Details

sample161.0ms

Algorithm

intervals

Results

82.0ms	108×	body	1280	valid
35.0ms	68×	body	640	valid
21.0ms	12×	body	2560	valid
6.0ms	21×	body	320	valid
4.0ms	40×	body	80	valid
2.0ms	7×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
2.5b	(tan (+ x eps))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

4×	`tan-quot` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `tan-sum` `frac-sub` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 25

Calls

2 calls:

16.0ms	(- (tan (+ x eps)) (tan x))
6.0ms	(tan (+ x eps))

series157.0ms

Counts

2 → 6

Calls

2 calls:

96.0ms	(- (tan (+ x eps)) (tan x))
61.0ms	(tan (+ x eps))

simplify1.6s

Counts

31 → 31

Iterations

Useful iterations: 4 (239.0ms)

Iter	Nodes	Cost
0	68	367
1	135	355
2	278	341
3	528	337
4	1109	335
5	2471	335
done	5000	335

prune90.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
2.7b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`tan-quot`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`flip3--` `flip3-+` `frac-add` `associate-/r/` `flip--` `flip-+` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

27.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
8.0ms	(+ (tan x) (tan eps))
16.0ms	(* (tan x) (tan eps))
76.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series795.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
96.0ms	(+ (tan x) (tan eps))
96.0ms	(* (tan x) (tan eps))
380.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.8s

Counts

98 → 98

Iterations

Useful iterations: 3 (618.0ms)

Iter	Nodes	Cost
0	172	1724
1	397	1649
2	1095	1579
3	2939	1563
done	5000	1563

prune281.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 13.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.2b	(/ (sin eps) (cos eps))
0.2b	(* (tan x) (tan eps))
6.1b	(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
19×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
5×	`tan-quot`
3×	`associate-r` `associate-l`
2×	`cbrt-undiv` `quot-tan` `frac-2neg` `div-exp` `clear-num` `div-inv` `difference-of-squares`
1×	`frac-times` `sub-neg` `flip3--` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `*-commutative` `frac-sub` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

8.0ms	(/ (sin x) (cos x))
8.0ms	(/ (sin eps) (cos eps))
14.0ms	(* (tan x) (tan eps))
260.0ms	(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (* (tan x) (tan eps)))) (tan x))

series531.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (sin x) (cos x))
20.0ms	(/ (sin eps) (cos eps))
95.0ms	(* (tan x) (tan eps))
397.0ms	(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.2s

Counts

105 → 105

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	205	1462
1	412	1433
2	1038	1331
3	2326	1312
done	5001	1310

prune433.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (cos eps))
0.2b	(* (sin x) (/ 1 (cos x)))
0.2b	(* (tan x) (tan eps))
8.5b	(- (/ (+ (/ (sin eps) (cos eps)) (* (sin x) (/ 1 (cos x)))) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
22×	`add-cube-cbrt`
21×	`times-frac`
17×	`add-exp-log`
16×	`associate-r`
13×	`add-cbrt-cube`
8×	`pow1`
6×	`associate-l` `add-log-exp`
5×	`tan-quot` `prod-exp`
4×	`unswap-sqr`
3×	`div-exp` `associate-/r` `cbrt-unprod` `associate-/l`
2×	`cbrt-undiv` `associate-r/` `pow-prod-down` `-commutative` `div-inv` `difference-of-squares`
1×	`frac-times` `sub-neg` `rec-exp` `quot-tan` `flip3--` `frac-2neg` `diff-log` `1-exp` `associate-*l/` `clear-num` `un-div-inv` `frac-sub` `flip--` `distribute-lft-out--`

Counts

4 → 101

Calls

4 calls:

8.0ms	(/ (sin eps) (cos eps))
18.0ms	(* (sin x) (/ 1 (cos x)))
15.0ms	(* (tan x) (tan eps))
153.0ms	(- (/ (+ (/ (sin eps) (cos eps)) (* (sin x) (/ 1 (cos x)))) (- 1 (* (tan x) (tan eps)))) (tan x))

series534.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (sin eps) (cos eps))
19.0ms	(* (sin x) (/ 1 (cos x)))
95.0ms	(* (tan x) (tan eps))
400.0ms	(- (/ (+ (/ (sin eps) (cos eps)) (* (sin x) (/ 1 (cos x)))) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.5s

Counts

113 → 113

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	229	1617
1	496	1462
2	1272	1330
3	2973	1307
done	5001	1297

prune381.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.5b

regimes127.0ms

Accuracy

0% (0.3b remaining)

Error of 13.0b against oracle of 12.6b and baseline of 13.0b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	32
1	29	32
done	29	32

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.7s	3272×	body	1280	valid
1.1s	641×	body	2560	valid
845.0ms	1783×	body	640	valid
245.0ms	758×	body	320	valid
119.0ms	1196×	body	80	valid
71.0ms	350×	body	160	valid