Details

sample225.0ms

Algorithm

intervals

Results

129.0ms	121×	body	1280	valid
36.0ms	17×	body	2560	valid
34.0ms	57×	body	640	valid
7.0ms	15×	body	320	valid
5.0ms	36×	body	80	valid
3.0ms	10×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	272
1	9	272
2	10	272
done	10	272

prune51.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.5b

localize33.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (tan (+ x eps)) (tan x))
4.6b	(tan (+ x eps))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `tan-quot` `add-log-exp`
2×	`pow1` `tan-sum` `add-cbrt-cube` `add-exp-log` `frac-sub` `add-cube-cbrt`
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))
6.0ms	(tan (+ x eps))

series204.0ms

Counts

2 → 6

Calls

2 calls:

118.0ms	(- (tan (+ x eps)) (tan x))
87.0ms	(tan (+ x eps))

simplify2.2s

Counts

31 → 31

Iterations

Useful iterations: 4 (799.0ms)

Iter	Nodes	Cost
0	68	11636
1	137	10793
2	298	10793
3	709	10753
4	1748	10712
done	5001	10712

prune209.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.8b

localize43.0ms

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

rewrite166.0ms

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-cbrt-cube` `add-exp-log` `add-log-exp`
6×	`pow1`
5×	`distribute-lft-out`
4×	`associate-/l*`
3×	`associate-/r` `associate-r` `associate-l*` `associate-/l/`
2×	`flip3-+` `flip3--` `frac-add` `associate-/r/` `flip-+` `flip--` `difference-of-squares`
1×	`frac-times` `cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

13.0ms	(+ (tan x) (tan eps))
29.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
15.0ms	(* (tan x) (tan eps))
105.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.2s

Counts

4 → 12

Calls

4 calls:

127.0ms	(+ (tan x) (tan eps))
337.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
129.0ms	(* (tan x) (tan eps))
580.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify4.1s

Counts

98 → 98

Iterations

Useful iterations: 3 (2.1s)

Iter	Nodes	Cost
0	170	46248
1	401	43757
2	1147	43637
3	4259	43517
done	5083	43517

prune630.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.6b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite274.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

52.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
15.0ms	(/ (* (tan x) (sin eps)) (cos eps))
17.0ms	(* (tan x) (sin eps))
184.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

339.0ms	(/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps))))
135.0ms	(/ (* (tan x) (sin eps)) (cos eps))
112.0ms	(* (tan x) (sin eps))
520.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify2.3s

Counts

120 → 120

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	217	70997
1	504	67932
2	1463	67452
done	5001	67332

prune744.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.6b

localize76.0ms

Local error

Found 4 expressions with local error:

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

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-cbrt-cube` `add-exp-log`
22×	`add-sqr-sqrt`
17×	`prod-exp` `cbrt-unprod`
16×	`*-un-lft-identity` `add-cube-cbrt`
15×	`pow1`
13×	`associate-r` `associate-l`
12×	`cbrt-undiv` `times-frac` `div-exp`
7×	`swap-sqr` `tan-quot`
6×	`add-log-exp`
5×	`frac-sub`
4×	`associate-*l/` `div-inv`
3×	`frac-times` `pow-prod-down` `associate-r/` `-commutative` `unswap-sqr`
2×	`flip3-+` `associate--l+` `flip-+`
1×	`pow2` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-plus` `flip3--` `diff-log` `pow-sqr` `pow-prod-up` `flip--`

Counts

4 → 113

Calls

4 calls:

11.0ms	(* (tan x) (sin eps))
14.0ms	(* (tan x) (sin eps))
60.0ms	(* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps)))
48.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

series1.8s

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (tan x) (sin eps))
70.0ms	(* (tan x) (sin eps))
187.0ms	(* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps)))
1.4s	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))

simplify4.9s

Counts

125 → 125

Iterations

Useful iterations: done (4.9s)

Iter	Nodes	Cost
0	232	65060
1	753	56462
2	3080	54221
done	5022	53941

prune743.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 14.6b

regimes415.0ms

Accuracy

87.3% (0.9b remaining)

Error of 15.4b against oracle of 14.5b and baseline of 21.8b

bsearch302.0ms

Steps

Iters	Range		Point
7	8.37711467695307e-66	1.2010323164908573e-63	1.0195913887540198e-64
8	-6.358562521077362e-50	-7.09086929250311e-54	-6.248907778173893e-50

simplify12.0ms

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	45	2196
1	61	2196
done	61	2196

end0.0ms

sample9.3s

Algorithm

intervals

Results

4.3s	3279×	body	1280	valid
2.1s	1836×	body	640	valid
2.0s	675×	body	2560	valid
311.0ms	760×	body	320	valid
184.0ms	1117×	body	80	valid
145.0ms	333×	body	160	valid