Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	59×	body	1280	valid
4.0ms	40×	body	640	valid
4.0ms	126×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	12×	body	160	valid

simplify7.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
2.5b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

99×	`*-un-lft-identity`
52×	`times-frac`
45×	`add-sqr-sqrt`
23×	`add-cube-cbrt`
18×	`distribute-lft-out` `distribute-lft-out--`
9×	`associate-/r*` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`pow1`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 104

Calls

3 calls:

12.0ms	(/ x (+ x 1.0))
27.0ms	(/ (+ x 1.0) (- x 1.0))
111.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series217.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ x (+ x 1.0))
41.0ms	(/ (+ x 1.0) (- x 1.0))
138.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify38.0ms

Counts: 113 → 113

prune220.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (- x 1.0) (+ x 1.0))
0.0b	(/ 1 (/ (- x 1.0) (+ x 1.0)))
2.5b	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

211×	`times-frac`
209×	`*-un-lft-identity`
166×	`add-sqr-sqrt`
91×	`add-cube-cbrt`
34×	`associate-/r*`
31×	`distribute-lft-out` `difference-of-squares`
25×	`distribute-lft-out--`
19×	`add-exp-log`
13×	`associate-/r/` `add-cbrt-cube`
11×	`associate-/l*`
9×	`div-exp`
8×	`div-inv`
6×	`flip3-+` `flip-+` `add-log-exp`
5×	`pow1` `cbrt-undiv`
3×	`frac-2neg` `clear-num`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`sub-neg` `pow-flip` `diff-log` `div-sub` `frac-sub` `inv-pow`

Counts

4 → 234

Calls

4 calls:

12.0ms	(/ x (+ x 1.0))
27.0ms	(/ (- x 1.0) (+ x 1.0))
26.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
145.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

series255.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ x (+ x 1.0))
41.0ms	(/ (- x 1.0) (+ x 1.0))
40.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
139.0ms	(- (/ x (+ x 1.0)) (/ 1 (/ (- x 1.0) (+ x 1.0))))

simplify82.0ms

Counts: 246 → 246

prune328.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (/ x (+ x 1.0)))
0.0b	(/ 1 (/ (- x 1.0) (+ x 1.0)))
2.5b	(- (log (exp (/ x (+ x 1.0)))) (/ 1 (/ (- x 1.0) (+ x 1.0))))
2.5b	(log (exp (/ x (+ x 1.0))))

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

188×	`times-frac`
179×	`*-un-lft-identity`
135×	`add-sqr-sqrt`
89×	`add-cube-cbrt`
36×	`exp-prod`
26×	`associate-/r*` `distribute-lft-out`
21×	`log-pow` `difference-of-squares`
20×	`distribute-lft-out--`
15×	`add-exp-log`
13×	`associate-/r/`
9×	`add-cbrt-cube` `div-inv`
8×	`pow1`
7×	`div-exp`
6×	`log-prod` `flip3-+` `flip-+` `add-log-exp`
3×	`cbrt-undiv` `associate--l+` `associate-/l*`
2×	`rec-exp` `1-exp`
1×	`sub-neg` `flip3--` `pow-flip` `frac-2neg` `diff-log` `rem-log-exp` `clear-num` `flip--` `rem-exp-log` `inv-pow`

Counts

4 → 208

Calls

4 calls:

22.0ms	(exp (/ x (+ x 1.0)))
26.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
281.0ms	(- (log (exp (/ x (+ x 1.0)))) (/ 1 (/ (- x 1.0) (+ x 1.0))))
23.0ms	(log (exp (/ x (+ x 1.0))))

series274.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(exp (/ x (+ x 1.0)))
40.0ms	(/ 1 (/ (- x 1.0) (+ x 1.0)))
140.0ms	(- (log (exp (/ x (+ x 1.0)))) (/ 1 (/ (- x 1.0) (+ x 1.0))))
37.0ms	(log (exp (/ x (+ x 1.0))))

simplify71.0ms

Counts: 220 → 220

prune339.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (/ x (+ x 1.0)))
0.1b	(* (/ 1 (- x 1.0)) (+ x 1.0))
2.5b	(log (exp (/ x (+ x 1.0))))
6.6b	(- (log (exp (/ x (+ x 1.0)))) (* (/ 1 (- x 1.0)) (+ x 1.0)))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
45×	`add-sqr-sqrt`
41×	`times-frac`
36×	`exp-prod`
32×	`add-cube-cbrt`
21×	`associate-l`
19×	`log-pow`
13×	`add-exp-log`
9×	`add-cbrt-cube`
7×	`pow1` `distribute-lft-out`
6×	`log-prod` `associate-/r/` `add-log-exp`
4×	`flip3-+` `associate-r` `prod-exp` `flip-+`
3×	`associate--l+` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `flip3--` `distribute-lft-in` `associate-*r/` `div-exp` `flip--` `cbrt-unprod` `associate--r+`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `rem-log-exp` `pow-prod-down` `associate-l/` `-commutative` `rem-exp-log`

Counts

4 → 123

Calls

4 calls:

21.0ms	(exp (/ x (+ x 1.0)))
48.0ms	(* (/ 1 (- x 1.0)) (+ x 1.0))
24.0ms	(log (exp (/ x (+ x 1.0))))
183.0ms	(- (log (exp (/ x (+ x 1.0)))) (* (/ 1 (- x 1.0)) (+ x 1.0)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(exp (/ x (+ x 1.0)))
39.0ms	(* (/ 1 (- x 1.0)) (+ x 1.0))
38.0ms	(log (exp (/ x (+ x 1.0))))
138.0ms	(- (log (exp (/ x (+ x 1.0)))) (* (/ 1 (- x 1.0)) (+ x 1.0)))

simplify57.0ms

Counts: 135 → 135

prune286.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.2b

bsearch92.0ms

Steps

Iters	Range		Point
9	1.494961173861339	216094143.84427205	8787.971449491997
10	-33483115176747636.0	-8327.681910469391	-10838.209322692901

simplify1.0ms

end0.0ms

sample954.0ms

Algorithm

intervals

Results

300.0ms	1719×	body	1280	valid
247.0ms	1226×	body	640	valid
148.0ms	4116×	body	80	valid
85.0ms	645×	body	320	valid
17.0ms	294×	body	160	valid