Details

sample172.0ms

Algorithm

intervals

Results

89.0ms	117×	body	1280	valid
39.0ms	24×	body	2560	valid
21.0ms	52×	body	640	valid
7.0ms	27×	body	320	valid
3.0ms	29×	body	80	valid
2.0ms	7×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.8b

localize9.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (tan (+ x eps)) (tan x))
2.2b	(tan (+ x eps))

rewrite23.0ms

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:

16.0ms	(- (tan (+ x eps)) (tan x))
6.0ms	(tan (+ x eps))

series152.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(- (tan (+ x eps)) (tan x))
58.0ms	(tan (+ x eps))

simplify79.0ms

Counts

31 → 31

Iterations

Useful iterations: 3 (24.0ms)

Iter	Nodes	Cost
0	134	211
1	295	202
2	757	200
3	2482	199
4	5001	199
done	5001	199

prune81.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.8b

localize11.0ms

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))
3.5b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite134.0ms

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:

30.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
8.0ms	(+ (tan x) (tan eps))
15.0ms	(* (tan x) (tan eps))
79.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series773.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
94.0ms	(+ (tan x) (tan eps))
95.0ms	(* (tan x) (tan eps))
365.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify43.0ms

Counts

98 → 98

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	397	1052
1	1432	1007
2	5001	996
done	5001	996

prune249.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
0.3b	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
6.4b	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

rewrite203.0ms

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:

16.0ms	(* (tan x) (tan eps))
22.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
25.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
132.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

series964.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (tan x) (tan eps))
272.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
213.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
383.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

simplify77.0ms

Counts

190 → 190

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	703	2793
1	3294	2509
2	5001	2506
done	5001	2506

prune372.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 16.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
0.3b	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
3.5b	(- (+ (/ (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)))

rewrite663.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

12.0ms	(* (sin x) (sin eps))
18.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
18.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
612.0ms	(- (+ (/ (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)))

series655.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sin x) (sin eps))
104.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
104.0ms	(/ (* (sin x) (sin eps)) (* (cos x) (cos eps)))
395.0ms	(- (+ (/ (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)))

simplify64.0ms

Counts

98 → 98

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	464	1846
1	2215	1611
2	5001	1611
done	5001	1611

prune312.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 16.6b

regimes186.0ms

Accuracy

78.6% (1.6b remaining)

Error of 16.6b against oracle of 15.0b and baseline of 22.6b

bsearch182.0ms

Steps

Iters	Range		Point
8	1.5609731741021842e-142	7.971820636382968e-140	7.898055614722725e-140
9	-7.799787465191151e-50	-5.8975419655003234e-58	-6.844251912285021e-54

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	55
1	43	55
done	43	55

end0.0ms

sample5.0s

Algorithm

intervals

Results

2.5s	3399×	body	1280	valid
1.1s	627×	body	2560	valid
761.0ms	1812×	body	640	valid
221.0ms	789×	body	320	valid
90.0ms	1048×	body	80	valid
57.0ms	325×	body	160	valid