Details

sample158.0ms

Algorithm

intervals

Results

66.0ms	97×	body	1280	valid
40.0ms	24×	body	2560	valid
25.0ms	64×	body	640	valid
11.0ms	28×	body	320	valid
3.0ms	31×	body	80	valid
2.0ms	12×	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: 39.0b

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (tan (+ x eps)) (tan x))
4.6b	(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))

series148.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(- (tan (+ x eps)) (tan x))
56.0ms	(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

prune83.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.9b

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))
3.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite149.0ms

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:

34.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
15.0ms	(+ (tan x) (tan eps))
18.0ms	(* (tan x) (tan eps))
79.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series787.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps))))
108.0ms	(+ (tan x) (tan eps))
93.0ms	(* (tan x) (tan eps))
361.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify47.0ms

Counts

98 → 98

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	397	1050
1	1432	1005
2	5001	995
done	5001	995

prune268.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 14.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan x) (tan eps))
0.2b	(* (sin x) (tan eps))
0.2b	(/ (* (sin x) (tan eps)) (cos x))
3.1b	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

rewrite177.0ms

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:

8.0ms	(+ (tan x) (tan eps))
14.0ms	(* (sin x) (tan eps))
14.0ms	(/ (* (sin x) (tan eps)) (cos x))
140.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series674.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(+ (tan x) (tan eps))
77.0ms	(* (sin x) (tan eps))
108.0ms	(/ (* (sin x) (tan eps)) (cos x))
390.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

simplify49.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	389	785
1	1406	711
2	5001	699
done	5001	699

prune270.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (cos x))
0.2b	(* (sin x) (tan eps))
0.2b	(/ (* (sin x) (tan eps)) (cos x))
7.2b	(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

rewrite362.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

8.0ms	(/ (sin x) (cos x))
14.0ms	(* (sin x) (tan eps))
14.0ms	(/ (* (sin x) (tan eps)) (cos x))
323.0ms	(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

series623.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (sin x) (cos x))
83.0ms	(* (sin x) (tan eps))
106.0ms	(/ (* (sin x) (tan eps)) (cos x))
414.0ms	(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))

simplify46.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	392	974
1	1457	879
2	5001	864
done	5001	864

prune356.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 13.3b

regimes161.0ms

Accuracy

95.3% (0.4b remaining)

Error of 13.9b against oracle of 13.5b and baseline of 22.2b

bsearch131.0ms

Steps

Iters	Range		Point
10	7.501151066748407e-20	1.7355052557369657e-07	1.349170156454841e-17
4	-3.4474604111501658e-22	-2.2519064934139983e-22	-3.3353772313624003e-22

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	46
1	50	46
done	50	46

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.4s	3238×	body	1280	valid
1.1s	685×	body	2560	valid
774.0ms	1899×	body	640	valid
202.0ms	755×	body	320	valid
100.0ms	1088×	body	80	valid
57.0ms	335×	body	160	valid