Details

sample347.0ms

Algorithm

intervals

Results

149.0ms	106×	body	1280	valid
81.0ms	28×	body	2560	valid
80.0ms	58×	body	640	valid
12.0ms	23×	body	320	valid
5.0ms	31×	body	80	valid
4.0ms	10×	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: 40.4b

localize11.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (tan (+ x eps)) (tan x))
4.5b	(tan (+ x eps))

rewrite73.0ms

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:

58.0ms	(- (tan (+ x eps)) (tan x))
13.0ms	(tan (+ x eps))

series221.0ms

Counts

2 → 6

Calls

2 calls:

136.0ms	(- (tan (+ x eps)) (tan x))
85.0ms	(tan (+ x eps))

simplify2.4s

Counts

31 → 31

Iterations

Useful iterations: 4 (386.0ms)

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

prune95.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
0.2b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
2.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite173.0ms

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:

38.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
11.0ms	(+ (tan x) (tan eps))
16.0ms	(* (tan x) (tan eps))
104.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

326.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
172.0ms	(+ (tan x) (tan eps))
139.0ms	(* (tan x) (tan eps))
556.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify2.3s

Counts

98 → 98

Iterations

Useful iterations: 3 (885.0ms)

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

prune433.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x)))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
2.8b	(- (+ (/ (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)))

rewrite987.0ms

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:

56.0ms	(/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x)))
23.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
30.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
871.0ms	(- (+ (/ (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)))

series1.2s

Counts

4 → 12

Calls

4 calls:

254.0ms	(/ (sin x) (* (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (cos x)))
167.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
163.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
573.0ms	(- (+ (/ (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)))

simplify1.4s

Counts

102 → 102

Iterations

Useful iterations: 2 (414.0ms)

Iter	Nodes	Cost
0	193	3410
1	537	3256
2	2139	2909
done	5000	2909

prune630.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.3b

localize37.0ms

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))
8.7b	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

rewrite165.0ms

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:

17.0ms	(* (tan x) (tan eps))
24.0ms	(* (tan x) (tan eps))
46.0ms	(* (+ (tan x) (tan eps)) (cos x))
75.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

series807.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(* (tan x) (tan eps))
163.0ms	(* (tan x) (tan eps))
173.0ms	(* (+ (tan x) (tan eps)) (cos x))
311.0ms	(- (* (+ (tan x) (tan eps)) (cos x)) (* (- 1 (* (tan x) (tan eps))) (sin x)))

simplify1.2s

Counts

94 → 94

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	173	1626
1	515	1476
2	1917	1418
done	5002	1416

prune486.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes113.0ms

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 (1.0ms)

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

end0.0ms

sample10.3s

Algorithm

intervals

Results

5.7s	3328×	body	1280	valid
1.6s	1824×	body	640	valid
1.6s	625×	body	2560	valid
546.0ms	354×	body	160	valid
354.0ms	817×	body	320	valid
183.0ms	1052×	body	80	valid