Details

sample323.0ms

Algorithm

intervals

Results

128.0ms	96×	body	1280	valid
95.0ms	24×	body	2560	valid
47.0ms	56×	body	640	valid
25.0ms	39×	body	320	valid
6.0ms	31×	body	80	valid
4.0ms	10×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.1b

localize19.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (tan (+ x eps)) (tan x))
6.3b	(tan (+ x eps))

rewrite50.0ms

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:

35.0ms	(- (tan (+ x eps)) (tan x))
13.0ms	(tan (+ x eps))

series268.0ms

Counts

2 → 6

Calls

2 calls:

151.0ms	(- (tan (+ x eps)) (tan x))
117.0ms	(tan (+ x eps))

simplify2.0s

Counts

31 → 31

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	68	367
1	181	355
2	700	339
done	5001	335

prune133.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.1b

localize24.0ms

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))
2.4b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite177.0ms

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:

43.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
9.0ms	(+ (tan x) (tan eps))
19.0ms	(* (tan x) (tan eps))
102.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

380.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
122.0ms	(+ (tan x) (tan eps))
158.0ms	(* (tan x) (tan eps))
534.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify8.7s

Counts

98 → 98

Iterations

Useful iterations: done (8.7s)

Iter	Nodes	Cost
0	172	1724
1	2655	1652
done	5002	1584

prune493.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.9b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.1b	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
0.2b	(* (tan x) (tan eps))
2.4b	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`tan-quot`
19×	`*-un-lft-identity`
18×	`associate-r`
15×	`add-exp-log`
14×	`add-cube-cbrt`
11×	`times-frac` `add-cbrt-cube`
8×	`pow1` `frac-sub` `add-log-exp`
7×	`frac-times` `associate-l` `associate-*l/`
5×	`flip3-+` `frac-add` `prod-exp` `flip-+`
4×	`unswap-sqr`
3×	`associate-*r/` `cbrt-unprod`
2×	`flip3--` `div-exp` `pow-prod-down` `associate-/r/` `un-div-inv` `*-commutative` `flip--` `distribute-lft-out`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rec-exp` `diff-log` `1-exp` `sum-log` `div-inv`

Counts

4 → 99

Calls

4 calls:

11.0ms	(+ (tan x) (tan eps))
75.0ms	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
17.0ms	(* (tan x) (tan eps))
68.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

152.0ms	(+ (tan x) (tan eps))
326.0ms	(* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps)))))
138.0ms	(* (tan x) (tan eps))
605.0ms	(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

simplify1.0s

Counts

111 → 111

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	225	2170
done	5000	1945

prune568.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.9b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (/ (* (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (cos x)) (- 1 (* (tan x) (tan eps)))) (* (* (cos x) (cos eps)) (sin x))) (* (* (cos x) (cos eps)) (cos x)))
0.2b	(* (* (cos x) (cos eps)) (cos x))
0.2b	(* (* (cos x) (cos eps)) (sin x))
2.4b	(- (/ (* (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (cos x)) (- 1 (* (tan x) (tan eps)))) (* (* (cos x) (cos eps)) (sin x)))

rewrite387.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
9×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `pow-prod-down` `add-log-exp`
5×	`associate-*l/` `cos-mult`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/l/` `associate-/l*`
2×	`flip3--` `associate-l` `*-commutative` `frac-sub` `flip--`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num` `associate-/r*` `associate-/r/` `div-inv`

Counts

4 → 79

Calls

4 calls:

218.0ms	(/ (- (/ (* (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (cos x)) (- 1 (* (tan x) (tan eps)))) (* (* (cos x) (cos eps)) (sin x))) (* (* (cos x) (cos eps)) (cos x)))
36.0ms	(* (* (cos x) (cos eps)) (cos x))
38.0ms	(* (* (cos x) (cos eps)) (sin x))
93.0ms	(- (/ (* (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (cos x)) (- 1 (* (tan x) (tan eps)))) (* (* (cos x) (cos eps)) (sin x)))

series1.7s

Counts

4 → 12

Calls

4 calls:

804.0ms	(/ (- (/ (* (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (cos x)) (- 1 (* (tan x) (tan eps)))) (* (* (cos x) (cos eps)) (sin x))) (* (* (cos x) (cos eps)) (cos x)))
85.0ms	(* (* (cos x) (cos eps)) (cos x))
97.0ms	(* (* (cos x) (cos eps)) (sin x))
677.0ms	(- (/ (* (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (cos x)) (- 1 (* (tan x) (tan eps)))) (* (* (cos x) (cos eps)) (sin x)))

simplify5.7s

Counts

91 → 91

Iterations

Useful iterations: done (5.7s)

Iter	Nodes	Cost
0	174	3030
1	1664	2927
done	5000	2411

prune576.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 5.2b

regimes346.0ms

Accuracy

96.6% (0.6b remaining)

Error of 6.3b against oracle of 5.7b and baseline of 21.9b

bsearch278.0ms

Steps

Iters	Range		Point
11	1.1123901126486127e-34	1.9762467893330864e-06	1.3424092820004812e-20
5	-2.9278891142885936e-51	-1.3141126890030885e-51	-2.8807489927501464e-51

simplify11.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	34	130
1	47	81
done	47	81

end0.0ms

sample11.9s

Algorithm

intervals

Results

5.7s	3277×	body	1280	valid
2.6s	640×	body	2560	valid
2.3s	1781×	body	640	valid
487.0ms	834×	body	320	valid
224.0ms	1104×	body	80	valid
127.0ms	364×	body	160	valid