Details

sample159.0ms

Algorithm

intervals

Results

71.0ms	95×	body	1280	valid
38.0ms	22×	body	2560	valid
23.0ms	58×	body	640	valid
12.0ms	25×	body	320	valid
3.0ms	18×	body	160	valid
3.0ms	38×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 34.0b

localize9.0ms

Local error

Found 2 expressions with local error:

2.6b	(- (tan (+ x eps)) (tan x))
3.9b	(tan (+ x eps))

rewrite11.0ms

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:

8.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series142.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(- (tan (+ x eps)) (tan x))
54.0ms	(tan (+ x eps))

simplify1.8s

Counts

31 → 31

Iterations

Useful iterations: 4 (214.0ms)

Iter	Nodes	Cost
0	68	367
1	135	355
2	288	341
3	540	337
4	1286	335
5	3457	335
done	5000	335

prune88.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps))))
0.1b	(+ (tan eps) (tan x))
0.2b	(* (tan x) (tan eps))
4.0b	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite63.0ms

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:

11.0ms	(/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps))))
3.0ms	(+ (tan eps) (tan x))
5.0ms	(* (tan x) (tan eps))
42.0ms	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps)))) (tan x))

series762.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps))))
91.0ms	(+ (tan eps) (tan x))
90.0ms	(* (tan x) (tan eps))
366.0ms	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.4s

Counts

98 → 98

Iterations

Useful iterations: 3 (698.0ms)

Iter	Nodes	Cost
0	170	1724
1	385	1649
2	1051	1579
3	2994	1565
done	5000	1565

prune282.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (- 1 (* (tan eps) (tan x))) (+ (tan x) (tan eps))))
0.2b	(* (tan eps) (tan x))
0.3b	(/ (- 1 (* (tan eps) (tan x))) (+ (tan x) (tan eps)))
7.1b	(- (/ 1 (/ (- 1 (* (tan eps) (tan x))) (+ (tan x) (tan eps)))) (tan x))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 178

Calls

4 calls:

12.0ms	(/ 1 (/ (- 1 (* (tan eps) (tan x))) (+ (tan x) (tan eps))))
5.0ms	(* (tan eps) (tan x))
10.0ms	(/ (- 1 (* (tan eps) (tan x))) (+ (tan x) (tan eps)))
78.0ms	(- (/ 1 (/ (- 1 (* (tan eps) (tan x))) (+ (tan x) (tan eps)))) (tan x))

series948.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(/ 1 (/ (- 1 (* (tan eps) (tan x))) (+ (tan x) (tan eps))))
90.0ms	(* (tan eps) (tan x))
264.0ms	(/ (- 1 (* (tan eps) (tan x))) (+ (tan x) (tan eps)))
375.0ms	(- (/ 1 (/ (- 1 (* (tan eps) (tan x))) (+ (tan x) (tan eps)))) (tan x))

simplify762.0ms

Counts

190 → 190

Iterations

Useful iterations: done (757.0ms)

Iter	Nodes	Cost
0	297	4576
1	697	4212
2	1819	3882
done	5000	3860

prune401.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan eps) (tan x))
0.2b	(/ (- (pow 1 3) (pow (* (tan eps) (tan x)) 3)) (* (+ (tan eps) (tan x)) (+ (* (* (tan x) (tan eps)) (+ 1 (* (tan eps) (tan x)))) 1)))
0.3b	(pow (* (tan eps) (tan x)) 3)
7.1b	(- (/ 1 (/ (- (pow 1 3) (pow (* (tan eps) (tan x)) 3)) (* (+ (tan eps) (tan x)) (+ (* (* (tan x) (tan eps)) (+ 1 (* (tan eps) (tan x)))) 1)))) (tan x))

rewrite420.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `difference-of-squares`
20×	`times-frac`
18×	`associate-/l*`
17×	`sqr-pow`
15×	`tan-quot`
14×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/r/`
9×	`pow1` `add-cube-cbrt` `unpow-prod-down` `cube-prod`
8×	`frac-times`
7×	`flip3-+` `flip-+`
6×	`distribute-lft-out--` `add-log-exp`
5×	`associate-*l/`
4×	`associate-*r/`
3×	`cube-div` `cube-mult` `pow-unpow` `associate-r` `associate-l` `frac-add` `prod-exp` `cbrt-unprod`
2×	`difference-cubes` `cbrt-undiv` `flip3--` `pow-pow` `div-exp` `pow-prod-down` `pow-exp` `flip--` `div-inv` `associate-/l/` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `frac-2neg` `diff-log` `unpow3` `div-sub` `clear-num` `associate-/r` `-commutative` `frac-sub` `unswap-sqr`

Counts

4 → 129

Calls

4 calls:

5.0ms	(* (tan eps) (tan x))
59.0ms	(/ (- (pow 1 3) (pow (* (tan eps) (tan x)) 3)) (* (+ (tan eps) (tan x)) (+ (* (* (tan x) (tan eps)) (+ 1 (* (tan eps) (tan x)))) 1)))
4.0ms	(pow (* (tan eps) (tan x)) 3)
347.0ms	(- (/ 1 (/ (- (pow 1 3) (pow (* (tan eps) (tan x)) 3)) (* (+ (tan eps) (tan x)) (+ (* (* (tan x) (tan eps)) (+ 1 (* (tan eps) (tan x)))) 1)))) (tan x))

series2.3s

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (tan eps) (tan x))
561.0ms	(/ (- (pow 1 3) (pow (* (tan eps) (tan x)) 3)) (* (+ (tan eps) (tan x)) (+ (* (* (tan x) (tan eps)) (+ 1 (* (tan eps) (tan x)))) 1)))
127.0ms	(pow (* (tan eps) (tan x)) 3)
1.6s	(- (/ 1 (/ (- (pow 1 3) (pow (* (tan eps) (tan x)) 3)) (* (+ (tan eps) (tan x)) (+ (* (* (tan x) (tan eps)) (+ 1 (* (tan eps) (tan x)))) 1)))) (tan x))

simplify1.5s

Counts

141 → 141

Iterations

Useful iterations: 2 (584.0ms)

Iter	Nodes	Cost
0	344	5016
1	1006	4562
2	4836	4165
done	5000	4165

prune484.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.1b

regimes143.0ms

Accuracy

91.7% (0.7b remaining)

Error of 14.1b against oracle of 13.4b and baseline of 21.9b

bsearch199.0ms

Steps

Iters	Range		Point
10	9.278264258908537e-20	9.143643357499823e-08	7.314284794445763e-19
9	-1.4200829193005852e-83	-1.539148050312635e-88	-1.4068122803532358e-83

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	92
1	57	92
done	57	92

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.5s	3289×	body	1280	valid
1.2s	686×	body	2560	valid
981.0ms	1815×	body	640	valid
211.0ms	736×	body	320	valid
93.0ms	1115×	body	80	valid
66.0ms	359×	body	160	valid