Details

sample315.0ms

Algorithm

intervals

Results

170.0ms	114×	body	1280	valid
65.0ms	21×	body	2560	valid
41.0ms	53×	body	640	valid
12.0ms	26×	body	320	valid
5.0ms	29×	body	80	valid
5.0ms	13×	body	160	valid

simplify9.0ms

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: 41.4b

localize20.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (tan (+ x eps)) (tan x))
3.6b	(tan (+ x eps))

rewrite105.0ms

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:

90.0ms	(- (tan (+ x eps)) (tan x))
14.0ms	(tan (+ x eps))

series248.0ms

Counts

2 → 6

Calls

2 calls:

166.0ms	(- (tan (+ x eps)) (tan x))
82.0ms	(tan (+ x eps))

simplify943.0ms

Counts

31 → 31

Iterations

Useful iterations: done (942.0ms)

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

prune116.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.2b

localize14.0ms

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))
0.3b	(* (tan x) (tan eps))
4.0b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite203.0ms

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:

49.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
14.0ms	(+ (tan x) (tan eps))
18.0ms	(* (tan x) (tan eps))
118.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.3s

Counts

4 → 12

Calls

4 calls:

391.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
140.0ms	(+ (tan x) (tan eps))
132.0ms	(* (tan x) (tan eps))
592.0ms	(- (/ (+ (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	1680	1579
done	5001	1578

prune448.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 19.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
0.3b	(* (tan x) (tan eps))
4.0b	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

17×	`tan-quot`
16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`frac-times` `associate-*r/` `frac-sub`
4×	`associate-*l/`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `associate--l+` `flip-+`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `diff-log` `flip--`

Counts

4 → 82

Calls

4 calls:

31.0ms	(* (tan x) (tan eps))
24.0ms	(* (tan x) (tan eps))
18.0ms	(* (tan x) (tan eps))
44.0ms	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

series1.9s

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (tan x) (tan eps))
145.0ms	(* (tan x) (tan eps))
112.0ms	(* (tan x) (tan eps))
1.5s	(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))

simplify2.0s

Counts

94 → 94

Iterations

Useful iterations: 2 (428.0ms)

Iter	Nodes	Cost
0	149	1880
1	456	1785
2	2812	1649
done	5002	1649

prune433.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 19.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
0.3b	(* (tan x) (tan eps))
0.3b	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
5.7b	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

rewrite366.0ms

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:

50.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
23.0ms	(* (tan x) (tan eps))
40.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
236.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

series1.4s

Counts

4 → 12

Calls

4 calls:

374.0ms	(/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))
129.0ms	(* (tan x) (tan eps))
317.0ms	(/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps))))
534.0ms	(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))

simplify3.1s

Counts

190 → 190

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	298	4576
1	782	4210
2	4832	3964
done	5001	3964

prune557.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 19.1b

regimes296.0ms

Accuracy

81.2% (1.4b remaining)

Error of 15.9b against oracle of 14.5b and baseline of 22.0b

bsearch360.0ms

Steps

Iters	Range		Point
8	5.50408705523778e-118	1.7769217153263766e-113	1.738904653256747e-113
9	-8.91844618026245e-89	-2.4994130436085512e-95	-8.784974285695472e-89

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	99
1	58	99
done	58	99

end0.0ms

sample11.6s

Algorithm

intervals

Results

5.4s	3327×	body	1280	valid
2.7s	647×	body	2560	valid
2.3s	1853×	body	640	valid
430.0ms	737×	body	320	valid
180.0ms	361×	body	160	valid
166.0ms	1075×	body	80	valid