Details

sample311.0ms

Algorithm

intervals

Results

147.0ms	106×	body	1280	valid
88.0ms	53×	body	640	valid
31.0ms	11×	body	2560	valid
15.0ms	27×	body	320	valid
8.0ms	44×	body	80	valid
5.0ms	15×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize13.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (tan (+ x eps)) (tan x))
3.9b	(tan (+ x eps))

rewrite26.0ms

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:

17.0ms	(- (tan (+ x eps)) (tan x))
8.0ms	(tan (+ x eps))

series566.0ms

Counts

2 → 6

Calls

2 calls:

465.0ms	(- (tan (+ x eps)) (tan x))
101.0ms	(tan (+ x eps))

simplify899.0ms

Counts

31 → 31

Iterations

Useful iterations: done (898.0ms)

Iter	Nodes	Cost
0	68	367
1	135	355
2	349	341
3	1136	337
done	5000	335

prune127.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(* (tan x) (tan eps))
2.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite228.0ms

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:

14.0ms	(+ (tan x) (tan eps))
39.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
31.0ms	(* (tan x) (tan eps))
140.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

148.0ms	(+ (tan x) (tan eps))
325.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
152.0ms	(* (tan x) (tan eps))
559.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.2s

Counts

98 → 98

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	172	1724
1	421	1649
2	1674	1579
done	5001	1578

prune450.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))
0.2b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.2b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
2.1b	(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`cbrt-undiv` `div-exp`
9×	`prod-exp` `cbrt-unprod` `add-log-exp`
6×	`add-cube-cbrt` `times-frac`
5×	`associate-/l*`
4×	`pow1` `associate-/r/`
3×	`frac-2neg` `clear-num` `associate-/r*` `frac-sub` `div-inv`
2×	`flip3--` `diff-log` `associate-*l/` `cos-mult` `flip--` `associate-/l/` `sin-mult` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3-+` `frac-add` `associate--l+` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 90

Calls

4 calls:

50.0ms	(/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))
19.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
31.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
961.0ms	(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

series1.1s

Counts

4 → 12

Calls

4 calls:

246.0ms	(/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))
151.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
140.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
516.0ms	(- (+ (/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x))) (/ (sin eps) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos eps)))) (/ (sin x) (cos x)))

simplify1.5s

Counts

102 → 102

Iterations

Useful iterations: 2 (363.0ms)

Iter	Nodes	Cost
0	194	3410
1	555	3256
2	2448	2910
done	5000	2910

prune613.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.7b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (tan x) (tan eps)) (cos x))
0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
6.4b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

rewrite114.0ms

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:

32.0ms	(* (+ (tan x) (tan eps)) (cos x))
16.0ms	(* (tan x) (tan eps))
16.0ms	(* (tan x) (tan eps))
47.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

series760.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(* (+ (tan x) (tan eps)) (cos x))
125.0ms	(* (tan x) (tan eps))
149.0ms	(* (tan x) (tan eps))
311.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify2.2s

Counts

94 → 94

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	173	1626
1	552	1476
2	3126	1418
done	5000	1416

prune487.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes100.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample10.0s

Algorithm

intervals

Results

5.4s	3367×	body	1280	valid
1.6s	648×	body	2560	valid
1.4s	1778×	body	640	valid
588.0ms	1094×	body	80	valid
455.0ms	769×	body	320	valid
253.0ms	344×	body	160	valid