Details

sample409.0ms

Algorithm

intervals

Results

236.0ms	101×	body	1280	valid
58.0ms	61×	body	640	valid
55.0ms	17×	body	2560	valid
21.0ms	32×	body	320	valid
7.0ms	36×	body	80	valid
4.0ms	9×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize23.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (tan (+ x eps)) (tan x))
3.0b	(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:

32.0ms	(- (tan (+ x eps)) (tan x))
10.0ms	(tan (+ x eps))

series280.0ms

Counts

2 → 6

Calls

2 calls:

185.0ms	(- (tan (+ x eps)) (tan x))
94.0ms	(tan (+ x eps))

simplify1.2s

Counts

31 → 31

Iterations

Useful iterations: done (1.2s)

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

prune256.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.8b

localize38.0ms

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

rewrite295.0ms

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:

61.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
22.0ms	(+ (tan x) (tan eps))
35.0ms	(* (tan x) (tan eps))
172.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series1.5s

Counts

4 → 12

Calls

4 calls:

440.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
178.0ms	(+ (tan x) (tan eps))
173.0ms	(* (tan x) (tan eps))
709.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify1.6s

Counts

98 → 98

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	172	1724
1	421	1649
2	1680	1579
done	5001	1578

prune819.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.6b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite353.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

16.0ms	(+ (tan x) (tan eps))
29.0ms	(/ (* (sin eps) (tan x)) (cos eps))
24.0ms	(* (sin eps) (tan x))
279.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin eps) (tan x)) (cos eps)))) (tan x))

series1.1s

Counts

4 → 12

Calls

4 calls:

154.0ms	(+ (tan x) (tan eps))
178.0ms	(/ (* (sin eps) (tan x)) (cos eps))
130.0ms	(* (sin eps) (tan x))
655.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin eps) (tan x)) (cos eps)))) (tan x))

simplify1.8s

Counts

82 → 82

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	165	1252
1	397	1226
2	1695	1118
done	5001	1098

prune720.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 12.6b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(* (sin eps) (tan x))
2.8b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (log (exp (* (sin eps) (tan x)))) (cos eps)))) (tan x))
3.0b	(log (exp (* (sin eps) (tan x))))

rewrite502.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
4×	`tan-quot`
3×	`log-prod` `associate-r` `associate-l` `log-pow`
2×	`difference-of-squares`
1×	`+-commutative` `sub-neg` `exp-prod` `flip3--` `exp-to-pow` `flip3-+` `times-frac` `diff-log` `associate-r/` `rem-log-exp` `pow-prod-down` `frac-add` `prod-exp` `sum-log` `-commutative` `frac-sub` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

15.0ms	(+ (tan x) (tan eps))
27.0ms	(* (sin eps) (tan x))
449.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (log (exp (* (sin eps) (tan x)))) (cos eps)))) (tan x))
8.0ms	(log (exp (* (sin eps) (tan x))))

series1.0s

Counts

4 → 12

Calls

4 calls:

156.0ms	(+ (tan x) (tan eps))
129.0ms	(* (sin eps) (tan x))
635.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (log (exp (* (sin eps) (tan x)))) (cos eps)))) (tan x))
129.0ms	(log (exp (* (sin eps) (tan x))))

simplify977.0ms

Counts

74 → 74

Iterations

Useful iterations: done (974.0ms)

Iter	Nodes	Cost
0	146	1180
1	326	1086
2	1081	1004
done	5001	986

prune690.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.6b

regimes464.0ms

Accuracy

88.4% (0.9b remaining)

Error of 15.3b against oracle of 14.4b and baseline of 21.9b

bsearch206.0ms

Steps

Iters	Range		Point
9	7.972879948037122e-33	5.461638927932447e-28	1.057153756992666e-28
2	-3.230948283787139e-65	-2.7814928919147504e-65	-2.8376748158987993e-65

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	35	73
1	47	73
done	47	73

end0.0ms

sample13.8s

Algorithm

intervals

Results

7.1s	3321×	body	1280	valid
2.9s	633×	body	2560	valid
2.1s	1825×	body	640	valid
664.0ms	764×	body	320	valid
323.0ms	1089×	body	80	valid
154.0ms	368×	body	160	valid