12.0ms	(- (exp (* a eps)) 1.0)
14.0ms	(- (exp (* b eps)) 1.0)
41.0ms	(- (exp (* (+ a b) eps)) 1.0)

series343.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
37.0ms	(- (exp (* a eps)) 1.0)
35.0ms	(- (exp (* b eps)) 1.0)
56.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify54.0ms

Counts: 85 → 85

prune354.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 19

Calls

1 calls:

23.0ms

(+ (/ 1 b) (/ 1 a))

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

(+ (/ 1 b) (/ 1 a))

simplify61.0ms

Counts: 22 → 22

prune55.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (/ 1 a)) a)
0.1b	(/ (/ 1 b) b)
4.3b	(+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b))
33.1b	(/ (+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

rewrite862.0ms

Algorithm

rewrite-expression-head

Rules

1240×	`times-frac`
1158×	`*-un-lft-identity`
577×	`add-sqr-sqrt`
241×	`add-cube-cbrt`
210×	`distribute-lft-out`
199×	`distribute-rgt-neg-in`
176×	`div-inv`
126×	`difference-of-squares`
98×	`distribute-lft-out--`
56×	`associate-/l*`
52×	`distribute-lft-neg-in`
25×	`associate-/r*`
17×	`add-exp-log`
13×	`add-cbrt-cube`
8×	`div-exp`
7×	`pow1`
6×	`add-log-exp`
5×	`cbrt-undiv` `associate-/l/`
4×	`neg-mul-1` `div-sub`
3×	`neg-sub0` `frac-2neg` `clear-num` `associate-/r/`
2×	`associate-+l-` `flip3-+` `frac-add` `flip-+` `pow-div`
1×	`+-commutative` `rec-exp` `flip3--` `pow-flip` `1-exp` `distribute-frac-neg` `sum-log` `frac-sub` `flip--` `distribute-neg-frac` `inv-pow`

Counts

4 → 533

Calls

4 calls:

17.0ms	(/ (- (/ 1 a)) a)
13.0ms	(/ (/ 1 b) b)
188.0ms	(+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b))
586.0ms	(/ (+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

series121.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (- (/ 1 a)) a)
17.0ms	(/ (/ 1 b) b)
33.0ms	(+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b))
43.0ms	(/ (+ (/ (- (/ 1 a)) a) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

simplify91.0ms

Counts: 545 → 545

prune702.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1 a))
0.6b	(cbrt (/ 1 a))
4.3b	(+ (* (/ (- (* (cbrt (/ 1 a)) (cbrt (/ 1 a)))) (* (cbrt a) (cbrt a))) (/ (cbrt (/ 1 a)) (cbrt a))) (/ (/ 1 b) b))
33.1b	(/ (+ (* (/ (- (* (cbrt (/ 1 a)) (cbrt (/ 1 a)))) (* (cbrt a) (cbrt a))) (/ (cbrt (/ 1 a)) (cbrt a))) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

147×	`times-frac`
146×	`add-sqr-sqrt`
114×	`*-un-lft-identity`
50×	`add-cube-cbrt`
36×	`difference-of-squares`
28×	`distribute-lft-out--`
26×	`cbrt-prod`
19×	`associate-/r*` `div-inv`
6×	`add-exp-log` `frac-add` `add-cbrt-cube` `add-log-exp`
5×	`associate-/l/`
4×	`pow1`
3×	`associate-/r/` `associate-/l*`
2×	`frac-times` `cbrt-div` `flip3-+` `pow1/3` `associate-r/` `associate-l/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `frac-sub` `flip--`

Counts

4 → 157

Calls

4 calls:

2.0ms	(cbrt (/ 1 a))
2.0ms	(cbrt (/ 1 a))
49.0ms	(+ (* (/ (- (* (cbrt (/ 1 a)) (cbrt (/ 1 a)))) (* (cbrt a) (cbrt a))) (/ (cbrt (/ 1 a)) (cbrt a))) (/ (/ 1 b) b))
189.0ms	(/ (+ (* (/ (- (* (cbrt (/ 1 a)) (cbrt (/ 1 a)))) (* (cbrt a) (cbrt a))) (/ (cbrt (/ 1 a)) (cbrt a))) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(cbrt (/ 1 a))
209.0ms	(cbrt (/ 1 a))
28.0ms	(+ (* (/ (- (* (cbrt (/ 1 a)) (cbrt (/ 1 a)))) (* (cbrt a) (cbrt a))) (/ (cbrt (/ 1 a)) (cbrt a))) (/ (/ 1 b) b))
44.0ms	(/ (+ (* (/ (- (* (cbrt (/ 1 a)) (cbrt (/ 1 a)))) (* (cbrt a) (cbrt a))) (/ (cbrt (/ 1 a)) (cbrt a))) (/ (/ 1 b) b)) (- (/ 1 b) (/ 1 a)))

simplify87.0ms

Counts: 169 → 169

prune433.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes107.0ms

Accuracy

0% (3.2b remaining)

Error of 3.5b against oracle of 0.3b and baseline of 3.5b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample11.3s

Algorithm

intervals

Results

4.0s	2598×	body	2560	valid
3.0s	3394×	body	1280	valid
2.9s	2009×	body	10240	exit
520.0ms	1058×	body	640	valid
293.0ms	10013×	pre	80	true
85.0ms	352×	body	320	valid
53.0ms	126×	body	160	valid
37.0ms	476×	body	80	valid