Details

sample157.0ms

Algorithm

intervals

Results

74.0ms	96×	body	1280	valid
32.0ms	19×	body	2560	valid
28.0ms	67×	body	640	valid
8.0ms	32×	body	320	valid
3.0ms	33×	body	80	valid
2.0ms	9×	body	160	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: 35.8b

localize9.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (tan (+ x eps)) (tan x))
3.7b	(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:

7.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series148.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(- (tan (+ x eps)) (tan x))
59.0ms	(tan (+ x eps))

simplify1.8s

Counts

31 → 31

Iterations

Useful iterations: 4 (261.0ms)

Iter	Nodes	Cost
0	68	367
1	135	355
2	288	341
3	540	337
4	1287	335
5	3485	335
done	5000	335

prune92.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 13.2b

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))
2.6b	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite62.0ms

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))
39.0ms	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps)))) (tan x))

series765.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps))))
94.0ms	(+ (tan eps) (tan x))
93.0ms	(* (tan x) (tan eps))
368.0ms	(- (/ (+ (tan eps) (tan x)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.6s

Counts

98 → 98

Iterations

Useful iterations: 3 (820.0ms)

Iter	Nodes	Cost
0	170	1724
1	385	1649
2	1051	1579
3	2998	1565
done	5001	1565

prune287.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos eps) (sin x))
0.2b	(* (tan x) (tan eps))
0.3b	(/ (+ (* (sin eps) (cos x)) (* (cos eps) (sin x))) (* (cos x) (cos eps)))
8.0b	(- (/ (/ (+ (* (sin eps) (cos x)) (* (cos eps) (sin x))) (* (cos x) (cos eps))) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

4.0ms	(* (cos eps) (sin x))
5.0ms	(* (tan x) (tan eps))
12.0ms	(/ (+ (* (sin eps) (cos x)) (* (cos eps) (sin x))) (* (cos x) (cos eps)))
56.0ms	(- (/ (/ (+ (* (sin eps) (cos x)) (* (cos eps) (sin x))) (* (cos x) (cos eps))) (- 1 (* (tan x) (tan eps)))) (tan x))

series655.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos eps) (sin x))
88.0ms	(* (tan x) (tan eps))
141.0ms	(/ (+ (* (sin eps) (cos x)) (* (cos eps) (sin x))) (* (cos x) (cos eps)))
380.0ms	(- (/ (/ (+ (* (sin eps) (cos x)) (* (cos eps) (sin x))) (* (cos x) (cos eps))) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify762.0ms

Counts

91 → 91

Iterations

Useful iterations: 2 (147.0ms)

Iter	Nodes	Cost
0	193	1836
1	471	1813
2	1558	1617
done	5001	1617

prune369.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
0.2b	(* (+ (tan x) (tan eps)) (cos x))
8.0b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

17×	`associate-*l/`
16×	`add-sqr-sqrt`
14×	`tan-quot`
12×	`*-un-lft-identity`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
9×	`associate-r`
6×	`frac-sub` `add-log-exp`
4×	`flip3--` `flip--`
3×	`flip3-+` `pow-prod-down` `frac-add` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
2×	`frac-times` `associate-*r/`
1×	`sub-neg` `diff-log` `distribute-lft-out`

Counts

4 → 82

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
12.0ms	(* (+ (tan x) (tan eps)) (cos x))
11.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (tan x) (tan eps))
92.0ms	(* (tan x) (tan eps))
118.0ms	(* (+ (tan x) (tan eps)) (cos x))
208.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify776.0ms

Counts

94 → 94

Iterations

Useful iterations: 2 (200.0ms)

Iter	Nodes	Cost
0	173	1626
1	524	1476
2	1878	1418
done	5001	1418

prune338.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes101.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	33
1	29	33
done	29	33

end0.0ms

sample5.1s

Algorithm

intervals

Results

2.5s	3276×	body	1280	valid
1.1s	646×	body	2560	valid
827.0ms	1863×	body	640	valid
216.0ms	766×	body	320	valid
106.0ms	1085×	body	80	valid
69.0ms	364×	body	160	valid